TEXT The sole text is Daniel Bonevac’s Today’s Moral Issues. This is an extremely accessible work that organizes the subject matter of ethics into well-structured units involving both general principles and focused ethical dilemmas. The instructor will guide the students through the pertinent readings and discussion topics. Exam #3: WAR ECONOMIC EQUALITY 1. Aquinas 5. Mill 2. Grotius 6. Hospers 3. Clausewitz 7. Anderson 4. Gandhi CONCERNING THE SHORT PAPER Choose one of our dilemma topics from our book as the focus of your short paper. If you have another topic in mind, please consult with me for permission. —length: 4 to 5 pages — format: typed —number of points: 10 — submission via Bb, under “Assignments” — Format: Microsoft Word — Line Spacing: Double-Spaced —Print: Black The following is merely a suggestion for the organization of the paper, but it might be useful as an indication of how it could look: a) Initial statement of your position concerning the moral dilemma; how to resolve it, how you plan to argue for/against it. b) Amplification of your position; your main points or position. c) Backup: some cited references and supporting evidence for your position. d) Your criticisms of alternative or contrary points of view. e) Your conclusion/summing up. Plagiarism is a serious breach of academic integrity. If you submit plagiarized materials you will receive a zero on the assignment. If you need an extension of the due date for the paper, please consult with me.

TEXT The sole text is Daniel Bonevac’s Today’s Moral Issues. This is an extremely accessible work that organizes the subject matter of ethics into well-structured units involving both general principles and focused ethical dilemmas. The instructor will guide the students through the pertinent readings and discussion topics. Exam #3: WAR ECONOMIC EQUALITY 1. Aquinas 5. Mill 2. Grotius 6. Hospers 3. Clausewitz 7. Anderson 4. Gandhi CONCERNING THE SHORT PAPER Choose one of our dilemma topics from our book as the focus of your short paper. If you have another topic in mind, please consult with me for permission. —length: 4 to 5 pages — format: typed —number of points: 10 — submission via Bb, under “Assignments” — Format: Microsoft Word — Line Spacing: Double-Spaced —Print: Black The following is merely a suggestion for the organization of the paper, but it might be useful as an indication of how it could look: a) Initial statement of your position concerning the moral dilemma; how to resolve it, how you plan to argue for/against it. b) Amplification of your position; your main points or position. c) Backup: some cited references and supporting evidence for your position. d) Your criticisms of alternative or contrary points of view. e) Your conclusion/summing up. Plagiarism is a serious breach of academic integrity. If you submit plagiarized materials you will receive a zero on the assignment. If you need an extension of the due date for the paper, please consult with me.

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Linkage analysis: The linkage shown below is the kinematic sketch for the rear suspension of a motorcycle. The dimensions are given in the drawing; consider BC = 2” along the AB direction for the given configuration. For the analysis, assume that the angular velocity of the input link (link 2) is constant and operating in the CW direction (corresponding to the motorcycle going over a bump). a. Calculate the mobility of the linkage. How many loop equations are needed to solve for the dependent joint variables? b. Formulate the loop equations. c. Solve the loop equations and give explicit expressions for the dependent variables as a function of the input angle ?. d. Compute the limits for the input angle ?. Is the linkage going to work as expected? (is the range of motion of ? enough?) e. Write the position vector of point C. Use Maple, GIM or similar software to plot the trajectory of point C over the range of ? calculated in d). f. Use Maple or similar software to plot ? and s as a function of ?. g. Use GIM to create a simulation for the motion of the linkage. Provide a snapshot. h. Compute the velocity vector for point C. Give the value of the velocity for the configuration shown in the kinematic sketch (? = 200o), for an input angular velocity of 200 rpm. i. Compute the velocity s of the slider. Plot this velocity as a function of ? for a constant input angular velocity of 200rpm. j. Plot the acceleration of the slide, s, as a function of ?, for the same constant input angular velocity

Linkage analysis: The linkage shown below is the kinematic sketch for the rear suspension of a motorcycle. The dimensions are given in the drawing; consider BC = 2” along the AB direction for the given configuration. For the analysis, assume that the angular velocity of the input link (link 2) is constant and operating in the CW direction (corresponding to the motorcycle going over a bump). a. Calculate the mobility of the linkage. How many loop equations are needed to solve for the dependent joint variables? b. Formulate the loop equations. c. Solve the loop equations and give explicit expressions for the dependent variables as a function of the input angle ?. d. Compute the limits for the input angle ?. Is the linkage going to work as expected? (is the range of motion of ? enough?) e. Write the position vector of point C. Use Maple, GIM or similar software to plot the trajectory of point C over the range of ? calculated in d). f. Use Maple or similar software to plot ? and s as a function of ?. g. Use GIM to create a simulation for the motion of the linkage. Provide a snapshot. h. Compute the velocity vector for point C. Give the value of the velocity for the configuration shown in the kinematic sketch (? = 200o), for an input angular velocity of 200 rpm. i. Compute the velocity s of the slider. Plot this velocity as a function of ? for a constant input angular velocity of 200rpm. j. Plot the acceleration of the slide, s, as a function of ?, for the same constant input angular velocity

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Lab 5 Math 551 Fall 2015 Goal: In this assignment we will look at two fractals, namely the Sierpinski fractal and the Barnsley Fern. During the lab session, your lab instructor will teach you the necessary MATLAB code to complete the assignment, which will be discussed in the lab on Thursday October 8th or Friday October 9th in the lab (CW 144 or CW 145). What you have to submit: An m- le containing all of the commands necessary to perform all the tasks described below. Submit this le on Canvas. Click: \Assignments”, click \MATLAB Project 5″, click \Submit Assignment”, then upload your .m le and click \Submit Assignment” again. Due date: Friday October 16, 5pm. No late submission will be accepted. TASKS A fractal can be de ned as a self-similar detailed pattern repeating itself. Some of the most well know fractals (the Mandelbrot set and Julia set) can be viewed here: http://classes.yale.edu/fractals/ The Sierpinski Fractal The program srnpnski(m,dist,n) gets its name from the mathematician W. Sierpinski. The only parameter that must be speci ed is m which determines the number of vertices that will be part of a regular polygon. For larger m it produces a graph which is similar to a snow ake. The program starts with a randomly chosen seed position given by the internal variable s. At each stage one of the vertices is chosen at random and a new point is produced which is dist away from the old point to the vertex. The value of dist should be between 0 and 1. The default value is 0.5. This process is repeated n times. The default value of n is 1500. 1. Create a new Matlab function: func t i on s rpns k i (m, di s t , n) %This c r e a t e s a snowf lake from m v e r t i c e s us ing n i t e r a t i o n s . i f nargin <3, n=1500; end i f nargin <2, d i s t =0.5; end c l f a x i s ( [ ?1 ,1 , ?1 ,1] ) p=exp (2 pi  i  ( 1 :m)/m) ; pl o t (p , '  ' ) hold s=rand+i  rand ; f o r j =1:n r=c e i l (m rand ) ; s=d i s t  s+(1?d i s t )p( r ) ; pl o t ( s , ' . ' ) end 2. Try out the following commands s rpns k i ( 3 ) s rpns k i ( 3 , 0 . 5 , 2 5 0 0 ) s rpns k i ( 3 , 0 . 5 , 5 0 0 0 ) s rpns k i ( 3 , 0 . 4 ) 1 s rpns k i ( 3 , 0 . 2 ) s rpns k i ( 5 ) s rpns k i ( 5 , 0 . 4 ) s rpns k i ( 5 , 0 . 3 ) s rpns k i ( 6 , 0 . 3 ) s rpns k i ( 8 , 0 . 3 , 5 0 0 0 ) The Barnsley Fern The following program is the famous Barnsley Fern. The only external parameter is n, the number of iterations. 3. Create a new Matlab function: func t i on f e r n (n) A1=[ 0 . 8 5 , 0 . 0 4 ; ?0 . 0 4 , 0 . 8 5 ] ; A2=[ ?0 . 1 5 , 0 . 2 8 ; 0 . 2 6 , 0 . 2 4 ] ; A3=[ 0 . 2 , ?0 . 2 6 ; 0 . 2 3 , 0 . 2 2 ] ; A4=[ 0 , 0 ; 0 , 0 . 1 6 ] ; T1=[ 0 ; 1 . 6 ] ; T2=[ 0 ; 0 . 4 4 ] ; T3=[ 0 ; 1 . 6 ] ; T4=[ 0 , 0 ] ; P1=0.85; P2=0.07; P3=0.07; P4=0.01; c l f ; s=rand ( 2 , 1 ) ; pl o t ( s ( 1 ) , s ( 2 ) , ' . ' ) hold f o r j =1:n r=rand ; i f r<=P1 , s=A1 s+T1 ; e l s e i f r<=P1+P2 , s=A2 s+T2 ; e l s e i f r<=P1+P2+P3 , s=A3 s+T3 ; e l s e s=A4 s ; end pl o t ( s ( 1 ) , s ( 2 ) , ' . ' ) end 4. Try the following commands: f e r n (100) f e r n (500) f e r n (1000) f e r n (3000) f e r n (5000) f e r n (10000) 2 5. Change the parameters in the fern program: A1=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; A2=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; A3=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; T1=[ 1 ; 1 ] ; T2=[ 1 ; 5 0 ] ; T3=[ 5 0 ; 5 0 ] ; P1=0.33; P2=0.33; P3=0.34; Call the new program srptri.m. Try the command s r p t r i (5000) You should see a familiar looking result. 6. Change the parameters in the fern program: A1=[ 0 , 0 ; 0 , 0 . 5 ] ; A2=[ 0 . 4 2 , ?0 . 4 2 ; 0 . 4 2 , 0 . 4 2 ] ; A3=[ 0 . 4 2 , 0 . 4 2 ; ?0 . 4 2 , 0 . 4 2 ] ; A4=[ 0 . 1 , 0 ; 0 , 0 . 1 ] ; T1=[ 0 ; 0 ] ; T2=[ 0 ; 0 . 2 ] ; T3=[ 0 ; 0 . 2 ] ; T4=[ 0 , 0 . 2 ] ; P1=0.05; P2=0.4; P3=0.4; P4=0.15; Call the new program srptree.m. Try the command s r p t r e e (5000) This is an example of a fractal tree. Some nice animations of fractal trees can be seen here: http://classes.yale.edu/fractals/ MATLAB commands to learn: Cl f , c e i l , imaginary uni t I , i f . . e l s e i f . . e l s e . . end 3

Lab 5 Math 551 Fall 2015 Goal: In this assignment we will look at two fractals, namely the Sierpinski fractal and the Barnsley Fern. During the lab session, your lab instructor will teach you the necessary MATLAB code to complete the assignment, which will be discussed in the lab on Thursday October 8th or Friday October 9th in the lab (CW 144 or CW 145). What you have to submit: An m- le containing all of the commands necessary to perform all the tasks described below. Submit this le on Canvas. Click: \Assignments”, click \MATLAB Project 5″, click \Submit Assignment”, then upload your .m le and click \Submit Assignment” again. Due date: Friday October 16, 5pm. No late submission will be accepted. TASKS A fractal can be de ned as a self-similar detailed pattern repeating itself. Some of the most well know fractals (the Mandelbrot set and Julia set) can be viewed here: http://classes.yale.edu/fractals/ The Sierpinski Fractal The program srnpnski(m,dist,n) gets its name from the mathematician W. Sierpinski. The only parameter that must be speci ed is m which determines the number of vertices that will be part of a regular polygon. For larger m it produces a graph which is similar to a snow ake. The program starts with a randomly chosen seed position given by the internal variable s. At each stage one of the vertices is chosen at random and a new point is produced which is dist away from the old point to the vertex. The value of dist should be between 0 and 1. The default value is 0.5. This process is repeated n times. The default value of n is 1500. 1. Create a new Matlab function: func t i on s rpns k i (m, di s t , n) %This c r e a t e s a snowf lake from m v e r t i c e s us ing n i t e r a t i o n s . i f nargin <3, n=1500; end i f nargin <2, d i s t =0.5; end c l f a x i s ( [ ?1 ,1 , ?1 ,1] ) p=exp (2 pi  i  ( 1 :m)/m) ; pl o t (p , '  ' ) hold s=rand+i  rand ; f o r j =1:n r=c e i l (m rand ) ; s=d i s t  s+(1?d i s t )p( r ) ; pl o t ( s , ' . ' ) end 2. Try out the following commands s rpns k i ( 3 ) s rpns k i ( 3 , 0 . 5 , 2 5 0 0 ) s rpns k i ( 3 , 0 . 5 , 5 0 0 0 ) s rpns k i ( 3 , 0 . 4 ) 1 s rpns k i ( 3 , 0 . 2 ) s rpns k i ( 5 ) s rpns k i ( 5 , 0 . 4 ) s rpns k i ( 5 , 0 . 3 ) s rpns k i ( 6 , 0 . 3 ) s rpns k i ( 8 , 0 . 3 , 5 0 0 0 ) The Barnsley Fern The following program is the famous Barnsley Fern. The only external parameter is n, the number of iterations. 3. Create a new Matlab function: func t i on f e r n (n) A1=[ 0 . 8 5 , 0 . 0 4 ; ?0 . 0 4 , 0 . 8 5 ] ; A2=[ ?0 . 1 5 , 0 . 2 8 ; 0 . 2 6 , 0 . 2 4 ] ; A3=[ 0 . 2 , ?0 . 2 6 ; 0 . 2 3 , 0 . 2 2 ] ; A4=[ 0 , 0 ; 0 , 0 . 1 6 ] ; T1=[ 0 ; 1 . 6 ] ; T2=[ 0 ; 0 . 4 4 ] ; T3=[ 0 ; 1 . 6 ] ; T4=[ 0 , 0 ] ; P1=0.85; P2=0.07; P3=0.07; P4=0.01; c l f ; s=rand ( 2 , 1 ) ; pl o t ( s ( 1 ) , s ( 2 ) , ' . ' ) hold f o r j =1:n r=rand ; i f r<=P1 , s=A1 s+T1 ; e l s e i f r<=P1+P2 , s=A2 s+T2 ; e l s e i f r<=P1+P2+P3 , s=A3 s+T3 ; e l s e s=A4 s ; end pl o t ( s ( 1 ) , s ( 2 ) , ' . ' ) end 4. Try the following commands: f e r n (100) f e r n (500) f e r n (1000) f e r n (3000) f e r n (5000) f e r n (10000) 2 5. Change the parameters in the fern program: A1=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; A2=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; A3=[ 0 . 5 , 0 ; 0 , 0 . 5 ] ; T1=[ 1 ; 1 ] ; T2=[ 1 ; 5 0 ] ; T3=[ 5 0 ; 5 0 ] ; P1=0.33; P2=0.33; P3=0.34; Call the new program srptri.m. Try the command s r p t r i (5000) You should see a familiar looking result. 6. Change the parameters in the fern program: A1=[ 0 , 0 ; 0 , 0 . 5 ] ; A2=[ 0 . 4 2 , ?0 . 4 2 ; 0 . 4 2 , 0 . 4 2 ] ; A3=[ 0 . 4 2 , 0 . 4 2 ; ?0 . 4 2 , 0 . 4 2 ] ; A4=[ 0 . 1 , 0 ; 0 , 0 . 1 ] ; T1=[ 0 ; 0 ] ; T2=[ 0 ; 0 . 2 ] ; T3=[ 0 ; 0 . 2 ] ; T4=[ 0 , 0 . 2 ] ; P1=0.05; P2=0.4; P3=0.4; P4=0.15; Call the new program srptree.m. Try the command s r p t r e e (5000) This is an example of a fractal tree. Some nice animations of fractal trees can be seen here: http://classes.yale.edu/fractals/ MATLAB commands to learn: Cl f , c e i l , imaginary uni t I , i f . . e l s e i f . . e l s e . . end 3

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A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.4 m/s. The block oscillates on the spring without friction. 1) What is the spring constant of the spring? N/m You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 2) What is the oscillation frequency? Hz You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 3) After t = 0.37 s what is the speed of the block? m/s You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 4) What is the magnitude of the maximum acceleration of the block? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) At t = 0.37 s what is the magnitude of the net force on the block? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) Where is the potential energy of the system the greatest? At the highest point of the oscillation. At the new equilibrium position of the oscillation. At the lowest point of the oscillation. You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 7) Below is some space to write notes on this problem A 5.2-kg object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force constantk = 717 N/m. The spring is stretched 7.9 cm from equilibrium and released. 1) (a) What is the frequency of the motion? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) (b) What is the period of the motion? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) (c) What is the amplitude of the motion? cm You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) (d) What is the maximum speed of the motion? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) (e) What is the maximum acceleration of the motion? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) (f) When does the object first reach its equilibrium position? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) (h) What is its acceleration at this time? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) An 86 kg person steps into a car of mass 2437 kg, causing it to sink 2.35 cm on its springs. Assuming no damping, with what frequency will the car and passenger vibrate on the springs? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) A 0.117-kg block is suspended from a spring. When a small pebble of mass 30 g is placed on the block, the spring stretches an additional 5.1 cm. With the pebble on the block, the block oscillates with an amplitude of 12 cm. Find the maximum amplitude of oscillation at which the pebble will remain in contact with the block. Block and Spring SHM ________________________________________ At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched? t1 = seconds You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. A simple pendulum with mass m = 1.9 kg and length L = 2.39 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.9° from the vertical and released at t = 0. 1) What is the period of oscillation? s You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 2) What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the maximum speed of the pendulum? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) What is the angular displacement at t = 3.5 s? (give the answer as a negative angle if the angle is to the left of the vertical) ° You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) Which of the following would change the frequency of oscillation of this simple pendulum? increasing the mass decreasing the initial angular displacement increasing the length hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 8) Below is some space to write notes on this problem 1) If the period of a 74-cm-long simple pendulum is 1.72 s, what is the value of g at the location of the pendulum? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Torsion Pendulum • 1 • 2 • 3 • 4 • 5 A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.66 m. A force of F = 44.8 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium. 1) What is the torsion constant of this pendulum? N-m/rad You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium? N-m You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the angular frequency of oscillation of this torsion pendulum? rad/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) Which of the following would change the period of oscillation of this torsion pendulum? increasing the mass decreasing the initial angular displacement replacing the disk with a sphere of equal mass and radius hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 5) Below is some space to write notes on this problem You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Physical Pendulum ________________________________________ A rigid rod of length L= 1 m and mass M = 2.5 kg is attached to a pivot mounted d = 0.17 m from one end. The rod can rotate in the vertical plane, and is influenced by gravity. What is the period for small oscillations of the pendulum shown? T = seconds A circular hoop of radius 57 cm is hung on a narrow horizontal rod and allowed to swing in the plane of the hoop. What is the period of its oscillation, assuming that the amplitude is small? s 1) You are given a wooden rod 68 cm long and asked to drill a small diameter hole in it so that when pivoted about the the hole the period of the pendulum will be a minimum. How far from the center should you drill the hole? cm

A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.4 m/s. The block oscillates on the spring without friction. 1) What is the spring constant of the spring? N/m You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 2) What is the oscillation frequency? Hz You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 3) After t = 0.37 s what is the speed of the block? m/s You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. 4) What is the magnitude of the maximum acceleration of the block? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) At t = 0.37 s what is the magnitude of the net force on the block? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) Where is the potential energy of the system the greatest? At the highest point of the oscillation. At the new equilibrium position of the oscillation. At the lowest point of the oscillation. You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 7) Below is some space to write notes on this problem A 5.2-kg object on a frictionless horizontal surface is attached to one end of a horizontal spring that has a force constantk = 717 N/m. The spring is stretched 7.9 cm from equilibrium and released. 1) (a) What is the frequency of the motion? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) (b) What is the period of the motion? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) (c) What is the amplitude of the motion? cm You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) (d) What is the maximum speed of the motion? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) (e) What is the maximum acceleration of the motion? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) (f) When does the object first reach its equilibrium position? s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) (h) What is its acceleration at this time? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) An 86 kg person steps into a car of mass 2437 kg, causing it to sink 2.35 cm on its springs. Assuming no damping, with what frequency will the car and passenger vibrate on the springs? Hz You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 1) A 0.117-kg block is suspended from a spring. When a small pebble of mass 30 g is placed on the block, the spring stretches an additional 5.1 cm. With the pebble on the block, the block oscillates with an amplitude of 12 cm. Find the maximum amplitude of oscillation at which the pebble will remain in contact with the block. Block and Spring SHM ________________________________________ At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the block next pass x = 0, the place where the spring is unstretched? t1 = seconds You currently have 1 submissions for this question. Only 10 submission are allowed. You can make 9 more submissions for this question. A simple pendulum with mass m = 1.9 kg and length L = 2.39 m hangs from the ceiling. It is pulled back to an small angle of θ = 9.9° from the vertical and released at t = 0. 1) What is the period of oscillation? s You currently have 2 submissions for this question. Only 10 submission are allowed. You can make 8 more submissions for this question. 2) What is the magnitude of the force on the pendulum bob perpendicular to the string at t=0? N You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the maximum speed of the pendulum? m/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) What is the angular displacement at t = 3.5 s? (give the answer as a negative angle if the angle is to the left of the vertical) ° You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5) What is the magnitude of the tangential acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 6) What is the magnitude of the radial acceleration as the pendulum passes through the equilibrium position? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 7) Which of the following would change the frequency of oscillation of this simple pendulum? increasing the mass decreasing the initial angular displacement increasing the length hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 8) Below is some space to write notes on this problem 1) If the period of a 74-cm-long simple pendulum is 1.72 s, what is the value of g at the location of the pendulum? m/s2 You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Torsion Pendulum • 1 • 2 • 3 • 4 • 5 A torsion pendulum is made from a disk of mass m = 6.6 kg and radius R = 0.66 m. A force of F = 44.8 N exerted on the edge of the disk rotates the disk 1/4 of a revolution from equilibrium. 1) What is the torsion constant of this pendulum? N-m/rad You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 2) What is the minimum torque needed to rotate the pendulum a full revolution from equilibrium? N-m You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 3) What is the angular frequency of oscillation of this torsion pendulum? rad/s You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) Which of the following would change the period of oscillation of this torsion pendulum? increasing the mass decreasing the initial angular displacement replacing the disk with a sphere of equal mass and radius hanging the pendulum in an elevator accelerating downward You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. (Survey Question) 5) Below is some space to write notes on this problem You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. Physical Pendulum ________________________________________ A rigid rod of length L= 1 m and mass M = 2.5 kg is attached to a pivot mounted d = 0.17 m from one end. The rod can rotate in the vertical plane, and is influenced by gravity. What is the period for small oscillations of the pendulum shown? T = seconds A circular hoop of radius 57 cm is hung on a narrow horizontal rod and allowed to swing in the plane of the hoop. What is the period of its oscillation, assuming that the amplitude is small? s 1) You are given a wooden rod 68 cm long and asked to drill a small diameter hole in it so that when pivoted about the the hole the period of the pendulum will be a minimum. How far from the center should you drill the hole? cm

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Chapter 10 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A One-Dimensional Inelastic Collision Block 1, of mass = 3.70 , moves along a frictionless air track with speed = 15.0 . It collides with block 2, of mass = 19.0 , which was initially at rest. The blocks stick together after the collision. Part A Find the magnitude of the total initial momentum of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: m1 kg v1 m/s m2 kg pi Part B Find , the magnitude of the final velocity of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: Part C What is the change in the two-block system’s kinetic energy due to the collision? Express your answer numerically in joules. You did not open hints for this part. ANSWER: pi = kg m/s vf vf = m/s K = Kfinal − Kinitial K = J Conservation of Energy Ranking Task Six pendulums of various masses are released from various heights above a tabletop, as shown in the figures below. All the pendulums have the same length and are mounted such that at the vertical position their lowest points are the height of the tabletop and just do not strike the tabletop when released. Assume that the size of each bob is negligible. Part A Rank each pendulum on the basis of its initial gravitational potential energy (before being released) relative to the tabletop. Rank from largest to smallest To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: m h Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Momentum and Kinetic Energy Consider two objects (Object 1 and Object 2) moving in the same direction on a frictionless surface. Object 1 moves with speed and has mass . Object 2 moves with speed and has mass . Part A Which object has the larger magnitude of its momentum? You did not open hints for this part. ANSWER: Part B Which object has the larger kinetic energy? You did not open hints for this part. ANSWER: v1 = v m1 = 2m v2 = 2v m2 = m Object 1 has the greater magnitude of its momentum. Object 2 has the greater magnitude of its momentum. Both objects have the same magnitude of their momenta. Object 1 has the greater kinetic energy. Object 2 has the greater kinetic energy. The objects have the same kinetic energy. Projectile Motion and Conservation of Energy Ranking Task Part A Six baseball throws are shown below. In each case the baseball is thrown at the same initial speed and from the same height above the ground. Assume that the effects of air resistance are negligible. Rank these throws according to the speed of the baseball the instant before it hits the ground. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: H PSS 10.1 Conservation of Mechanical Energy Learning Goal: To practice Problem-Solving Strategy 10.1 for conservation of mechanical energy problems. Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 20 that makes an angle of 45 with the vertical, steps off his tree limb, and swings down and then up to Jane’s open arms. When he arrives, his vine makes an angle of 30 with the vertical. Determine whether he gives her a tender embrace or knocks her off her limb by calculating Tarzan’s speed just before he reaches Jane. You can ignore air resistance and the mass of the vine. PROBLEM-SOLVING STRATEGY 10.1 Conservation of mechanical energy MODEL: Choose a system without friction or other losses of mechanical energy. m   VISUALIZE: Draw a before-and-after pictorial representation. Define symbols that will be used in the problem, list known values, and identify what you’re trying to find. SOLVE: The mathematical representation is based on the law of conservation of mechanical energy: . ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model The problem does not involve friction, nor are there losses of mechanical energy, so conservation of mechanical energy applies. Model Tarzan and the vine as a pendulum. Visualize Part A Which of the following sketches can be used in drawing a before-and-after pictorial representation? ANSWER: Kf + Uf = Ki + Ui Solve Part B What is Tarzan’s speed just before he reaches Jane? Express your answer in meters per second to two significant figures. You did not open hints for this part. ANSWER: Assess Part C This question will be shown after you complete previous question(s). Bungee Jumping Diagram A Diagram B Diagram C Diagram D vf vf = m/s Kate, a bungee jumper, wants to jump off the edge of a bridge that spans a river below. Kate has a mass , and the surface of the bridge is a height above the water. The bungee cord, which has length when unstretched, will first straighten and then stretch as Kate falls. Assume the following: The bungee cord behaves as an ideal spring once it begins to stretch, with spring constant . Kate doesn’t actually jump but simply steps off the edge of the bridge and falls straight downward. Kate’s height is negligible compared to the length of the bungee cord. Hence, she can be treated as a point particle. Use for the magnitude of the acceleration due to gravity. Part A How far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finally to rest? Assume that she doesn’t touch the water. Express the distance in terms of quantities given in the problem introduction. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Spinning Mass on a Spring An object of mass is attached to a spring with spring constant whose unstretched length is , and whose far end is fixed to a shaft that is rotating with angular speed . Neglect gravity and assume that the mass rotates with angular speed as shown. When solving this problem use an inertial coordinate system, as drawn here. m h L k g d = M k L Part A Given the angular speed , find the radius at which the mass rotates without moving toward or away from the origin. Express the radius in terms of , , , and . You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C R( ) k L M R( ) = This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). ± Baby Bounce with a Hooke One of the pioneers of modern science, Sir Robert Hooke (1635-1703), studied the elastic properties of springs and formulated the law that bears his name. Hooke found the relationship among the force a spring exerts, , the distance from equilibrium the end of the spring is displaced, , and a number called the spring constant (or, sometimes, the force constant of the spring). According to Hooke, the force of the spring is directly proportional to its displacement from equilibrium, or . In its scalar form, this equation is simply . The negative sign indicates that the force that the spring exerts and its displacement have opposite directions. The value of depends on the geometry and the material of the spring; it can be easily determined experimentally using this scalar equation. Toy makers have always been interested in springs for the entertainment value of the motion they produce. One well-known application is a baby bouncer,which consists of a harness seat for a toddler, attached to a spring. The entire contraption hooks onto the top of a doorway. The idea is for the baby to hang in the seat with his or her feet just touching the ground so that a good push up will get the baby bouncing, providing potentially hours of entertainment. F  x k F = −kx F = −kx k Part A The following chart and accompanying graph depict an experiment to determine the spring constant for a baby bouncer. Displacement from equilibrium, ( ) Force exerted on the spring, ( ) 0 0 0.005 2.5 0.010 5.0 0.015 7.5 0.020 10 What is the spring constant of the spring being tested for the baby bouncer? Express your answer to two significant figures in newtons per meter. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Shooting a ball into a box Two children are trying to shoot a marble of mass into a small box using a spring-loaded gun that is fixed on a table and shoots horizontally from the edge of the table. The edge of the table is a height above the top of the box (the height of which is negligibly small), and the center of the box is a distance from the edge of the table. x m F N k k = N/m m H d The spring has a spring constant . The first child compresses the spring a distance and finds that the marble falls short of its target by a horizontal distance . Part A By what distance, , should the second child compress the spring so that the marble lands in the middle of the box? (Assume that height of the box is negligible, so that there is no chance that the marble will hit the side of the box before it lands in the bottom.) Express the distance in terms of , , , , and . You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). k x1 d12 x2 m k g H d x2 = Elastic Collision in One Dimension Block 1, of mass , moves across a frictionless surface with speed . It collides elastically with block 2, of mass , which is at rest ( ). After the collision, block 1 moves with speed , while block 2 moves with speed . Assume that , so that after the collision, the two objects move off in the direction of the first object before the collision. Part A This collision is elastic. What quantities, if any, are conserved in this collision? You did not open hints for this part. ANSWER: Part B What is the final speed of block 1? m1 ui m2 vi = 0 uf vf m1 > m2 kinetic energy only momentum only kinetic energy and momentum uf Express in terms of , , and . You did not open hints for this part. ANSWER: Part C What is the final speed of block 2? Express in terms of , , and . You did not open hints for this part. ANSWER: Ballistic Pendulum In a ballistic pendulum an object of mass is fired with an initial speed at a pendulum bob. The bob has a mass , which is suspended by a rod of length and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement as shown . uf m1 m2 ui uf = vf vf m1 m2 ui vf = m v0 M L  Part A Find an expression for , the initial speed of the fired object. Express your answer in terms of some or all of the variables , , , and and the acceleration due to gravity, . You did not open hints for this part. ANSWER: Part B An experiment is done to compare the initial speed of bullets fired from different handguns: a 9.0 and a .44 caliber. The guns are fired into a 10- pendulum bob of length . Assume that the 9.0- bullet has a mass of 6.0 and the .44-caliber bullet has a mass of 12 . If the 9.0- bullet causes the pendulum to swing to a maximum angular displacement of 4.3 and the .44-caliber bullet causes a displacement of 10.1 , find the ratio of the initial speed of the 9.0- bullet to the speed of the .44-caliber bullet, . Express your answer numerically. You did not open hints for this part. ANSWER: v0 m M L  g v0 = mm kg L mm g g mm   mm (v /( 0 )9.0 v0)44 Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. (v0 )9.0/(v0 )44 =

Chapter 10 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A One-Dimensional Inelastic Collision Block 1, of mass = 3.70 , moves along a frictionless air track with speed = 15.0 . It collides with block 2, of mass = 19.0 , which was initially at rest. The blocks stick together after the collision. Part A Find the magnitude of the total initial momentum of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: m1 kg v1 m/s m2 kg pi Part B Find , the magnitude of the final velocity of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: Part C What is the change in the two-block system’s kinetic energy due to the collision? Express your answer numerically in joules. You did not open hints for this part. ANSWER: pi = kg m/s vf vf = m/s K = Kfinal − Kinitial K = J Conservation of Energy Ranking Task Six pendulums of various masses are released from various heights above a tabletop, as shown in the figures below. All the pendulums have the same length and are mounted such that at the vertical position their lowest points are the height of the tabletop and just do not strike the tabletop when released. Assume that the size of each bob is negligible. Part A Rank each pendulum on the basis of its initial gravitational potential energy (before being released) relative to the tabletop. Rank from largest to smallest To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: m h Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Momentum and Kinetic Energy Consider two objects (Object 1 and Object 2) moving in the same direction on a frictionless surface. Object 1 moves with speed and has mass . Object 2 moves with speed and has mass . Part A Which object has the larger magnitude of its momentum? You did not open hints for this part. ANSWER: Part B Which object has the larger kinetic energy? You did not open hints for this part. ANSWER: v1 = v m1 = 2m v2 = 2v m2 = m Object 1 has the greater magnitude of its momentum. Object 2 has the greater magnitude of its momentum. Both objects have the same magnitude of their momenta. Object 1 has the greater kinetic energy. Object 2 has the greater kinetic energy. The objects have the same kinetic energy. Projectile Motion and Conservation of Energy Ranking Task Part A Six baseball throws are shown below. In each case the baseball is thrown at the same initial speed and from the same height above the ground. Assume that the effects of air resistance are negligible. Rank these throws according to the speed of the baseball the instant before it hits the ground. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: H PSS 10.1 Conservation of Mechanical Energy Learning Goal: To practice Problem-Solving Strategy 10.1 for conservation of mechanical energy problems. Tarzan, in one tree, sights Jane in another tree. He grabs the end of a vine with length 20 that makes an angle of 45 with the vertical, steps off his tree limb, and swings down and then up to Jane’s open arms. When he arrives, his vine makes an angle of 30 with the vertical. Determine whether he gives her a tender embrace or knocks her off her limb by calculating Tarzan’s speed just before he reaches Jane. You can ignore air resistance and the mass of the vine. PROBLEM-SOLVING STRATEGY 10.1 Conservation of mechanical energy MODEL: Choose a system without friction or other losses of mechanical energy. m   VISUALIZE: Draw a before-and-after pictorial representation. Define symbols that will be used in the problem, list known values, and identify what you’re trying to find. SOLVE: The mathematical representation is based on the law of conservation of mechanical energy: . ASSESS: Check that your result has the correct units, is reasonable, and answers the question. Model The problem does not involve friction, nor are there losses of mechanical energy, so conservation of mechanical energy applies. Model Tarzan and the vine as a pendulum. Visualize Part A Which of the following sketches can be used in drawing a before-and-after pictorial representation? ANSWER: Kf + Uf = Ki + Ui Solve Part B What is Tarzan’s speed just before he reaches Jane? Express your answer in meters per second to two significant figures. You did not open hints for this part. ANSWER: Assess Part C This question will be shown after you complete previous question(s). Bungee Jumping Diagram A Diagram B Diagram C Diagram D vf vf = m/s Kate, a bungee jumper, wants to jump off the edge of a bridge that spans a river below. Kate has a mass , and the surface of the bridge is a height above the water. The bungee cord, which has length when unstretched, will first straighten and then stretch as Kate falls. Assume the following: The bungee cord behaves as an ideal spring once it begins to stretch, with spring constant . Kate doesn’t actually jump but simply steps off the edge of the bridge and falls straight downward. Kate’s height is negligible compared to the length of the bungee cord. Hence, she can be treated as a point particle. Use for the magnitude of the acceleration due to gravity. Part A How far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finally to rest? Assume that she doesn’t touch the water. Express the distance in terms of quantities given in the problem introduction. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Spinning Mass on a Spring An object of mass is attached to a spring with spring constant whose unstretched length is , and whose far end is fixed to a shaft that is rotating with angular speed . Neglect gravity and assume that the mass rotates with angular speed as shown. When solving this problem use an inertial coordinate system, as drawn here. m h L k g d = M k L Part A Given the angular speed , find the radius at which the mass rotates without moving toward or away from the origin. Express the radius in terms of , , , and . You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C R( ) k L M R( ) = This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). ± Baby Bounce with a Hooke One of the pioneers of modern science, Sir Robert Hooke (1635-1703), studied the elastic properties of springs and formulated the law that bears his name. Hooke found the relationship among the force a spring exerts, , the distance from equilibrium the end of the spring is displaced, , and a number called the spring constant (or, sometimes, the force constant of the spring). According to Hooke, the force of the spring is directly proportional to its displacement from equilibrium, or . In its scalar form, this equation is simply . The negative sign indicates that the force that the spring exerts and its displacement have opposite directions. The value of depends on the geometry and the material of the spring; it can be easily determined experimentally using this scalar equation. Toy makers have always been interested in springs for the entertainment value of the motion they produce. One well-known application is a baby bouncer,which consists of a harness seat for a toddler, attached to a spring. The entire contraption hooks onto the top of a doorway. The idea is for the baby to hang in the seat with his or her feet just touching the ground so that a good push up will get the baby bouncing, providing potentially hours of entertainment. F  x k F = −kx F = −kx k Part A The following chart and accompanying graph depict an experiment to determine the spring constant for a baby bouncer. Displacement from equilibrium, ( ) Force exerted on the spring, ( ) 0 0 0.005 2.5 0.010 5.0 0.015 7.5 0.020 10 What is the spring constant of the spring being tested for the baby bouncer? Express your answer to two significant figures in newtons per meter. You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Shooting a ball into a box Two children are trying to shoot a marble of mass into a small box using a spring-loaded gun that is fixed on a table and shoots horizontally from the edge of the table. The edge of the table is a height above the top of the box (the height of which is negligibly small), and the center of the box is a distance from the edge of the table. x m F N k k = N/m m H d The spring has a spring constant . The first child compresses the spring a distance and finds that the marble falls short of its target by a horizontal distance . Part A By what distance, , should the second child compress the spring so that the marble lands in the middle of the box? (Assume that height of the box is negligible, so that there is no chance that the marble will hit the side of the box before it lands in the bottom.) Express the distance in terms of , , , , and . You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). k x1 d12 x2 m k g H d x2 = Elastic Collision in One Dimension Block 1, of mass , moves across a frictionless surface with speed . It collides elastically with block 2, of mass , which is at rest ( ). After the collision, block 1 moves with speed , while block 2 moves with speed . Assume that , so that after the collision, the two objects move off in the direction of the first object before the collision. Part A This collision is elastic. What quantities, if any, are conserved in this collision? You did not open hints for this part. ANSWER: Part B What is the final speed of block 1? m1 ui m2 vi = 0 uf vf m1 > m2 kinetic energy only momentum only kinetic energy and momentum uf Express in terms of , , and . You did not open hints for this part. ANSWER: Part C What is the final speed of block 2? Express in terms of , , and . You did not open hints for this part. ANSWER: Ballistic Pendulum In a ballistic pendulum an object of mass is fired with an initial speed at a pendulum bob. The bob has a mass , which is suspended by a rod of length and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement as shown . uf m1 m2 ui uf = vf vf m1 m2 ui vf = m v0 M L  Part A Find an expression for , the initial speed of the fired object. Express your answer in terms of some or all of the variables , , , and and the acceleration due to gravity, . You did not open hints for this part. ANSWER: Part B An experiment is done to compare the initial speed of bullets fired from different handguns: a 9.0 and a .44 caliber. The guns are fired into a 10- pendulum bob of length . Assume that the 9.0- bullet has a mass of 6.0 and the .44-caliber bullet has a mass of 12 . If the 9.0- bullet causes the pendulum to swing to a maximum angular displacement of 4.3 and the .44-caliber bullet causes a displacement of 10.1 , find the ratio of the initial speed of the 9.0- bullet to the speed of the .44-caliber bullet, . Express your answer numerically. You did not open hints for this part. ANSWER: v0 m M L  g v0 = mm kg L mm g g mm   mm (v /( 0 )9.0 v0)44 Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. (v0 )9.0/(v0 )44 =

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Assignment 11 Due: 11:59pm on Wednesday, April 30, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 13.2 The gravitational force of a star on orbiting planet 1 is . Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force . Part A What is the ratio ? ANSWER: Correct Conceptual Question 13.3 A 1500 satellite and a 2200 satellite follow exactly the same orbit around the earth. Part A What is the ratio of the force on the first satellite to that on the second satellite? ANSWER: Correct F1 F2 F1 F2 = 2 F1 F2 kg kg F1 F2 = 0.682 F1 F2 Part B What is the ratio of the acceleration of the first satellite to that of the second satellite? ANSWER: Correct Problem 13.2 The centers of a 15.0 lead ball and a 90.0 lead ball are separated by 9.00 . Part A What gravitational force does each exert on the other? Express your answer with the appropriate units. ANSWER: Correct Part B What is the ratio of this gravitational force to the weight of the 90.0 ball? ANSWER: a1 a2 = 1 a1 a2 kg g cm 1.11×10−8 N g 1.26×10−8 Typesetting math: 100% Correct Problem 13.6 The space shuttle orbits 310 above the surface of the earth. Part A What is the gravitational force on a 7.5 sphere inside the space shuttle? Express your answer with the appropriate units. ANSWER: Correct ± A Satellite in Orbit A satellite used in a cellular telephone network has a mass of 2310 and is in a circular orbit at a height of 650 above the surface of the earth. Part A What is the gravitational force on the satellite? Take the gravitational constant to be = 6.67×10−11 , the mass of the earth to be = 5.97×1024 , and the radius of the Earth to be = 6.38×106 . Express your answer in newtons. Hint 1. How to approach the problem Use the equation for the law of gravitation to calculate the force on the satellite. Be careful about the units when performing the calculations. km kg Fe on s = 67.0 N kg km Fgrav G N m2/kg2 me kg re m Typesetting math: 100% Hint 2. Law of gravitation According to Newton’s law of gravitation, , where is the gravitational constant, and are the masses of the two objects, and is the distance between the centers of mass of the two objects. Hint 3. Calculate the distance between the centers of mass What is the distance from the center of mass of the satellite to the center of mass of the earth? Express your answer in meters. ANSWER: ANSWER: Correct Part B What fraction is this of the satellite’s weight at the surface of the earth? Take the free-fall acceleration at the surface of the earth to be = 9.80 . Hint 1. How to approach the problem All you need to do is to take the ratio of the gravitational force on the satellite to the weight of the satellite at ground level. There are two ways to do this, depending on how you define the force of gravity at the surface of the earth. ANSWER: F = Gm1m2/r2 G m1 m2 r r = 7.03×10r 6 m = 1.86×10Fgrav 4 N g m/s2 0.824 Typesetting math: 100% Correct Although it is easy to find the weight of the satellite using the constant acceleration due to gravity, it is instructional to consider the weight calculated using the law of gravitation: . Dividing the gravitational force on the satellite by , we find that the ratio of the forces due to the earth’s gravity is simply the square of the ratio of the earth’s radius to the sum of the earth’s radius and the height of the orbit of the satellite above the earth, . This will also be the fraction of the weight of, say, an astronaut in an orbit at the same altitude. Notice that an astronaut’s weight is never zero. When people speak of “weightlessness” in space, what they really mean is “free fall.” Problem 13.8 Part A What is the free-fall acceleration at the surface of the moon? Express your answer with the appropriate units. ANSWER: Correct Part B What is the free-fall acceleration at the surface of the Jupiter? Express your answer with the appropriate units. ANSWER: Correct w = G m/ me r2e Fgrav = Gmem/(re + h)2 w [re/(re + h)]2 gmoon = 1.62 m s2 gJupiter = 25.9 m s2 Typesetting math: 100% Enhanced EOC: Problem 13.14 A rocket is launched straight up from the earth’s surface at a speed of 1.90×104 . You may want to review ( pages 362 – 365) . For help with math skills, you may want to review: Mathematical Expressions Involving Squares Part A What is its speed when it is very far away from the earth? Express your answer with the appropriate units. Hint 1. How to approach the problem What is conserved in this problem? What is the rocket’s initial kinetic energy in terms of its unknown mass, ? What is the rocket’s initial gravitational potential energy in terms of its unknown mass, ? When the rocket is very far away from the Earth, what is its gravitational potential energy? Using conservation of energy, what is the rocket’s kinetic energy when it is very far away from the Earth? Therefore, what is the rocket’s velocity when it is very far away from the Earth? ANSWER: Correct Problem 13.13 Part A m/s m m 1.54×104 ms Typesetting math: 100% What is the escape speed from Venus? Express your answer with the appropriate units. ANSWER: Correct Problem 13.17 The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 4.2 earth years. Part A What is the asteroid’s orbital radius? Express your answer with the appropriate units. ANSWER: Correct Part B What is the asteroid’s orbital speed? Express your answer with the appropriate units. ANSWER: vescape = 10.4 km s = 3.89×1011 R m = 1.85×104 v ms Typesetting math: 100% Correct Problem 13.32 Part A At what height above the earth is the acceleration due to gravity 15.0% of its value at the surface? Express your answer with the appropriate units. ANSWER: Correct Part B What is the speed of a satellite orbiting at that height? Express your answer with the appropriate units. ANSWER: Correct Problem 13.36 Two meteoroids are heading for earth. Their speeds as they cross the moon’s orbit are 2 . 1.01×107 m 4920 ms km/s Typesetting math: 100% Part A The first meteoroid is heading straight for earth. What is its speed of impact? Express your answer with the appropriate units. ANSWER: Correct Part B The second misses the earth by 5500 . What is its speed at its closest point? Express your answer with the appropriate units. ANSWER: Incorrect; Try Again Problem 14.2 An air-track glider attached to a spring oscillates between the 11.0 mark and the 67.0 mark on the track. The glider completes 11.0 oscillations in 32.0 . Part A What is the period of the oscillations? Express your answer with the appropriate units. v1 = 11.3 km s km v2 = cm cm s Typesetting math: 100% ANSWER: Correct Part B What is the frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part C What is the angular frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part D What is the amplitude? Express your answer with the appropriate units. 2.91 s 0.344 Hz 2.16 rad s Typesetting math: 100% ANSWER: Correct Part E What is the maximum speed of the glider? Express your answer with the appropriate units. ANSWER: Correct Good Vibes: Introduction to Oscillations Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion. Motion that repeats itself over and over is called periodic motion. There are many examples of periodic motion: the earth revolving around the sun, an elastic ball bouncing up and down, or a block attached to a spring oscillating back and forth. The last example differs from the first two, in that it represents a special kind of periodic motion called simple harmonic motion. The conditions that lead to simple harmonic motion are as follows: There must be a position of stable equilibrium. There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object’s displacement from its equilibrium position. Mathematically, the restoring force is given by , where is the displacement from equilibrium and is a constant that depends on the properties of the oscillating system. The resistive forces in the system must be reasonably small. In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them. Consider a block of mass attached to a spring with force constant , as shown in the figure. The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at . If the 28.0 cm 60.5 cms F  F = −kx x k m k x = 0 Typesetting math: 100% block is pulled to the right a distance and then released, will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. Part A After the block is released from , it will ANSWER: Correct As the block begins its motion to the left, it accelerates. Although the restoring force decreases as the block approaches equilibrium, it still pulls the block to the left, so by the time the equilibrium position is reached, the block has gained some speed. It will, therefore, pass the equilibrium position and keep moving, compressing the spring. The spring will now be pushing the block to the right, and the block will slow down, temporarily coming to rest at . After is reached, the block will begin its motion to the right, pushed by the spring. The block will pass the equilibrium position and continue until it reaches , completing one cycle of motion. The motion will then repeat; if, as we’ve assumed, there is no friction, the motion will repeat indefinitely. The time it takes the block to complete one cycle is called the period. Usually, the period is denoted and is measured in seconds. The frequency, denoted , is the number of cycles that are completed per unit of time: . In SI units, is measured in inverse seconds, or hertz ( ). A A x = A remain at rest. move to the left until it reaches equilibrium and stop there. move to the left until it reaches and stop there. move to the left until it reaches and then begin to move to the right. x = −A x = −A x = −A x = −A x = A T f f = 1/T f Hz Typesetting math: 100% Part B If the period is doubled, the frequency is ANSWER: Correct Part C An oscillating object takes 0.10 to complete one cycle; that is, its period is 0.10 . What is its frequency ? Express your answer in hertz. ANSWER: Correct unchanged. doubled. halved. s s f f = 10 Hz Typesetting math: 100% Part D If the frequency is 40 , what is the period ? Express your answer in seconds. ANSWER: Correct The following questions refer to the figure that graphically depicts the oscillations of the block on the spring. Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time. Part E Which points on the x axis are located a distance from the equilibrium position? ANSWER: Hz T T = 0.025 s A Typesetting math: 100% Correct Part F Suppose that the period is . Which of the following points on the t axis are separated by the time interval ? ANSWER: Correct Now assume for the remaining Parts G – J, that the x coordinate of point R is 0.12 and the t coordinate of point K is 0.0050 . Part G What is the period ? Express your answer in seconds. Hint 1. How to approach the problem In moving from the point to the point K, what fraction of a full wavelength is covered? Call that fraction . Then you can set . Dividing by the fraction will give the R only Q only both R and Q T T K and L K and M K and P L and N M and P m s T t = 0 a aT = 0.005 s a Typesetting math: 100% period . ANSWER: Correct Part H How much time does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? Express your answer in seconds. ANSWER: Correct Part I What distance does the object cover during one period of oscillation? Express your answer in meters. ANSWER: Correct Part J What distance does the object cover between the moments labeled K and N on the graph? T T = 0.02 s t t = 0.01 s d d = 0.48 m d Typesetting math: 100% Express your answer in meters. ANSWER: Correct Problem 14.4 Part A What is the amplitude of the oscillation shown in the figure? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct d = 0.36 m A = 20.0 cm Typesetting math: 100% Part B What is the frequency of this oscillation? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the phase constant? Express your answer to two significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Problem 14.10 An air-track glider attached to a spring oscillates with a period of 1.50 . At the glider is 4.60 left of the equilibrium position and moving to the right at 33.4 . Part A What is the phase constant? Express your answer to three significant figures and include the appropriate units. ANSWER: f = 0.25 Hz 0 = s t = 0 s cm cm/s Typesetting math: 100% Incorrect; Try Again Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Problem 14.12 A 140 air-track glider is attached to a spring. The glider is pushed in 12.2 and released. A student with a stopwatch finds that 14.0 oscillations take 19.0 . Part A What is the spring constant? Express your answer with the appropriate units. ANSWER: 0 = g cm s Typesetting math: 100% Correct Problem 14.14 The position of a 50 g oscillating mass is given by , where is in s. If necessary, round your answers to three significant figures. Determine: Part A The amplitude. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B The period. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C 3.00 Nm x(t) = (2.0 cm)cos(10t − /4) t 2.00 cm 0.628 s Typesetting math: 100% The spring constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Part D The phase constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G Typesetting math: 100% This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). Part I This question will be shown after you complete previous question(s). Enhanced EOC: Problem 14.17 A spring with spring constant 16 hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 4.0 and released. The ball makes 35 oscillations in 18 seconds. You may want to review ( pages 389 – 391) . For help with math skills, you may want to review: Differentiation of Trigonometric Functions Part A What is its the mass of the ball? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the period of oscillation? What is the angular frequency of the oscillations? How is the angular frequency related to the mass and spring constant? What is the mass? N/m cm s Typesetting math: 100% ANSWER: Correct Part B What is its maximum speed? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the amplitude of the oscillations? How is the maximum speed related to the amplitude of the oscillations and the angular frequency? ANSWER: Correct Changing the Period of a Pendulum A simple pendulum consisting of a bob of mass attached to a string of length swings with a period . Part A If the bob’s mass is doubled, approximately what will the pendulum’s new period be? Hint 1. Period of a simple pendulum The period of a simple pendulum of length is given by m = 110 g vmax = 49 cms m L T Typesetting math: 10T0% L , where is the acceleration due to gravity. ANSWER: Correct Part B If the pendulum is brought on the moon where the gravitational acceleration is about , approximately what will its period now be? Hint 1. How to approach the problem Recall the formula of the period of a simple pendulum. Since the gravitational acceleration appears in the denominator, the period must increase when the gravitational acceleration decreases. ANSWER: T = 2 Lg −−  g T/2 T &2T 2T g/6 T/6 T/&6 &6T 6T Typesetting math: 100% Correct Part C If the pendulum is taken into the orbiting space station what will happen to the bob? Hint 1. How to approach the problem Recall that the oscillations of a simple pendulum occur when a pendulum bob is raised above its equilibrium position and let go, causing the pendulum bob to fall. The gravitational force acts to bring the bob back to its equilibrium position. In the space station, the earth’s gravity acts on both the station and everything inside it, giving them the same acceleration. These objects are said to be in free fall. ANSWER: Correct In the space station, where all objects undergo the same acceleration due to the earth’s gravity, the tension in the string is zero and the bob does not fall relative to the point to which the string is attached. Problem 14.20 A 175 ball is tied to a string. It is pulled to an angle of 8.0 and released to swing as a pendulum. A student with a stopwatch finds that 15 oscillations take 13 . Part A How long is the string? Express your answer to two significant figures and include the appropriate units. It will continue to oscillate in a vertical plane with the same period. It will no longer oscillate because there is no gravity in space. It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall. It will oscillate much faster with a period that approaches zero. g ( s Typesetting math: 100% ANSWER: Correct Problem 14.22 Part A What is the length of a pendulum whose period on the moon matches the period of a 2.1- -long pendulum on the earth? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.42 An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( = 0.17 ) driven back and forth in SHM at by an electromagnetic coil. Part A The maximum restoring force that can be applied to the disk without breaking it is 4.4×104 . What is the maximum oscillation amplitude that won’t rupture the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: L = 19 cm m lmoon = 0.35 m m g 1.0 MHz N amax = 6.6 μm Typesetting math: 100% Correct Part B What is the disk’s maximum speed at this amplitude? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 81.4%. You received 117.25 out of a possible total of 144 points. vmax = 41 ms

Assignment 11 Due: 11:59pm on Wednesday, April 30, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 13.2 The gravitational force of a star on orbiting planet 1 is . Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force . Part A What is the ratio ? ANSWER: Correct Conceptual Question 13.3 A 1500 satellite and a 2200 satellite follow exactly the same orbit around the earth. Part A What is the ratio of the force on the first satellite to that on the second satellite? ANSWER: Correct F1 F2 F1 F2 = 2 F1 F2 kg kg F1 F2 = 0.682 F1 F2 Part B What is the ratio of the acceleration of the first satellite to that of the second satellite? ANSWER: Correct Problem 13.2 The centers of a 15.0 lead ball and a 90.0 lead ball are separated by 9.00 . Part A What gravitational force does each exert on the other? Express your answer with the appropriate units. ANSWER: Correct Part B What is the ratio of this gravitational force to the weight of the 90.0 ball? ANSWER: a1 a2 = 1 a1 a2 kg g cm 1.11×10−8 N g 1.26×10−8 Typesetting math: 100% Correct Problem 13.6 The space shuttle orbits 310 above the surface of the earth. Part A What is the gravitational force on a 7.5 sphere inside the space shuttle? Express your answer with the appropriate units. ANSWER: Correct ± A Satellite in Orbit A satellite used in a cellular telephone network has a mass of 2310 and is in a circular orbit at a height of 650 above the surface of the earth. Part A What is the gravitational force on the satellite? Take the gravitational constant to be = 6.67×10−11 , the mass of the earth to be = 5.97×1024 , and the radius of the Earth to be = 6.38×106 . Express your answer in newtons. Hint 1. How to approach the problem Use the equation for the law of gravitation to calculate the force on the satellite. Be careful about the units when performing the calculations. km kg Fe on s = 67.0 N kg km Fgrav G N m2/kg2 me kg re m Typesetting math: 100% Hint 2. Law of gravitation According to Newton’s law of gravitation, , where is the gravitational constant, and are the masses of the two objects, and is the distance between the centers of mass of the two objects. Hint 3. Calculate the distance between the centers of mass What is the distance from the center of mass of the satellite to the center of mass of the earth? Express your answer in meters. ANSWER: ANSWER: Correct Part B What fraction is this of the satellite’s weight at the surface of the earth? Take the free-fall acceleration at the surface of the earth to be = 9.80 . Hint 1. How to approach the problem All you need to do is to take the ratio of the gravitational force on the satellite to the weight of the satellite at ground level. There are two ways to do this, depending on how you define the force of gravity at the surface of the earth. ANSWER: F = Gm1m2/r2 G m1 m2 r r = 7.03×10r 6 m = 1.86×10Fgrav 4 N g m/s2 0.824 Typesetting math: 100% Correct Although it is easy to find the weight of the satellite using the constant acceleration due to gravity, it is instructional to consider the weight calculated using the law of gravitation: . Dividing the gravitational force on the satellite by , we find that the ratio of the forces due to the earth’s gravity is simply the square of the ratio of the earth’s radius to the sum of the earth’s radius and the height of the orbit of the satellite above the earth, . This will also be the fraction of the weight of, say, an astronaut in an orbit at the same altitude. Notice that an astronaut’s weight is never zero. When people speak of “weightlessness” in space, what they really mean is “free fall.” Problem 13.8 Part A What is the free-fall acceleration at the surface of the moon? Express your answer with the appropriate units. ANSWER: Correct Part B What is the free-fall acceleration at the surface of the Jupiter? Express your answer with the appropriate units. ANSWER: Correct w = G m/ me r2e Fgrav = Gmem/(re + h)2 w [re/(re + h)]2 gmoon = 1.62 m s2 gJupiter = 25.9 m s2 Typesetting math: 100% Enhanced EOC: Problem 13.14 A rocket is launched straight up from the earth’s surface at a speed of 1.90×104 . You may want to review ( pages 362 – 365) . For help with math skills, you may want to review: Mathematical Expressions Involving Squares Part A What is its speed when it is very far away from the earth? Express your answer with the appropriate units. Hint 1. How to approach the problem What is conserved in this problem? What is the rocket’s initial kinetic energy in terms of its unknown mass, ? What is the rocket’s initial gravitational potential energy in terms of its unknown mass, ? When the rocket is very far away from the Earth, what is its gravitational potential energy? Using conservation of energy, what is the rocket’s kinetic energy when it is very far away from the Earth? Therefore, what is the rocket’s velocity when it is very far away from the Earth? ANSWER: Correct Problem 13.13 Part A m/s m m 1.54×104 ms Typesetting math: 100% What is the escape speed from Venus? Express your answer with the appropriate units. ANSWER: Correct Problem 13.17 The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 4.2 earth years. Part A What is the asteroid’s orbital radius? Express your answer with the appropriate units. ANSWER: Correct Part B What is the asteroid’s orbital speed? Express your answer with the appropriate units. ANSWER: vescape = 10.4 km s = 3.89×1011 R m = 1.85×104 v ms Typesetting math: 100% Correct Problem 13.32 Part A At what height above the earth is the acceleration due to gravity 15.0% of its value at the surface? Express your answer with the appropriate units. ANSWER: Correct Part B What is the speed of a satellite orbiting at that height? Express your answer with the appropriate units. ANSWER: Correct Problem 13.36 Two meteoroids are heading for earth. Their speeds as they cross the moon’s orbit are 2 . 1.01×107 m 4920 ms km/s Typesetting math: 100% Part A The first meteoroid is heading straight for earth. What is its speed of impact? Express your answer with the appropriate units. ANSWER: Correct Part B The second misses the earth by 5500 . What is its speed at its closest point? Express your answer with the appropriate units. ANSWER: Incorrect; Try Again Problem 14.2 An air-track glider attached to a spring oscillates between the 11.0 mark and the 67.0 mark on the track. The glider completes 11.0 oscillations in 32.0 . Part A What is the period of the oscillations? Express your answer with the appropriate units. v1 = 11.3 km s km v2 = cm cm s Typesetting math: 100% ANSWER: Correct Part B What is the frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part C What is the angular frequency of the oscillations? Express your answer with the appropriate units. ANSWER: Correct Part D What is the amplitude? Express your answer with the appropriate units. 2.91 s 0.344 Hz 2.16 rad s Typesetting math: 100% ANSWER: Correct Part E What is the maximum speed of the glider? Express your answer with the appropriate units. ANSWER: Correct Good Vibes: Introduction to Oscillations Learning Goal: To learn the basic terminology and relationships among the main characteristics of simple harmonic motion. Motion that repeats itself over and over is called periodic motion. There are many examples of periodic motion: the earth revolving around the sun, an elastic ball bouncing up and down, or a block attached to a spring oscillating back and forth. The last example differs from the first two, in that it represents a special kind of periodic motion called simple harmonic motion. The conditions that lead to simple harmonic motion are as follows: There must be a position of stable equilibrium. There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object’s displacement from its equilibrium position. Mathematically, the restoring force is given by , where is the displacement from equilibrium and is a constant that depends on the properties of the oscillating system. The resistive forces in the system must be reasonably small. In this problem, we will introduce some of the basic quantities that describe oscillations and the relationships among them. Consider a block of mass attached to a spring with force constant , as shown in the figure. The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at . If the 28.0 cm 60.5 cms F  F = −kx x k m k x = 0 Typesetting math: 100% block is pulled to the right a distance and then released, will be the amplitude of the resulting oscillations. Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block. Part A After the block is released from , it will ANSWER: Correct As the block begins its motion to the left, it accelerates. Although the restoring force decreases as the block approaches equilibrium, it still pulls the block to the left, so by the time the equilibrium position is reached, the block has gained some speed. It will, therefore, pass the equilibrium position and keep moving, compressing the spring. The spring will now be pushing the block to the right, and the block will slow down, temporarily coming to rest at . After is reached, the block will begin its motion to the right, pushed by the spring. The block will pass the equilibrium position and continue until it reaches , completing one cycle of motion. The motion will then repeat; if, as we’ve assumed, there is no friction, the motion will repeat indefinitely. The time it takes the block to complete one cycle is called the period. Usually, the period is denoted and is measured in seconds. The frequency, denoted , is the number of cycles that are completed per unit of time: . In SI units, is measured in inverse seconds, or hertz ( ). A A x = A remain at rest. move to the left until it reaches equilibrium and stop there. move to the left until it reaches and stop there. move to the left until it reaches and then begin to move to the right. x = −A x = −A x = −A x = −A x = A T f f = 1/T f Hz Typesetting math: 100% Part B If the period is doubled, the frequency is ANSWER: Correct Part C An oscillating object takes 0.10 to complete one cycle; that is, its period is 0.10 . What is its frequency ? Express your answer in hertz. ANSWER: Correct unchanged. doubled. halved. s s f f = 10 Hz Typesetting math: 100% Part D If the frequency is 40 , what is the period ? Express your answer in seconds. ANSWER: Correct The following questions refer to the figure that graphically depicts the oscillations of the block on the spring. Note that the vertical axis represents the x coordinate of the oscillating object, and the horizontal axis represents time. Part E Which points on the x axis are located a distance from the equilibrium position? ANSWER: Hz T T = 0.025 s A Typesetting math: 100% Correct Part F Suppose that the period is . Which of the following points on the t axis are separated by the time interval ? ANSWER: Correct Now assume for the remaining Parts G – J, that the x coordinate of point R is 0.12 and the t coordinate of point K is 0.0050 . Part G What is the period ? Express your answer in seconds. Hint 1. How to approach the problem In moving from the point to the point K, what fraction of a full wavelength is covered? Call that fraction . Then you can set . Dividing by the fraction will give the R only Q only both R and Q T T K and L K and M K and P L and N M and P m s T t = 0 a aT = 0.005 s a Typesetting math: 100% period . ANSWER: Correct Part H How much time does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement? Express your answer in seconds. ANSWER: Correct Part I What distance does the object cover during one period of oscillation? Express your answer in meters. ANSWER: Correct Part J What distance does the object cover between the moments labeled K and N on the graph? T T = 0.02 s t t = 0.01 s d d = 0.48 m d Typesetting math: 100% Express your answer in meters. ANSWER: Correct Problem 14.4 Part A What is the amplitude of the oscillation shown in the figure? Express your answer to three significant figures and include the appropriate units. ANSWER: Correct d = 0.36 m A = 20.0 cm Typesetting math: 100% Part B What is the frequency of this oscillation? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the phase constant? Express your answer to two significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Problem 14.10 An air-track glider attached to a spring oscillates with a period of 1.50 . At the glider is 4.60 left of the equilibrium position and moving to the right at 33.4 . Part A What is the phase constant? Express your answer to three significant figures and include the appropriate units. ANSWER: f = 0.25 Hz 0 = s t = 0 s cm cm/s Typesetting math: 100% Incorrect; Try Again Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Problem 14.12 A 140 air-track glider is attached to a spring. The glider is pushed in 12.2 and released. A student with a stopwatch finds that 14.0 oscillations take 19.0 . Part A What is the spring constant? Express your answer with the appropriate units. ANSWER: 0 = g cm s Typesetting math: 100% Correct Problem 14.14 The position of a 50 g oscillating mass is given by , where is in s. If necessary, round your answers to three significant figures. Determine: Part A The amplitude. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part B The period. Express your answer to three significant figures and include the appropriate units. ANSWER: Correct Part C 3.00 Nm x(t) = (2.0 cm)cos(10t − /4) t 2.00 cm 0.628 s Typesetting math: 100% The spring constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Part D The phase constant. Express your answer to three significant figures and include the appropriate units. ANSWER: Incorrect; Try Again Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G Typesetting math: 100% This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). Part I This question will be shown after you complete previous question(s). Enhanced EOC: Problem 14.17 A spring with spring constant 16 hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 4.0 and released. The ball makes 35 oscillations in 18 seconds. You may want to review ( pages 389 – 391) . For help with math skills, you may want to review: Differentiation of Trigonometric Functions Part A What is its the mass of the ball? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the period of oscillation? What is the angular frequency of the oscillations? How is the angular frequency related to the mass and spring constant? What is the mass? N/m cm s Typesetting math: 100% ANSWER: Correct Part B What is its maximum speed? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the amplitude of the oscillations? How is the maximum speed related to the amplitude of the oscillations and the angular frequency? ANSWER: Correct Changing the Period of a Pendulum A simple pendulum consisting of a bob of mass attached to a string of length swings with a period . Part A If the bob’s mass is doubled, approximately what will the pendulum’s new period be? Hint 1. Period of a simple pendulum The period of a simple pendulum of length is given by m = 110 g vmax = 49 cms m L T Typesetting math: 10T0% L , where is the acceleration due to gravity. ANSWER: Correct Part B If the pendulum is brought on the moon where the gravitational acceleration is about , approximately what will its period now be? Hint 1. How to approach the problem Recall the formula of the period of a simple pendulum. Since the gravitational acceleration appears in the denominator, the period must increase when the gravitational acceleration decreases. ANSWER: T = 2 Lg −−  g T/2 T &2T 2T g/6 T/6 T/&6 &6T 6T Typesetting math: 100% Correct Part C If the pendulum is taken into the orbiting space station what will happen to the bob? Hint 1. How to approach the problem Recall that the oscillations of a simple pendulum occur when a pendulum bob is raised above its equilibrium position and let go, causing the pendulum bob to fall. The gravitational force acts to bring the bob back to its equilibrium position. In the space station, the earth’s gravity acts on both the station and everything inside it, giving them the same acceleration. These objects are said to be in free fall. ANSWER: Correct In the space station, where all objects undergo the same acceleration due to the earth’s gravity, the tension in the string is zero and the bob does not fall relative to the point to which the string is attached. Problem 14.20 A 175 ball is tied to a string. It is pulled to an angle of 8.0 and released to swing as a pendulum. A student with a stopwatch finds that 15 oscillations take 13 . Part A How long is the string? Express your answer to two significant figures and include the appropriate units. It will continue to oscillate in a vertical plane with the same period. It will no longer oscillate because there is no gravity in space. It will no longer oscillate because both the pendulum and the point to which it is attached are in free fall. It will oscillate much faster with a period that approaches zero. g ( s Typesetting math: 100% ANSWER: Correct Problem 14.22 Part A What is the length of a pendulum whose period on the moon matches the period of a 2.1- -long pendulum on the earth? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 14.42 An ultrasonic transducer, of the type used in medical ultrasound imaging, is a very thin disk ( = 0.17 ) driven back and forth in SHM at by an electromagnetic coil. Part A The maximum restoring force that can be applied to the disk without breaking it is 4.4×104 . What is the maximum oscillation amplitude that won’t rupture the disk? Express your answer to two significant figures and include the appropriate units. ANSWER: L = 19 cm m lmoon = 0.35 m m g 1.0 MHz N amax = 6.6 μm Typesetting math: 100% Correct Part B What is the disk’s maximum speed at this amplitude? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 81.4%. You received 117.25 out of a possible total of 144 points. vmax = 41 ms

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Problem 3 (25 Points) A bracket is subjected to a 610 N force as shown in the figure. (a) Express the force in Cartesian vector form. (8 points) (b) Determine the moment of the force about point C. (10 points) (c) Determine the moment of the force about line CD. (7 points)

Problem 3 (25 Points) A bracket is subjected to a 610 N force as shown in the figure. (a) Express the force in Cartesian vector form. (8 points) (b) Determine the moment of the force about point C. (10 points) (c) Determine the moment of the force about line CD. (7 points)

  Problem 3 (25 Points) A bracket is subjected to … Read More...
The Classic Five-Part Structure 1. Introduce the topic to be argued. Establish its importance. 2. Provide background information so readers will be able to follow your discussion. 3. State your claim (your argumentative thesis) and develop your argument by making a logical appeal. Support your claims with facts, opinions, and examples. If appropriate, mix an emotional appeal or an appeal to authority with your logical appeals. 4. Acknowledge counterarguments and treat them with respect. Rebut these arguments. Reject their evidence or their logic or concede some validity and modify your claim accordingly. Be flexible; you might split the counterarguments and rebut them one at a time at different locations in the paper, or you might begin the paper with a counterargument, rebut it, and then move on to your own claim. 5. Conclude by summarizing the main points of your argument. Then remind readers of what you want them to believe or do. Give them something to remember. The Problem-Solution Structure I. There is a serious problem. A. The problem exists and is growing. (Provide support for argument.) B. The problem is serious. (Provide support.) C. Current methods cannot cope with the problem. (Provide support.) II. There is a solution to the problem. (Your claim goes here.) A. The solution is practical. (Provide support.) B. The solution is desirable. (Provide support.) C. We can implement the solution. (Provide support.) D. Alternate solutions are not as strong as the proposed solution. (Review – and reject – competing solutions.) In both cases, you know before you begin writing whether you will use an inductive (analytic) or deductive (synthetic) arrangement for your argument. The decision to move inductively or deductively is about strategy. Induction moves from support to a claim. Deduction moves from a claim to support – to particular facts, opinions, and examples. This is the preferred form for most writing in the humanities. You can position your claim at the beginning, middle, or end of your presentation. In the problem/solution structure, the claim is made only after the writer introduces a problem. With the five-part structure, you have more flexibility in positioning your claim. One factor that can help determine placement is the likelihood of your audience agreeing with you. When your audience is likely to be neutral or supportive, making your claim early on will not alienate readers (synthetic presentation). When your audience is likely to disagree, placing your thesis at the end of your presentation allows you time to build a consensus, step by step, until you reach your conclusion (analytical presentation).

The Classic Five-Part Structure 1. Introduce the topic to be argued. Establish its importance. 2. Provide background information so readers will be able to follow your discussion. 3. State your claim (your argumentative thesis) and develop your argument by making a logical appeal. Support your claims with facts, opinions, and examples. If appropriate, mix an emotional appeal or an appeal to authority with your logical appeals. 4. Acknowledge counterarguments and treat them with respect. Rebut these arguments. Reject their evidence or their logic or concede some validity and modify your claim accordingly. Be flexible; you might split the counterarguments and rebut them one at a time at different locations in the paper, or you might begin the paper with a counterargument, rebut it, and then move on to your own claim. 5. Conclude by summarizing the main points of your argument. Then remind readers of what you want them to believe or do. Give them something to remember. The Problem-Solution Structure I. There is a serious problem. A. The problem exists and is growing. (Provide support for argument.) B. The problem is serious. (Provide support.) C. Current methods cannot cope with the problem. (Provide support.) II. There is a solution to the problem. (Your claim goes here.) A. The solution is practical. (Provide support.) B. The solution is desirable. (Provide support.) C. We can implement the solution. (Provide support.) D. Alternate solutions are not as strong as the proposed solution. (Review – and reject – competing solutions.) In both cases, you know before you begin writing whether you will use an inductive (analytic) or deductive (synthetic) arrangement for your argument. The decision to move inductively or deductively is about strategy. Induction moves from support to a claim. Deduction moves from a claim to support – to particular facts, opinions, and examples. This is the preferred form for most writing in the humanities. You can position your claim at the beginning, middle, or end of your presentation. In the problem/solution structure, the claim is made only after the writer introduces a problem. With the five-part structure, you have more flexibility in positioning your claim. One factor that can help determine placement is the likelihood of your audience agreeing with you. When your audience is likely to be neutral or supportive, making your claim early on will not alienate readers (synthetic presentation). When your audience is likely to disagree, placing your thesis at the end of your presentation allows you time to build a consensus, step by step, until you reach your conclusion (analytical presentation).

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PHET ElectroMagnetism Key to this Document Instructions are in black. Experimental questions that you need to solve through experimentation with an online animation are in green highlighted. Important instructions are in red highlighted. Items that need a response from you are in yellow highlighted. Please put your answers to this activity in RED. Part I- Comparing Permanent Magnets and Electromagnets: 1. Select the simulation “Magnets and Electromagnets.” It is at this link: http://phet.colorado.edu/new/simulations/sims.php?sim=Magnets_and_Electromagnets 2. Move the compass slowly along a semicircular path above the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 3. Move the compass along a semicircular path below the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 4. What do you suppose the compass needles drawn all over the screen tell you? 5. Use page 10 in your book to look up what it looks like when scientists use a drawing to represent a magnetic field. Describe the field around a bar magnet here. 6. Put the compass to the left or right of the magnet. Click “flip polarity” and notice what happens to the compass. Using the compass needle as your observation tool, describe the effect that flipping the poles of the magnet has on the magnetic field. 7. Click on the electromagnet tab along the top of the simulation window. Place the compass on the left side of the coil so that the compass center lies along the axis of the coil. <--like this 8. Move the compass along a semicircular path above the coil until you’ve put it on the opposite side of the coil. Then do the same below the coil. Notice what happens to the compass needle. Compare this answer to the answer you got to Number 2 and 3. 9. Compare the shape of the magnetic field of a bar magnet to the magnetic field of an electromagnet. 10. Use the voltage slider to change the direction of the current and investigate the shape of the magnetic field the coil using the compass after you’ve let the compass stabilize. Summarize, the effect that the direction of current has on the shape of the magnetic field around an electrified coil of wires. 11. What happens to the current in the coil when you set the voltage of the battery to zero? 12. What happens to the magnetic field around the coil when you set the voltage of the battery to zero? Part II – Investigating relationships- No Answers are written on this document after this point. All three data tables, graphs and conclusion statements go on the Google Spreadsheet that you can download from Ms. Pogge’s website. Experimental Question #1: How does distance affect the strength of the magnetic field around an electromagnet? 1. Using the Electromagnet simulation, click on “Show Field Meter.” 2. Set the battery voltage to 10V where the positive is on the right of the battery (slide the switch all the way to the right). 3. Magnetic field strength (symbol B on the top line of the meter) is measured in gauss (G). You’ll only need to record the value on the top line of the Field Meter. 4. Position zero will be right on top of the coil. Negative number positions will be to the left and positive number positions to the right of the coil. 5. Move the field meter one compass needle to the right and record the value of B at position 1. 6. This data table below will be used to help you fill in the first spreadsheet you downloaded from Ms. Pogge’s website. You will end up with 3 data tables, 3 graphs and 3 conclusion statements in your document, one for each mini-experiment you are doing. a. NOTE: Be sure to take all of your values along the horizontal axis of the coil. You’ll know you’re on the axis because the B-y measurement of the magnetic field is zero along the axis. Compass position (no units) Magnetic Field Strength ( )<--Fill in units! -5 (5 needles to the left of coil) Don’t fill in the table here...do it on the Google Spreadsheet you downloaded -4 -3 -2 -1 0 (middle of coil) 1 2 3 4 5 (5 needles to right of coil) 7. In your Google Spreadsheet: Graph the compass position on the horizontal (x) axis and magnetic field magnitude on the vertical (y) axis. 8. Make sure to label the axes and title the graph. Share this spreadsheet with your teacher. 9. Analyze your graph to discover how the two variables are related, and report the relationship between magnetic field strength and position using 1-3 complete sentences. Experimental Question #2: How does the number of coils affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the number of coils. Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet. Experimental Question #3: How does the amount of current affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the Current. (Recall that voltage is directly proportional to current….Ohm’s Law.) Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet.

PHET ElectroMagnetism Key to this Document Instructions are in black. Experimental questions that you need to solve through experimentation with an online animation are in green highlighted. Important instructions are in red highlighted. Items that need a response from you are in yellow highlighted. Please put your answers to this activity in RED. Part I- Comparing Permanent Magnets and Electromagnets: 1. Select the simulation “Magnets and Electromagnets.” It is at this link: http://phet.colorado.edu/new/simulations/sims.php?sim=Magnets_and_Electromagnets 2. Move the compass slowly along a semicircular path above the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 3. Move the compass along a semicircular path below the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 4. What do you suppose the compass needles drawn all over the screen tell you? 5. Use page 10 in your book to look up what it looks like when scientists use a drawing to represent a magnetic field. Describe the field around a bar magnet here. 6. Put the compass to the left or right of the magnet. Click “flip polarity” and notice what happens to the compass. Using the compass needle as your observation tool, describe the effect that flipping the poles of the magnet has on the magnetic field. 7. Click on the electromagnet tab along the top of the simulation window. Place the compass on the left side of the coil so that the compass center lies along the axis of the coil. <--like this 8. Move the compass along a semicircular path above the coil until you’ve put it on the opposite side of the coil. Then do the same below the coil. Notice what happens to the compass needle. Compare this answer to the answer you got to Number 2 and 3. 9. Compare the shape of the magnetic field of a bar magnet to the magnetic field of an electromagnet. 10. Use the voltage slider to change the direction of the current and investigate the shape of the magnetic field the coil using the compass after you’ve let the compass stabilize. Summarize, the effect that the direction of current has on the shape of the magnetic field around an electrified coil of wires. 11. What happens to the current in the coil when you set the voltage of the battery to zero? 12. What happens to the magnetic field around the coil when you set the voltage of the battery to zero? Part II – Investigating relationships- No Answers are written on this document after this point. All three data tables, graphs and conclusion statements go on the Google Spreadsheet that you can download from Ms. Pogge’s website. Experimental Question #1: How does distance affect the strength of the magnetic field around an electromagnet? 1. Using the Electromagnet simulation, click on “Show Field Meter.” 2. Set the battery voltage to 10V where the positive is on the right of the battery (slide the switch all the way to the right). 3. Magnetic field strength (symbol B on the top line of the meter) is measured in gauss (G). You’ll only need to record the value on the top line of the Field Meter. 4. Position zero will be right on top of the coil. Negative number positions will be to the left and positive number positions to the right of the coil. 5. Move the field meter one compass needle to the right and record the value of B at position 1. 6. This data table below will be used to help you fill in the first spreadsheet you downloaded from Ms. Pogge’s website. You will end up with 3 data tables, 3 graphs and 3 conclusion statements in your document, one for each mini-experiment you are doing. a. NOTE: Be sure to take all of your values along the horizontal axis of the coil. You’ll know you’re on the axis because the B-y measurement of the magnetic field is zero along the axis. Compass position (no units) Magnetic Field Strength ( )<--Fill in units! -5 (5 needles to the left of coil) Don’t fill in the table here...do it on the Google Spreadsheet you downloaded -4 -3 -2 -1 0 (middle of coil) 1 2 3 4 5 (5 needles to right of coil) 7. In your Google Spreadsheet: Graph the compass position on the horizontal (x) axis and magnetic field magnitude on the vertical (y) axis. 8. Make sure to label the axes and title the graph. Share this spreadsheet with your teacher. 9. Analyze your graph to discover how the two variables are related, and report the relationship between magnetic field strength and position using 1-3 complete sentences. Experimental Question #2: How does the number of coils affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the number of coils. Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet. Experimental Question #3: How does the amount of current affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the Current. (Recall that voltage is directly proportional to current….Ohm’s Law.) Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet.