Problem 3a: (6pts) As shown below, a two-dimensional vector can be defined by its x and y coordinates in an x-y Cartesian coordinate system. The vector can also be defined by its x ‘ and y ‘ coordinates in an x ‘− y’ Cartesian coordinate system that is rotated by a positive angle θ with respect to the x-y Cartesian coordinate system The relation between the two sets of coordinates, (x, y) and ( x ‘ , y ‘), is defined by the following transformation: A x y ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = x ‘ y ‘ ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ where the transformation matrix is given by: A = cosθ sinθ −sinθ cosθ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (i) Determine the inverse of the matrix A. (4 pts) (ii) Show that the inverse determined in Part (a) is the transformation matrix corresponding to rotation by a negative angle (i.e., rotation by –θ). (2 pts) Hint: cos(θ) = cos (−θ) and sin (θ) = −sin (−θ)

Problem 3a: (6pts) As shown below, a two-dimensional vector can be defined by its x and y coordinates in an x-y Cartesian coordinate system. The vector can also be defined by its x ‘ and y ‘ coordinates in an x ‘− y’ Cartesian coordinate system that is rotated by a positive angle θ with respect to the x-y Cartesian coordinate system The relation between the two sets of coordinates, (x, y) and ( x ‘ , y ‘), is defined by the following transformation: A x y ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ = x ‘ y ‘ ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ where the transformation matrix is given by: A = cosθ sinθ −sinθ cosθ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ (i) Determine the inverse of the matrix A. (4 pts) (ii) Show that the inverse determined in Part (a) is the transformation matrix corresponding to rotation by a negative angle (i.e., rotation by –θ). (2 pts) Hint: cos(θ) = cos (−θ) and sin (θ) = −sin (−θ)

Solution ( ) ( ) A 1 1 adj A … Read More...
light that has a wavelength equal to 420 nm falls normally on four slits. Each slit is 2.00 um wide and the center-to-center separation between it and the next slit is 8.00 um. (a) find the angular width of the central intensity maximum of the single slit diffraction pattern on a distant screen. This is the angle between the two minima adjacent to the central bright maximum of one of the four slits. (b) Find the angular position of all of the interference intensity maxima that lie inside the central diffraction maximum . sketch the positions of these maxima.

light that has a wavelength equal to 420 nm falls normally on four slits. Each slit is 2.00 um wide and the center-to-center separation between it and the next slit is 8.00 um. (a) find the angular width of the central intensity maximum of the single slit diffraction pattern on a distant screen. This is the angle between the two minima adjacent to the central bright maximum of one of the four slits. (b) Find the angular position of all of the interference intensity maxima that lie inside the central diffraction maximum . sketch the positions of these maxima.

Physics Lab 1 Projectile Motion We will use this 2-D “Golf Simulation” to explore combined horizontal and vertical motion (select experiment #7). This simulation provides a fun-filled way to examine 2-D projectile motion with and without air resistance. Before to start the experiment, take a few minutes playing with the simulation. Adjust the initial velocity by adjusting the launch speed and launch angle. See how many adjustments you have to make in order to get a hole-in-one. Turn the air on and off, turn the trails on and off, notice the time, and notice the shape of the curves. Instructions: • Go to http://www.physicslessons.com/exp7b.htm • Set the launch velocity to 60 m/s, trail “on” and “no air”. • Change the launch angle to 15 degree, click the launch button and take note of the horizontal displacement x. Repeat the experiment (changing the angle) and fill the first table (at the left). • Click the “no air” button (so it changes to “air”), repeat the experiments and fill the second table (at the right). Displacement [without air] Displacement [with air] Set launch speed, Vo = 60 m/s Set launch speed, Vo = 60 m/s Angle,  (deg) x (m) Angle,  (deg) H-Dis, x (m) 15 15 25 25 35 35 40 40 43 43 45 45 47 47 50 50 55 55 65 65 75 75 Questions: 1. What angle corresponds to the greatest horizontal range for the “without air” condition? What angle corresponds to the greatest horizontal range for the “with air” condition? Why is there a difference? 2. Describe the difference between the general shape of the trails for the two separate cases. 3. Do you notice any symmetry between high and low angles for either case? Describe the symmetry. 4. When practicing (playing) with the simulation earlier, how many tries did it typically take you to land the ball in the hole?

Physics Lab 1 Projectile Motion We will use this 2-D “Golf Simulation” to explore combined horizontal and vertical motion (select experiment #7). This simulation provides a fun-filled way to examine 2-D projectile motion with and without air resistance. Before to start the experiment, take a few minutes playing with the simulation. Adjust the initial velocity by adjusting the launch speed and launch angle. See how many adjustments you have to make in order to get a hole-in-one. Turn the air on and off, turn the trails on and off, notice the time, and notice the shape of the curves. Instructions: • Go to http://www.physicslessons.com/exp7b.htm • Set the launch velocity to 60 m/s, trail “on” and “no air”. • Change the launch angle to 15 degree, click the launch button and take note of the horizontal displacement x. Repeat the experiment (changing the angle) and fill the first table (at the left). • Click the “no air” button (so it changes to “air”), repeat the experiments and fill the second table (at the right). Displacement [without air] Displacement [with air] Set launch speed, Vo = 60 m/s Set launch speed, Vo = 60 m/s Angle,  (deg) x (m) Angle,  (deg) H-Dis, x (m) 15 15 25 25 35 35 40 40 43 43 45 45 47 47 50 50 55 55 65 65 75 75 Questions: 1. What angle corresponds to the greatest horizontal range for the “without air” condition? What angle corresponds to the greatest horizontal range for the “with air” condition? Why is there a difference? 2. Describe the difference between the general shape of the trails for the two separate cases. 3. Do you notice any symmetry between high and low angles for either case? Describe the symmetry. 4. When practicing (playing) with the simulation earlier, how many tries did it typically take you to land the ball in the hole?

Assignment 3 Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 2.68 As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 36.0 . Part A How fast is the watermelon going when it passes Superman? Express your answer with the appropriate units. ANSWER: Correct Problem 2.63 A motorist is driving at when she sees that a traffic light ahead has just turned red. She knows that this light stays red for , and she wants to reach the light just as it turns green again. It takes her to step on the brakes and begin slowing. Part A What is her speed as she reaches the light at the instant it turns green? Express your answer with the appropriate units. ANSWER: m/s 72.0 ms 20 m/s 200 m 15 s 1.0 s 5.71 ms Correct Conceptual Question 4.1 Part A At this instant, is the particle in the figurespeeding up, slowing down, or traveling at constant speed? ANSWER: Correct Part B Is this particle curving to the right, curving to the left, or traveling straight? Speeding up Slowing down Traveling at constant speed ANSWER: Correct Conceptual Question 4.2 Part A At this instant, is the particle in the following figure speeding up, slowing down, or traveling at constant speed? ANSWER: Curving to the right Curving to the left Traveling straight Correct Part B Is this particle curving upward, curving downward, or traveling straight? ANSWER: Correct Problem 4.8 A particle’s trajectory is described by and , where is in s. Part A What is the particle’s speed at ? ANSWER: The particle is speeding up. The particle is slowing down. The particle is traveling at constant speed. The particle is curving upward. The particle is curving downward. The particle is traveling straight. x = ( 1 −2 ) m 2 t3 t2 y = ( 1 −2t) m 2 t2 t t = 0 s v = 2 m/s Correct Part B What is the particle’s speed at ? Express your answer using two significant figures. ANSWER: Correct Part C What is the particle’s direction of motion, measured as an angle from the x-axis, at ? Express your answer using two significant figures. ANSWER: Correct Part D What is the particle’s direction of motion, measured as an angle from the x-axis, at ? Express your answer using two significant figures. ANSWER: t = 5.0s v = 18 m/s t = 0 s  = -90  counterclockwise from the +x axis. t = 5.0s  = 9.7  counterclockwise from the +x axis. Correct Problem 4.9 A rocket-powered hockey puck moves on a horizontal frictionless table. The figure shows the graph of and the figure shows the graph of , the x- and y-components of the puck’s velocity, respectively. The puck starts at the origin. Part A In which direction is the puck moving at = 3 ? Give your answer as an angle from the x-axis. Express your answer using two significant figures. ANSWER: Correct Part B vx vy t s = 51   above the x-axis How far from the origin is the puck at 5 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 4.13 A rifle is aimed horizontally at a target 51.0 away. The bullet hits the target 1.50 below the aim point. You may want to review ( pages 91 – 95) . For help with math skills, you may want to review: Quadratic Equations Part A What was the bullet’s flight time? Express your answer with the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the bullet’s trajectory, including where it leaves the gun and where it hits the target. You can assume that the gun was held parallel to the ground. Label the distances given in the problem. Choose an x-y coordinate system, making sure to label the origin. It is conventional to have x in the horizontal direction and y in the vertical direction. What is the y coordinate when the bullet leaves the gun? What is the y coordinate when it hits the target? What is the initial velocity in the y direction? What is the acceleration in the y direction? What is the equation that describes the motion in the vertical y direction as a function of time? Can you use the equation for to determine the time of flight? Why was it not necessary to include the motion in the x direction? s s = 180 cm m cm y(t) y(t) ANSWER: Correct Part B What was the bullet’s speed as it left the barrel? Express your answer with the appropriate units. Hint 1. How to approach the problem In the coordinate system introduced in Part A, what are the x coordinates when the bullet leaves the gun and when it hits the target? Is there any acceleration in the x direction? What is the equation that describes the motion in the horizontal x direction as a function of time? Can you use the equation for to determine the initial velocity? ANSWER: Correct Introduction to Projectile Motion Learning Goal: To understand the basic concepts of projectile motion. Projectile motion may seem rather complex at first. However, by breaking it down into components, you will find that it is really no different than the one-dimensional motions that you have already studied. One of the most often used techniques in physics is to divide two- and three-dimensional quantities into components. For instance, in projectile motion, a particle has some initial velocity . In general, this velocity can point in any direction on the xy plane and can have any magnitude. To make a problem more managable, it is common to break up such a quantity into its x component and its y component . 5.53×10−2 s x(t) x(t) 922 ms v vx vy Consider a particle with initial velocity that has magnitude 12.0 and is directed 60.0 above the negative x axis. Part A What is the x component of ? Express your answer in meters per second. ANSWER: Correct Part B What is the y component of ? Express your answer in meters per second. ANSWER: Correct Breaking up the velocities into components is particularly useful when the components do not affect each other. Eventually, you will learn about situations in which the components of velocity do affect one another, but for now you will only be looking at problems where they do not. So, if there is acceleration in the x direction but not in the y direction, then the x component of the velocity will change, but the y component of the velocity will not. Part C Look at this applet. The motion diagram for a projectile is displayed, as are the motion diagrams for each component. The x-component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you shined a spotlight to the left and recorded the particle’s shadow, you would get the motion diagram for its y component. How would you describe the two motion diagrams for the components? ANSWER: v m/s degrees vx v vx = -6.00 m/s vy v vy = 10.4 m/s Correct As you can see, the two components of the motion obey their own independent kinematic laws. For the vertical component, there is an acceleration downward with magnitude . Thus, you can calculate the vertical position of the particle at any time using the standard kinematic equation . Similarly, there is no acceleration in the horizontal direction, so the horizontal position of the particle is given by the standard kinematic equation . Now, consider this applet. Two balls are simultaneously dropped from a height of 5.0 . Part D How long does it take for the balls to reach the ground? Use 10 for the magnitude of the acceleration due to gravity. Express your answer in seconds to two significant figures. Hint 1. How to approach the problem The balls are released from rest at a height of 5.0 at time . Using these numbers and basic kinematics, you can determine the amount of time it takes for the balls to reach the ground. ANSWER: Correct This situation, which you have dealt with before (motion under the constant acceleration of gravity), is actually a special case of projectile motion. Think of this as projectile motion where the horizontal component of the initial velocity is zero. Both the vertical and horizontal components exhibit motion with constant nonzero acceleration. The vertical component exhibits motion with constant nonzero acceleration, whereas the horizontal component exhibits constant-velocity motion. The vertical component exhibits constant-velocity motion, whereas the horizontal component exhibits motion with constant nonzero acceleration. Both the vertical and horizontal components exhibit motion with constant velocity. g = 10 m/s2 y = y0 + v0 t + (1/2)at2 x = x0 + v0 t m tg m/s2 m t = 0 s tg = 1.0 s Part E Imagine the ball on the left is given a nonzero initial speed in the horizontal direction, while the ball on the right continues to fall with zero initial velocity. What horizontal speed must the ball on the left start with so that it hits the ground at the same position as the ball on the right? Remember that the two balls are released, starting a horizontal distance of 3.0 apart. Express your answer in meters per second to two significant figures. Hint 1. How to approach the problem Recall from Part B that the horizontal component of velocity does not change during projectile motion. Therefore, you need to find the horizontal component of velocity such that, in a time , the ball will move horizontally 3.0 . You can assume that its initial x coordinate is . ANSWER: Correct You can adjust the horizontal speeds in this applet. Notice that regardless of what horizontal speeds you give to the balls, they continue to move vertically in the same way (i.e., they are at the same y coordinate at the same time). Problem 4.12 A ball thrown horizontally at 27 travels a horizontal distance of 49 before hitting the ground. Part A From what height was the ball thrown? Express your answer using two significant figures with the appropriate units. ANSWER: vx m vx tg = 1.0 s m x0 = 0.0 m vx = 3.0 m/s m/s m h = 16 m Correct Enhanced EOC: Problem 4.20 The figure shows the angular-velocity-versus-time graph for a particle moving in a circle. You may want to review ( page ) . For help with math skills, you may want to review: The Definite Integral Part A How many revolutions does the object make during the first 3.5 ? Express your answer using two significant figures. You did not open hints for this part. ANSWER: s n = Incorrect; Try Again Problem 4.26 To withstand “g-forces” of up to 10 g’s, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a “human centrifuge.” 10 g’s is an acceleration of . Part A If the length of the centrifuge arm is 10.0 , at what speed is the rider moving when she experiences 10 g’s? Express your answer with the appropriate units. ANSWER: Correct Problem 4.28 Your roommate is working on his bicycle and has the bike upside down. He spins the 60.0 -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. Part A What is the pebble’s speed? Express your answer with the appropriate units. ANSWER: Correct 98 m/s2 m 31.3 ms cm 5.65 ms Part B What is the pebble’s acceleration? Express your answer with the appropriate units. ANSWER: Correct Enhanced EOC: Problem 4.43 On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The acceleration due to gravity on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 13 at an angle 50 above the horizontal. You may want to review ( pages 90 – 95) . For help with math skills, you may want to review: Quadratic Equations Part A How much farther did the ball travel on the moon than it would have on earth? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the path of the golf ball, showing its starting and ending points. Choose a coordinate system, and label the origin. It is conventional to let x be the horizontal direction and y the vertical direction. What is the initial velocity in the x and y directions? What is the acceleration in the x and y directions on the moon and on the earth? What are the equations for and as a function of time, and , respectively? What is the y coordinate when the golf ball hits the ground? Can you use this information to determine the time of flight on the moon and on the earth? 107 m s2 m/s  x y x(t) y(t) Once you have the time of flight, how can you use the equation to determine the total distance traveled? Compare the distance traveled on the moon to the distance traveled on the earth . ANSWER: Correct Part B For how much more time was the ball in flight? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the equation describing as a function of time? What is the initial x component of the ball’s velocity? How are the initial x component of the ball’s velocity and the distance traveled related to the time of flight? What is the difference between the time of flight on the moon and on earth? ANSWER: Correct Problem 4.42 In the Olympic shotput event, an athlete throws the shot with an initial speed of 12 at a 40.0 angle from the horizontal. The shot leaves her hand at a height of 1.8 above the ground. x(t) L = 85 m x(t) x t = 10 s m/s  m Part A How far does the shot travel? Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part B Repeat the calculation of part (a) for angles of 42.5 , 45.0 , and 47.5 . Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part C Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part D x = 16.36 m    x(42.5 ) = 16.39 m x(45.0 ) = 16.31 m Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part E At what angle of release does she throw the farthest? ANSWER: Correct Problem 4.44 A ball is thrown toward a cliff of height with a speed of 32 and an angle of 60 above horizontal. It lands on the edge of the cliff 3.2 later. Part A How high is the cliff? Express your answer to two significant figures and include the appropriate units. ANSWER: x(47.5 ) = 16.13 m 40.0 42.5 45.0 47.5 h m/s  s h = 39 m Answer Requested Part B What was the maximum height of the ball? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the ball’s impact speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 4.58 A typical laboratory centrifuge rotates at 3600 . Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. Part A What is the acceleration at the end of a test tube that is 10 from the axis of rotation? Express your answer with the appropriate units. hmax = 39 m v = 16 ms rpm cm ANSWER: Correct Part B For comparison, what is the magnitude of the acceleration a test tube would experience if dropped from a height of 1.0 and stopped in a 1.7-ms-long encounter with a hard floor? Express your answer with the appropriate units. ANSWER: Correct Problem 4.62 Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is , and the altitude of a geosynchronous orbit is ( 22000 miles). Part A What is the speed of a satellite in a geosynchronous orbit? Express your answer with the appropriate units. ANSWER: Correct a = 1.42×104 m s2 m a = 2610 m s2 6.37 × 106m 3.58 × 107m  v = 3070 ms Part B What is the magnitude of the acceleration of a satellite in a geosynchronous orbit? Express your answer with the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 89.5%. You received 103.82 out of a possible total of 116 points. a = 0.223 m s2

Assignment 3 Due: 11:59pm on Friday, February 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 2.68 As a science project, you drop a watermelon off the top of the Empire State Building, 320 m above the sidewalk. It so happens that Superman flies by at the instant you release the watermelon. Superman is headed straight down with a speed of 36.0 . Part A How fast is the watermelon going when it passes Superman? Express your answer with the appropriate units. ANSWER: Correct Problem 2.63 A motorist is driving at when she sees that a traffic light ahead has just turned red. She knows that this light stays red for , and she wants to reach the light just as it turns green again. It takes her to step on the brakes and begin slowing. Part A What is her speed as she reaches the light at the instant it turns green? Express your answer with the appropriate units. ANSWER: m/s 72.0 ms 20 m/s 200 m 15 s 1.0 s 5.71 ms Correct Conceptual Question 4.1 Part A At this instant, is the particle in the figurespeeding up, slowing down, or traveling at constant speed? ANSWER: Correct Part B Is this particle curving to the right, curving to the left, or traveling straight? Speeding up Slowing down Traveling at constant speed ANSWER: Correct Conceptual Question 4.2 Part A At this instant, is the particle in the following figure speeding up, slowing down, or traveling at constant speed? ANSWER: Curving to the right Curving to the left Traveling straight Correct Part B Is this particle curving upward, curving downward, or traveling straight? ANSWER: Correct Problem 4.8 A particle’s trajectory is described by and , where is in s. Part A What is the particle’s speed at ? ANSWER: The particle is speeding up. The particle is slowing down. The particle is traveling at constant speed. The particle is curving upward. The particle is curving downward. The particle is traveling straight. x = ( 1 −2 ) m 2 t3 t2 y = ( 1 −2t) m 2 t2 t t = 0 s v = 2 m/s Correct Part B What is the particle’s speed at ? Express your answer using two significant figures. ANSWER: Correct Part C What is the particle’s direction of motion, measured as an angle from the x-axis, at ? Express your answer using two significant figures. ANSWER: Correct Part D What is the particle’s direction of motion, measured as an angle from the x-axis, at ? Express your answer using two significant figures. ANSWER: t = 5.0s v = 18 m/s t = 0 s  = -90  counterclockwise from the +x axis. t = 5.0s  = 9.7  counterclockwise from the +x axis. Correct Problem 4.9 A rocket-powered hockey puck moves on a horizontal frictionless table. The figure shows the graph of and the figure shows the graph of , the x- and y-components of the puck’s velocity, respectively. The puck starts at the origin. Part A In which direction is the puck moving at = 3 ? Give your answer as an angle from the x-axis. Express your answer using two significant figures. ANSWER: Correct Part B vx vy t s = 51   above the x-axis How far from the origin is the puck at 5 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 4.13 A rifle is aimed horizontally at a target 51.0 away. The bullet hits the target 1.50 below the aim point. You may want to review ( pages 91 – 95) . For help with math skills, you may want to review: Quadratic Equations Part A What was the bullet’s flight time? Express your answer with the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the bullet’s trajectory, including where it leaves the gun and where it hits the target. You can assume that the gun was held parallel to the ground. Label the distances given in the problem. Choose an x-y coordinate system, making sure to label the origin. It is conventional to have x in the horizontal direction and y in the vertical direction. What is the y coordinate when the bullet leaves the gun? What is the y coordinate when it hits the target? What is the initial velocity in the y direction? What is the acceleration in the y direction? What is the equation that describes the motion in the vertical y direction as a function of time? Can you use the equation for to determine the time of flight? Why was it not necessary to include the motion in the x direction? s s = 180 cm m cm y(t) y(t) ANSWER: Correct Part B What was the bullet’s speed as it left the barrel? Express your answer with the appropriate units. Hint 1. How to approach the problem In the coordinate system introduced in Part A, what are the x coordinates when the bullet leaves the gun and when it hits the target? Is there any acceleration in the x direction? What is the equation that describes the motion in the horizontal x direction as a function of time? Can you use the equation for to determine the initial velocity? ANSWER: Correct Introduction to Projectile Motion Learning Goal: To understand the basic concepts of projectile motion. Projectile motion may seem rather complex at first. However, by breaking it down into components, you will find that it is really no different than the one-dimensional motions that you have already studied. One of the most often used techniques in physics is to divide two- and three-dimensional quantities into components. For instance, in projectile motion, a particle has some initial velocity . In general, this velocity can point in any direction on the xy plane and can have any magnitude. To make a problem more managable, it is common to break up such a quantity into its x component and its y component . 5.53×10−2 s x(t) x(t) 922 ms v vx vy Consider a particle with initial velocity that has magnitude 12.0 and is directed 60.0 above the negative x axis. Part A What is the x component of ? Express your answer in meters per second. ANSWER: Correct Part B What is the y component of ? Express your answer in meters per second. ANSWER: Correct Breaking up the velocities into components is particularly useful when the components do not affect each other. Eventually, you will learn about situations in which the components of velocity do affect one another, but for now you will only be looking at problems where they do not. So, if there is acceleration in the x direction but not in the y direction, then the x component of the velocity will change, but the y component of the velocity will not. Part C Look at this applet. The motion diagram for a projectile is displayed, as are the motion diagrams for each component. The x-component motion diagram is what you would get if you shined a spotlight down on the particle as it moved and recorded the motion of its shadow. Similarly, if you shined a spotlight to the left and recorded the particle’s shadow, you would get the motion diagram for its y component. How would you describe the two motion diagrams for the components? ANSWER: v m/s degrees vx v vx = -6.00 m/s vy v vy = 10.4 m/s Correct As you can see, the two components of the motion obey their own independent kinematic laws. For the vertical component, there is an acceleration downward with magnitude . Thus, you can calculate the vertical position of the particle at any time using the standard kinematic equation . Similarly, there is no acceleration in the horizontal direction, so the horizontal position of the particle is given by the standard kinematic equation . Now, consider this applet. Two balls are simultaneously dropped from a height of 5.0 . Part D How long does it take for the balls to reach the ground? Use 10 for the magnitude of the acceleration due to gravity. Express your answer in seconds to two significant figures. Hint 1. How to approach the problem The balls are released from rest at a height of 5.0 at time . Using these numbers and basic kinematics, you can determine the amount of time it takes for the balls to reach the ground. ANSWER: Correct This situation, which you have dealt with before (motion under the constant acceleration of gravity), is actually a special case of projectile motion. Think of this as projectile motion where the horizontal component of the initial velocity is zero. Both the vertical and horizontal components exhibit motion with constant nonzero acceleration. The vertical component exhibits motion with constant nonzero acceleration, whereas the horizontal component exhibits constant-velocity motion. The vertical component exhibits constant-velocity motion, whereas the horizontal component exhibits motion with constant nonzero acceleration. Both the vertical and horizontal components exhibit motion with constant velocity. g = 10 m/s2 y = y0 + v0 t + (1/2)at2 x = x0 + v0 t m tg m/s2 m t = 0 s tg = 1.0 s Part E Imagine the ball on the left is given a nonzero initial speed in the horizontal direction, while the ball on the right continues to fall with zero initial velocity. What horizontal speed must the ball on the left start with so that it hits the ground at the same position as the ball on the right? Remember that the two balls are released, starting a horizontal distance of 3.0 apart. Express your answer in meters per second to two significant figures. Hint 1. How to approach the problem Recall from Part B that the horizontal component of velocity does not change during projectile motion. Therefore, you need to find the horizontal component of velocity such that, in a time , the ball will move horizontally 3.0 . You can assume that its initial x coordinate is . ANSWER: Correct You can adjust the horizontal speeds in this applet. Notice that regardless of what horizontal speeds you give to the balls, they continue to move vertically in the same way (i.e., they are at the same y coordinate at the same time). Problem 4.12 A ball thrown horizontally at 27 travels a horizontal distance of 49 before hitting the ground. Part A From what height was the ball thrown? Express your answer using two significant figures with the appropriate units. ANSWER: vx m vx tg = 1.0 s m x0 = 0.0 m vx = 3.0 m/s m/s m h = 16 m Correct Enhanced EOC: Problem 4.20 The figure shows the angular-velocity-versus-time graph for a particle moving in a circle. You may want to review ( page ) . For help with math skills, you may want to review: The Definite Integral Part A How many revolutions does the object make during the first 3.5 ? Express your answer using two significant figures. You did not open hints for this part. ANSWER: s n = Incorrect; Try Again Problem 4.26 To withstand “g-forces” of up to 10 g’s, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a “human centrifuge.” 10 g’s is an acceleration of . Part A If the length of the centrifuge arm is 10.0 , at what speed is the rider moving when she experiences 10 g’s? Express your answer with the appropriate units. ANSWER: Correct Problem 4.28 Your roommate is working on his bicycle and has the bike upside down. He spins the 60.0 -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. Part A What is the pebble’s speed? Express your answer with the appropriate units. ANSWER: Correct 98 m/s2 m 31.3 ms cm 5.65 ms Part B What is the pebble’s acceleration? Express your answer with the appropriate units. ANSWER: Correct Enhanced EOC: Problem 4.43 On the Apollo 14 mission to the moon, astronaut Alan Shepard hit a golf ball with a 6 iron. The acceleration due to gravity on the moon is 1/6 of its value on earth. Suppose he hits the ball with a speed of 13 at an angle 50 above the horizontal. You may want to review ( pages 90 – 95) . For help with math skills, you may want to review: Quadratic Equations Part A How much farther did the ball travel on the moon than it would have on earth? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the path of the golf ball, showing its starting and ending points. Choose a coordinate system, and label the origin. It is conventional to let x be the horizontal direction and y the vertical direction. What is the initial velocity in the x and y directions? What is the acceleration in the x and y directions on the moon and on the earth? What are the equations for and as a function of time, and , respectively? What is the y coordinate when the golf ball hits the ground? Can you use this information to determine the time of flight on the moon and on the earth? 107 m s2 m/s  x y x(t) y(t) Once you have the time of flight, how can you use the equation to determine the total distance traveled? Compare the distance traveled on the moon to the distance traveled on the earth . ANSWER: Correct Part B For how much more time was the ball in flight? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the equation describing as a function of time? What is the initial x component of the ball’s velocity? How are the initial x component of the ball’s velocity and the distance traveled related to the time of flight? What is the difference between the time of flight on the moon and on earth? ANSWER: Correct Problem 4.42 In the Olympic shotput event, an athlete throws the shot with an initial speed of 12 at a 40.0 angle from the horizontal. The shot leaves her hand at a height of 1.8 above the ground. x(t) L = 85 m x(t) x t = 10 s m/s  m Part A How far does the shot travel? Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part B Repeat the calculation of part (a) for angles of 42.5 , 45.0 , and 47.5 . Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part C Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part D x = 16.36 m    x(42.5 ) = 16.39 m x(45.0 ) = 16.31 m Express your answer to four significant figures and include the appropriate units. ANSWER: Correct Part E At what angle of release does she throw the farthest? ANSWER: Correct Problem 4.44 A ball is thrown toward a cliff of height with a speed of 32 and an angle of 60 above horizontal. It lands on the edge of the cliff 3.2 later. Part A How high is the cliff? Express your answer to two significant figures and include the appropriate units. ANSWER: x(47.5 ) = 16.13 m 40.0 42.5 45.0 47.5 h m/s  s h = 39 m Answer Requested Part B What was the maximum height of the ball? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the ball’s impact speed? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 4.58 A typical laboratory centrifuge rotates at 3600 . Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. Part A What is the acceleration at the end of a test tube that is 10 from the axis of rotation? Express your answer with the appropriate units. hmax = 39 m v = 16 ms rpm cm ANSWER: Correct Part B For comparison, what is the magnitude of the acceleration a test tube would experience if dropped from a height of 1.0 and stopped in a 1.7-ms-long encounter with a hard floor? Express your answer with the appropriate units. ANSWER: Correct Problem 4.62 Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. These are called geosynchronous orbits. The radius of the earth is , and the altitude of a geosynchronous orbit is ( 22000 miles). Part A What is the speed of a satellite in a geosynchronous orbit? Express your answer with the appropriate units. ANSWER: Correct a = 1.42×104 m s2 m a = 2610 m s2 6.37 × 106m 3.58 × 107m  v = 3070 ms Part B What is the magnitude of the acceleration of a satellite in a geosynchronous orbit? Express your answer with the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 89.5%. You received 103.82 out of a possible total of 116 points. a = 0.223 m s2

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Chapter 1 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Curved Motion Diagram The motion diagram shown in the figure represents a pendulum released from rest at an angle of 45 from the vertical. The dots in the motion diagram represent the positions of the pendulum bob at eleven moments separated by equal time intervals. The green arrows represent the average velocity between adjacent dots. Also given is a “compass rose” in which directions are labeled with the letters of the alphabet. 

Chapter 1 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Curved Motion Diagram The motion diagram shown in the figure represents a pendulum released from rest at an angle of 45 from the vertical. The dots in the motion diagram represent the positions of the pendulum bob at eleven moments separated by equal time intervals. The green arrows represent the average velocity between adjacent dots. Also given is a “compass rose” in which directions are labeled with the letters of the alphabet. 

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Physics 220 – HW #1 (Homework) halsalem::app-6@purdue Summer-2013-PHYS-22000-01-XLST, Summer 1 2013 Instructor: Shawn Slavin Current Score : 2 / 20 Due : Wednesday, May 22 2013 11:59 PM EDT 1. –/2 points SerCP9 1.P.006. Kinetic energy KE has dimensions kg · m 2 /s 2 . It can be written in terms of the momentum p and mass m as (a) Determine the proper units for momentum using dimensional analysis. (b) Force has the SI units kg · m/s2. Given the units of force, write a simple equation relating a constant force F exerted on an object, an interval of time t during which the force is applied, and the resulting momentum of the object, p. (Do this on paper. Your instructor may ask you to turn in this work.) Show My Work (Optional) 2. 2/2 points | Previous Answers SerCP9 1.P.502.XP. You can obtain a rough estimate of the size of a molecule by the following simple experiment. Let a droplet of oil spread out on a smooth surface of water. The resulting oil slick will be approximately one molecule thick. Given an oil droplet of mass 8.0 10 -7 kg and density 914 kg/m 3 that spreads out into a circle of radius 41.8 cm on the water surface, what is the order of magnitude of the diameter of an oil molecule? Show My Work (Optional) 3. –/2 points SerCP9 1.P.016. A small turtle moves at a speed of 163 furlongs per fortnight. Find the speed of the turtle in centimeters per second. Note that 1 furlong = 220 yards and 1 fortnight = 14 days. cm/s Show My Work (Optional) 4. –/2 points SerCP9 1.P.035.MI.FB. A point is located in a polar coordinate system by the coordinates r = 4.6 m and θ = 24°. Find the x- and y-coordinates of this point, assuming that the two coordinate systems have the same origin. x = m y = m Show My Work (Optional) WebAssign KE = P . 2 2m kg · m/s2 kg · m/s kg · m2/s kg2 · m/s 10−5 10−7 10−9 10−11 10−14 Physics 220 – HW #1 http://www.webassign.net/web/Student/Assignment-Responses/last?d… 1 of 3 19-05-2013 13:35 5. –/2 points SerCP9 1.P.045. In the figure below, find each of the following. (a) the side opposite θ (b) the side adjacent to (c) cos θ (d) sin (e) tan Show My Work (Optional) 6. –/2 points SerCP9 2.P.028.WI. In 1865, Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.) m/s2 Compare your answer with the free-fall acceleration, 9.80 m/s 2 (i.e. how many times stronger than gravity is this force?). g Show My Work (Optional) 7. –/2 points SerCP9 2.P.045. A ball is thrown vertically upward with a speed of 10.0 m/s. (a) How high does it rise? m (b) How long does it take to reach its highest point? s (c) How long does the ball take to hit the ground after it reaches its highest point? s (d) What is its velocity when it returns to the level from which it started? m/s Show My Work (Optional) Physics 220 – HW #1 http://www.webassign.net/web/Student/Assignment-Responses/last?d… 2 of 3 19-05-2013 13:35 8. –/2 points SerCP9 3.P.001. Vector has a magnitude of 28 units and points in the positive y-direction. When vector is added to the resultant vector points in the negative y-direction with a magnitude of 13 units. Find the magnitude and direction of magnitude unit(s) direction Show My Work (Optional) 9. –/2 points SerCP9 3.P.010. A person walks 24.0° north of east for 2.30 km. How far due north and how far due east would she have to walk to arrive at the same location? north km east km Show My Work (Optional) 10.–/2 points SerCP9 3.P.025.WI. The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45°. With what speed must the animal leave the ground to reach that height? m/s Show My Work (Optional) A B A, A + B B? Physics 220 – HW #1 http://www.webassign.net/web/Student/Assignment-Responses/last?d… 3 of 3 19-05-2013 13:35

Physics 220 – HW #1 (Homework) halsalem::app-6@purdue Summer-2013-PHYS-22000-01-XLST, Summer 1 2013 Instructor: Shawn Slavin Current Score : 2 / 20 Due : Wednesday, May 22 2013 11:59 PM EDT 1. –/2 points SerCP9 1.P.006. Kinetic energy KE has dimensions kg · m 2 /s 2 . It can be written in terms of the momentum p and mass m as (a) Determine the proper units for momentum using dimensional analysis. (b) Force has the SI units kg · m/s2. Given the units of force, write a simple equation relating a constant force F exerted on an object, an interval of time t during which the force is applied, and the resulting momentum of the object, p. (Do this on paper. Your instructor may ask you to turn in this work.) Show My Work (Optional) 2. 2/2 points | Previous Answers SerCP9 1.P.502.XP. You can obtain a rough estimate of the size of a molecule by the following simple experiment. Let a droplet of oil spread out on a smooth surface of water. The resulting oil slick will be approximately one molecule thick. Given an oil droplet of mass 8.0 10 -7 kg and density 914 kg/m 3 that spreads out into a circle of radius 41.8 cm on the water surface, what is the order of magnitude of the diameter of an oil molecule? Show My Work (Optional) 3. –/2 points SerCP9 1.P.016. A small turtle moves at a speed of 163 furlongs per fortnight. Find the speed of the turtle in centimeters per second. Note that 1 furlong = 220 yards and 1 fortnight = 14 days. cm/s Show My Work (Optional) 4. –/2 points SerCP9 1.P.035.MI.FB. A point is located in a polar coordinate system by the coordinates r = 4.6 m and θ = 24°. Find the x- and y-coordinates of this point, assuming that the two coordinate systems have the same origin. x = m y = m Show My Work (Optional) WebAssign KE = P . 2 2m kg · m/s2 kg · m/s kg · m2/s kg2 · m/s 10−5 10−7 10−9 10−11 10−14 Physics 220 – HW #1 http://www.webassign.net/web/Student/Assignment-Responses/last?d… 1 of 3 19-05-2013 13:35 5. –/2 points SerCP9 1.P.045. In the figure below, find each of the following. (a) the side opposite θ (b) the side adjacent to (c) cos θ (d) sin (e) tan Show My Work (Optional) 6. –/2 points SerCP9 2.P.028.WI. In 1865, Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.) m/s2 Compare your answer with the free-fall acceleration, 9.80 m/s 2 (i.e. how many times stronger than gravity is this force?). g Show My Work (Optional) 7. –/2 points SerCP9 2.P.045. A ball is thrown vertically upward with a speed of 10.0 m/s. (a) How high does it rise? m (b) How long does it take to reach its highest point? s (c) How long does the ball take to hit the ground after it reaches its highest point? s (d) What is its velocity when it returns to the level from which it started? m/s Show My Work (Optional) Physics 220 – HW #1 http://www.webassign.net/web/Student/Assignment-Responses/last?d… 2 of 3 19-05-2013 13:35 8. –/2 points SerCP9 3.P.001. Vector has a magnitude of 28 units and points in the positive y-direction. When vector is added to the resultant vector points in the negative y-direction with a magnitude of 13 units. Find the magnitude and direction of magnitude unit(s) direction Show My Work (Optional) 9. –/2 points SerCP9 3.P.010. A person walks 24.0° north of east for 2.30 km. How far due north and how far due east would she have to walk to arrive at the same location? north km east km Show My Work (Optional) 10.–/2 points SerCP9 3.P.025.WI. The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45°. With what speed must the animal leave the ground to reach that height? m/s Show My Work (Optional) A B A, A + B B? Physics 220 – HW #1 http://www.webassign.net/web/Student/Assignment-Responses/last?d… 3 of 3 19-05-2013 13:35

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Lab Report Name Simple Harmonic motion Date: Objective or purpose: The main objective of this lab is to find the value of the spring constant (k) according to Hooke’s law. This lab also teaches us curve fitting and its application here in this lab.

Lab Report Name Simple Harmonic motion Date: Objective or purpose: The main objective of this lab is to find the value of the spring constant (k) according to Hooke’s law. This lab also teaches us curve fitting and its application here in this lab.

Name Simple Harmonic motion Date:           … Read More...
QUESTION 1 1. Convert 30 degrees 2 minutes to decimal degrees. Give this answer to 6 decimal places. Do not provide units. You know those are decimal degrees. 5 points QUESTION 2 1. Convert 342 degrees 6 minutes and 41 seconds to decimal degrees. Show your answers to only 6 decimal places. Do not give units. 5 points QUESTION 3 1. COMPUTE the sin of 52 degrees. Give the answer to 6 decimal places. 5 points QUESTION 4 1. What is the sine of 277 degrees and 16 minutes? Give your answer to 6 decimal places. Pay attention to rounding. 5 points QUESTION 5 1. This is a right triangle problem. Angle A is 90 degrees. Draw the triangle and label it as we did in lecture. If angle B is 24 degrees 43 minutes and side c is 395.82 feet, what is the distance in feet of side b? Give your answer to two decimal places. Do not provide units. Those are in feet – right? 10 points QUESTION 6 1. This is a right triangle problem with angle A being the 90 degree angle. It should look like the one from lecture. If angle B is 25 degrees 18 minutes and side c is 206.1 feet, what is the distance to two decimal places of side a? Give your answer to two decimal places. Do not provide units – those are in feet. 10 points QUESTION 7 1. You are given a right triangle with angle A being the 90 degree angle – just like in lecture. If angle C is 42 degrees 9 minutes and side a is 401.73 feet, what is the length of side c? Give your answer to two decimal places. The units are feet – don’t list those. 10 points QUESTION 8 Ad by Browse Safe | Close 1. It is desired to determine the height of a flagpole. Assuming that the ground is level, an instrument is set up 227.59 feet from the flagpole with its telescope centered 5.31 feet above the ground. The telescope is sighted horizontally to a point 5.31 feet from the bottom of the flagpole and then the angle at the instrument looking to the top of the pole is measured. That angle is 26 degrees 51 minutes. How tall is the flagpole from its base? Give your answer to two decimal places with NO units. 10 points QUESTION 9 1. You are hiking in the mountains. For every 100.00 feet you would be walking horizontally, you have increased your elevation by 4 feet. At what grade are you climbing? Give your answer to three decimal places. Hint: Your units will be in ft/ft. 5 points QUESTION 10 1. A grade of -0.9 percent is being considered for a mountain roadway. The elevation at the initial point is 2,848.25 feet and a horizontal distance of 4,377.51 needs to be covered. What is the elevation at the end of the grade? 10 points QUESTION 11 1. A slope distance was measured between two points (A and T) and determined to be 4,788.68 feet. At point A the elevation is 857.23 feet and at point T the elevation is 877.96 feet. What is the horizontal distance between A and T?

QUESTION 1 1. Convert 30 degrees 2 minutes to decimal degrees. Give this answer to 6 decimal places. Do not provide units. You know those are decimal degrees. 5 points QUESTION 2 1. Convert 342 degrees 6 minutes and 41 seconds to decimal degrees. Show your answers to only 6 decimal places. Do not give units. 5 points QUESTION 3 1. COMPUTE the sin of 52 degrees. Give the answer to 6 decimal places. 5 points QUESTION 4 1. What is the sine of 277 degrees and 16 minutes? Give your answer to 6 decimal places. Pay attention to rounding. 5 points QUESTION 5 1. This is a right triangle problem. Angle A is 90 degrees. Draw the triangle and label it as we did in lecture. If angle B is 24 degrees 43 minutes and side c is 395.82 feet, what is the distance in feet of side b? Give your answer to two decimal places. Do not provide units. Those are in feet – right? 10 points QUESTION 6 1. This is a right triangle problem with angle A being the 90 degree angle. It should look like the one from lecture. If angle B is 25 degrees 18 minutes and side c is 206.1 feet, what is the distance to two decimal places of side a? Give your answer to two decimal places. Do not provide units – those are in feet. 10 points QUESTION 7 1. You are given a right triangle with angle A being the 90 degree angle – just like in lecture. If angle C is 42 degrees 9 minutes and side a is 401.73 feet, what is the length of side c? Give your answer to two decimal places. The units are feet – don’t list those. 10 points QUESTION 8 Ad by Browse Safe | Close 1. It is desired to determine the height of a flagpole. Assuming that the ground is level, an instrument is set up 227.59 feet from the flagpole with its telescope centered 5.31 feet above the ground. The telescope is sighted horizontally to a point 5.31 feet from the bottom of the flagpole and then the angle at the instrument looking to the top of the pole is measured. That angle is 26 degrees 51 minutes. How tall is the flagpole from its base? Give your answer to two decimal places with NO units. 10 points QUESTION 9 1. You are hiking in the mountains. For every 100.00 feet you would be walking horizontally, you have increased your elevation by 4 feet. At what grade are you climbing? Give your answer to three decimal places. Hint: Your units will be in ft/ft. 5 points QUESTION 10 1. A grade of -0.9 percent is being considered for a mountain roadway. The elevation at the initial point is 2,848.25 feet and a horizontal distance of 4,377.51 needs to be covered. What is the elevation at the end of the grade? 10 points QUESTION 11 1. A slope distance was measured between two points (A and T) and determined to be 4,788.68 feet. At point A the elevation is 857.23 feet and at point T the elevation is 877.96 feet. What is the horizontal distance between A and T?

Question no Assignment 2 1 30.0333333 degrees 2 342.111389 degrees … Read More...
Two force vectors F1 and F2 are applied at the origin of the system of coordinates, point O of coordinates (0,0,0). The two force are expressed in Newton units (N). The vector expressed of the first fore is F1=(-120i+60j+40k) N. The second force F2 has a magnitude of 85 N and its direction is defined by the line between point O and B (4, -3, 5), where these coordinates are in meters (m). (a) Find unit vector ef1alone F1. (b) Find unit vector ef2alone F2. (c) find the angle O between F1 and F2 using the dot product operation. (d) Find the force vector resultant R=F1+F2. (e) find the direction cosine, cosOxof vector R.

Two force vectors F1 and F2 are applied at the origin of the system of coordinates, point O of coordinates (0,0,0). The two force are expressed in Newton units (N). The vector expressed of the first fore is F1=(-120i+60j+40k) N. The second force F2 has a magnitude of 85 N and its direction is defined by the line between point O and B (4, -3, 5), where these coordinates are in meters (m). (a) Find unit vector ef1alone F1. (b) Find unit vector ef2alone F2. (c) find the angle O between F1 and F2 using the dot product operation. (d) Find the force vector resultant R=F1+F2. (e) find the direction cosine, cosOxof vector R.

MCE 260 Fall 2015 Homework 9, due November 12, 2015. PRESENT CLEARLY HOW YOU DEVELOPED THE SOLUTION TO THE PROBLEMS Each problem is worth up to 5 points. Points are given as follows: 5 points: Work was complete and presented clearly, the answer is correct 4 points: Work was complete, but not clearly presented or some errors in calculation 3 points: Some errors or omissions in methods or presentation 2 points: Major errors or omissions in methods or presentation 1 point: Problem was understood but incorrect approach was used 1. The radial compressor shown above (with dimensions) has a crank that rotates at 120 RPM. What is the maximal acceleration of each piston? 2. Design a follower displacement profile for a double-dwell (RDFD) cam, with these performance specifications: Machine cycle is 5 seconds. Rise from 0 to 22 mm in 45 degrees. Dwell for 45 degrees. Fall from 22 mm back to zero in 90 degrees. Dwell for the remainder of the machine cycle. You may use any profile that satisfies the fundamental law of cam design. Write equations for follower displacement (s) as a function of cam angle (θ) for each of the four segments of the cam. 3. (10% extra credit) What is the maximal acceleration of the follower? At which point in the cycle does it occur? Page 1 of 1

MCE 260 Fall 2015 Homework 9, due November 12, 2015. PRESENT CLEARLY HOW YOU DEVELOPED THE SOLUTION TO THE PROBLEMS Each problem is worth up to 5 points. Points are given as follows: 5 points: Work was complete and presented clearly, the answer is correct 4 points: Work was complete, but not clearly presented or some errors in calculation 3 points: Some errors or omissions in methods or presentation 2 points: Major errors or omissions in methods or presentation 1 point: Problem was understood but incorrect approach was used 1. The radial compressor shown above (with dimensions) has a crank that rotates at 120 RPM. What is the maximal acceleration of each piston? 2. Design a follower displacement profile for a double-dwell (RDFD) cam, with these performance specifications: Machine cycle is 5 seconds. Rise from 0 to 22 mm in 45 degrees. Dwell for 45 degrees. Fall from 22 mm back to zero in 90 degrees. Dwell for the remainder of the machine cycle. You may use any profile that satisfies the fundamental law of cam design. Write equations for follower displacement (s) as a function of cam angle (θ) for each of the four segments of the cam. 3. (10% extra credit) What is the maximal acceleration of the follower? At which point in the cycle does it occur? Page 1 of 1

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