## a stone is dropped from the top of a cliff. it is seen to hit the ground 3.5 seconds later. how high is the cliff?

## Economics topic Assignment 2 Value: 40% Due date: 01-Sep-2014 Return date: 22-Sep-2014 Length: about 1500-2000 words each Submission method options Alternative submission method Task Analytical essays…Corporations law Individual Research Assignment 1 1. There are two questions in this assignment. Answer both questions. 2. You must include at least one page of references. QUESTION 1 (10 Marks) …STATS1900 Business Statistics Minor Assignment â€“ 2nd Semester, 2014 Due: week 4 Total Marks: 30, Worth: 10% of final assessment This assignment requires a considerable amount of computer work and…CASE BSB, INC.: THE PIZZA WARS COME TO CAMPUS Renee Kershaw, manager of food services at a medium-sized private university in the Southeast, has just had the wind taken out of her sails. 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Their shop lot occup…Critically analyses the following case and say whether or not you think that the plaintiff will succeed under the tort of negligence: John was the batsman in a cricket match. He hit the ball so hard …Critically analyses the following case and say whether or not you think that the plaintiff will succeed under the tort of negligence: John was the batsman in a cricket match. He hit the ball so hard …CRICOS Provider No. 00103D Page 1 of 4 Ethics Assignment Term 2, 2014 Topic Freedom of Speech Due Date Week 6 â€“ Friday, 29 August 2014, 5:00 pm Worth 20% (40 marks â€“ ITECH 3203) 20% (50 marks â€“ …HI5018 BUSINESS LAW TRIMESTER 2, 2014 Assignment 1 â€“ Case Studies Assessment Value: 20% Word Length 1500- 2000 words Date Due: Week 5 Friday by 5pm submitted via Level 6 Question 1. 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(15%) Your journal should cover following aspects: D…HI5018 BUSINESS LAW TRIMESTER 2, 2014 Assignment 1 â€“ Case Studies Assessment Value: 20% Word Length 1500- 2000 words Date Due: Week 5 Friday by 5pm submitted via Level 6 Question 1. (10marks) Using…Please check the attached assignmentPRBE001 â€“ ECONOMICS FOR MANAGERS ASSIGNMENT 1 2014 TITLE: â€œMACROECONOMIC POLICIES AND THEIR IMPACTSâ€ OBJECTIVE: To critically evaluate the effects of a macroeconomic policy decision upon busines… HI5004 Marketing Management Tri1 2014 Individual Essay Guidelines Worth 20% Due Week 5 Marks 20 Words 1500 â€¢ Choice of Topic from the subject outline more marks if they choose a s…4.1 Individual Assignment Word length: 1000 words Format: Research Plan 1. Select an overall topic area that you wish to explore. Give a description of the topic and the particular area in which you …

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## Phys4A: Practice problems for the 1st midterm test Fall 2015 1 If K has dimensions ML2/T 2, the k in K = kmv 2 must be: Answer: dimensionless 2. A 8.7 hour trip is made at an average speed of 73.0 km/h. If the first third of the trip (chronologically) was driven at 96.5 km/h, what was the average speed for the rest of the journey? Answer: 61 km/h 3. A car travels 95 km to the north at 70.0 km/h, then turns around and travels 21.9 km at 80.0 km/h. What is the difference between the average speed and the average velocity on this trip? Answer: 27 km/h 4. A particle confined to motion along the x axis moves with constant acceleration from x = 2.0 m to x = 8.0 m during a 2.5s time interval. The velocity of the particle at x = 8.0 m is 2.8 m/s. What is the acceleration during this time interval? Answer: 0.32 m/s2 5. A package is dropped from a helicopter moving upward at 15 m/s. If it takes 16.0 s before the package strikes the ground, how high above the ground was the package when it was released? (Disregard air resistance.) Answer: 1000m 6. If vector B is added to vector A, the result is 6i + j. If B is subtracted from A, the result is –4i + 7j. What is the magnitude of A? Answer: 4.1 7. Starting from one oasis, a camel walks 25 km in a direction 30° south of west and then walks 30 km toward the north to a second oasis. What is the direction from the first oasis to the second oasis? Answer: 51° W of N 8 A river 1.00 mile wide flows with a constant speed of 1.00 mi/h. A man can row a boat at 2.00 mi/h. He crosses the river in a direction that puts him directly across the river from the starting point, and then he returns in a direction that puts him back at the starting point in the shortest time possible. The travel time for the man is, Answer: 1.15 h 9 An airplane is heading due east. The airspeed indicator shows that the plane is moving at a speed of 370 km/h relative to the air. If the wind is blowing from the south at 92.5 km/h, the velocity of the airplane relative to the ground is: Answer: 381 km/h at 76o east of north 10. A rock is projected from the edge of the top of a building with an initial velocity of 12.2 m/s at an angle of 53° above the horizontal. The rock strikes the ground a horizontal distance of 25 m from the base of the building. Assume that the ground is level and that the side of the building is vertical. How tall is the building? Answer: 23.6m 11. A boy throws a rock with an initial velocity of 3.13 m/s at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory? Answer: 0.160 s 12. A helicopter is traveling at 54 m/s at a constant altitude of 100 m over a level field. If a wheel falls off the helicopter, with what speed will it hit the ground? Note: air resistance negligible. Answer: 70 m/s 13 A rescue airplane is diving at an angle of 37º below the horizontal with a speed of 250 m/s. It releases a survival package when it is at an altitude of 600 m. If air resistance is ignored, the horizontal distance of the point of impact from the plane at the moment of the package’s release is, Answer: 720 m 14. A hobby rocket reaches a height of 72.3 m and lands 111 m from the launch point. What was the angle of launch? Answer: 69.0° 15. An object moving at a constant speed requires 6.0 s to go once around a circle with a diameter of 4.0 m. What is the magnitude of the instantaneous acceleration of the particle during this time? Answer: 2.2 m/s2 16 A ball is whirled in a horizontal circle of radius r and speed v. The radius is increased to 2r keeping the speed of the ball constant. The period of the ball changes by a factor of Answer: two

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## Aristotle’s breadth of knowledge and exploration is amazing. Some of his most interesting ideas center around the ideas of happiness and virtue. What do you think about Aristotle’s suggestions for the happy life and the cultivation of virtue. Choose a virtue (e.g., courage, moderation, patience, responsibility, etc.) and also determine the excess and deficiency. Explore the meaning of this virtue and practice it through the week. As you hit the “mean” do you find yourself more happy?

“Happiness depends on ourselves.” additional than anyone else, Aristotle preserve … Read More...

## 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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## Assignment 7 Due: 11:59pm on Friday, March 21, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 8.5 The figure shows two balls of equal mass moving in vertical circles. Part A Is the tension in string A greater than, less than, or equal to the tension in string B if the balls travel over the top of the circle with equal speed? ANSWER: Correct The tension in string A is less than the tension in string B. The tension in string A is equal to the tension in string B. The tension in string A is greater than the tension in string B. Part B Is the tension in string A greater than, less than, or equal to the tension in string B if the balls travel over the top of the circle with equal angular velocity? ANSWER: Correct A Mass on a Turntable: Conceptual A small metal cylinder rests on a circular turntable that is rotating at a constant rate, as illustrated in the diagram. Part A Which of the following sets of vectors best describes the velocity, acceleration, and net force acting on the cylinder at the point indicated in the diagram? The tension in string A is less than the tension in string B. The tension in string A is equal to the tension in string B. The tension in string A is greater than the tension in string B. Typesetting math: 100% Hint 1. The direction of acceleration can be determined from Newton’s second law According to Newton’s second law, the acceleration of an object has the same direction as the net force acting on that object. ANSWER: Correct Part B Let be the distance between the cylinder and the center of the turntable. Now assume that the cylinder is moved to a new location from the center of the turntable. Which of the following statements accurately describe the motion of the cylinder at the new location? Check all that apply. a b c d e R R/2 Typesetting math: 100% Hint 1. Find the speed of the cylinder Find the speed of the cylinder at the new location. Assume that the cylinder makes one complete turn in a period of time . Express your answer in terms of and . ANSWER: Hint 2. Find the acceleration of the cylinder Find the magnitude of the acceleration of the cylinder at the new location. Assume that the cylinder makes one complete turn in a period of time . Express your answer in terms of and . Hint 1. Centripetal acceleration Recall that the acceleration of an object that moves in a circular path of radius with constant speed has magnitude given by . Note that both the velocity and radius of the trajectory change when the cylinder is moved. ANSWER: ANSWER: v T R T v = R T a T R T r v a = v2 r a = 22R T 2 Typesetting math: 100% Correct Accelerating along a Racetrack A road race is taking place along the track shown in the figure . All of the cars are moving at constant speeds. The car at point F is traveling along a straight section of the track, whereas all the other cars are moving along curved segments of the track. Part A Let be the velocity of the car at point A. What can you say about the acceleration of the car at that point? Hint 1. Acceleration along a curved path The speed of the cylinder has decreased. The speed of the cylinder has increased. The magnitude of the acceleration of the cylinder has decreased. The magnitude of the acceleration of the cylinder has increased. The speed and the acceleration of the cylinder have not changed. v A Typesetting math: 100% Since acceleration is a vector quantity, an object moving at constant speed along a curved path has nonzero acceleration because the direction of its velocity is changing, even though the magnitude of its velocity (the speed) is constant. Moreover, if the speed is constant, the object’s acceleration is always perpendicular to the velocity vector at each point along the curved path and is directed toward the center of curvature of the path. ANSWER: Correct Part B Let be the velocity of the car at point C. What can you say about the acceleration of the car at that point? Hint 1. Acceleration along a curved path Since acceleration is a vector quantity, an object moving at constant speed along a curved path has nonzero acceleration because the direction of its velocity is changing, even though the magnitude of its velocity (the speed) is constant. Moreover, if the speed is constant, the object’s acceleration is always perpendicular to the velocity vector at each point along the curved path and is directed toward the center of curvature of the path. ANSWER: v v The acceleration is parallel to . The acceleration is perpendicular to and directed toward the inside of the track. The acceleration is perpendicular to and directed toward the outside of the track. The acceleration is neither parallel nor perpendicular to . The acceleration is zero. v A v A v A v A v C v v Typesetting math: 100% Correct Part C Let be the velocity of the car at point D. What can you say about the acceleration of the car at that point? Hint 1. Acceleration along a curved path Since acceleration is a vector quantity, an object moving at constant speed along a curved path has nonzero acceleration because the direction of its velocity is changing, even though the magnitude of its velocity (the speed) is constant. Moreover, if the speed is constant, the object’s acceleration is always perpendicular to the velocity vector at each point along the curved path and is directed toward the center of curvature of the path. ANSWER: Correct The acceleration is parallel to . The acceleration is perpendicular to and pointed toward the inside of the track. The acceleration is perpendicular to and pointed toward the outside of the track. The acceleration is neither parallel nor perpendicular to . The acceleration is zero. v C v C v C v C v D v v The acceleration is parallel to . The acceleration is perpendicular to and pointed toward the inside of the track. The acceleration is perpendicular to and pointed toward the outside of the track. The acceleration is neither parallel nor perpendicular to . The acceleration is zero. v D v D v D v D Typesetting math: 100% Part D Let be the velocity of the car at point F. What can you say about the acceleration of the car at that point? Hint 1. Acceleration along a straight path The velocity of an object that moves along a straight path is always parallel to the direction of the path, and the object has a nonzero acceleration only if the magnitude of its velocity changes in time. ANSWER: Correct Part E Assuming that all cars have equal speeds, which car has the acceleration of the greatest magnitude, and which one has the acceleration of the least magnitude? Use A for the car at point A, B for the car at point B, and so on. Express your answer as the name the car that has the greatest magnitude of acceleration followed by the car with the least magnitude of accelation, and separate your answers with a comma. Hint 1. How to approach the problem Recall that the magnitude of the acceleration of an object that moves at constant speed along a curved path is inversely proportional to the radius of curvature of the path. ANSWER: v F The acceleration is parallel to . The acceleration is perpendicular to and pointed toward the inside of the track. The acceleration is perpendicular to and pointed toward the outside of the track. The acceleration is neither parallel nor perpendicular to . The acceleration is zero. v F v F v F v F Typesetting math: 100% Correct Part F Assume that the car at point A and the one at point E are traveling along circular paths that have the same radius. If the car at point A now moves twice as fast as the car at point E, how is the magnitude of its acceleration related to that of car E. Hint 1. Find the acceleration of the car at point E Let be the radius of the two curves along which the cars at points A and E are traveling. What is the magnitude of the acceleration of the car at point E? Express your answer in terms of the radius of curvature and the speed of car E. Hint 1. Uniform circular motion The magnitude of the acceleration of an object that moves with constant speed along a circular path of radius is given by . ANSWER: Hint 2. Find the acceleration of the car at point A If , what is the acceleration of the car at point A? Let be the radius of the two curves along which the cars at points A and E are traveling. Express your answer in terms of the speed of the car at E and the radius . r aE r vE a v r a = v2 r aE = vE 2 r vA = 2vE aA r vE r Typesetting math: 100% Hint 1. Uniform circular motion The magnitude of the acceleration of an object that moves with constant speed along a circular path of radius is given by . ANSWER: ANSWER: Correct Problem 8.5 A 1300 car takes a 50- -radius unbanked curve at 13 . Part A What is the size of the friction force on the car? Express your answer to two significant figures and include the appropriate units. ANSWER: v r a = v2 r aA = 4vE 2 r The magnitude of the acceleration of the car at point A is twice that of the car at point E. The magnitude of the acceleration of the car at point A is the same as that of the car at point E. The magnitude of the acceleration of the car at point A is half that of the car at point E. The magnitude of the acceleration of the car at point A is four times that of the car at point E. kg m m/s Typesetting math: 100% Correct Problem 8.10 It is proposed that future space stations create an artificial gravity by rotating. Suppose a space station is constructed as a 1600- -diameter cylinder that rotates about its axis. The inside surface is the deck of the space station. Part A What rotation period will provide “normal” gravity? Express your answer with the appropriate units. ANSWER: Correct Problem 8.7 In the Bohr model of the hydrogen atom, an electron orbits a proton at a distance of . The proton pulls on the electron with an electric force of . Part A How many revolutions per second does the electron make? Express your answer with the appropriate units. ANSWER: fs = 4400 N m T = 56.8 s (mass m = 9.1 × 10−31 kg) 5.3 × 10−11 m 8.2 × 10−8 N Typesetting math: 100% Correct Problem 8.14 The weight of passengers on a roller coaster increases by 56 as the car goes through a dip with a 38 radius of curvature. Part A What is the car’s speed at the bottom of the dip? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 8.18 While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 14 , and you use your watch to find that each loop around takes 24 . Part A What is your speed? Express your answer to two significant figures and include the appropriate units. ANSWER: 6.56×1015 rev s % m v = 14 ms m s v = 3.7 ms Typesetting math: 100% Correct Part B What is the magnitude of your acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the ratio of your weight at the top of the ride to your weight while standing on the ground? Express your answer using two significant figures. ANSWER: Correct Part D What is the ratio of your weight at the bottom of the ride to your weight while standing on the ground? Express your answer using two significant figures. ANSWER: a = 0.96 m s2 = 0.90 wtop FG Typesetting math: 100% Correct Enhanced EOC: Problem 8.46 A heavy ball with a weight of 120 is hung from the ceiling of a lecture hall on a 4.4- -long rope. The ball is pulled to one side and released to swing as a pendulum, reaching a speed of 5.6 as it passes through the lowest point. You may want to review ( pages 201 – 204) . For help with math skills, you may want to review: Solutions of Systems of Equations Part A What is the tension in the rope at that point? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Start by drawing a free-body diagram indicating the forces acting on the ball when it is at its lowest point. Choose a coordinate system. What is the direction of the acceleration in your chosen coordinate system? What is the magnitude of the acceleration for the mass, which is moving in a circular path? What is Newton’s second law applied to the mass at the bottom of its swing? Make sure to use your coordinate system when determining the signs of all the forces and the acceleration. What is the tension in the rope at this point? ANSWER: = 1.1 wbottom FG N m m/s T = 210 N Typesetting math: 100% Correct Problem 8.43 In an amusement park ride called The Roundup, passengers stand inside a 16.0 -diameter rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure . Part A Suppose the ring rotates once every 4.80 . If a rider’s mass is 54.0 , with how much force does the ring push on her at the top of the ride? Express your answer with the appropriate units. ANSWER: Correct Part B m s kg 211 N Typesetting math: 100% Suppose the ring rotates once every 4.80 . If a rider’s mass is 54.0 , with how much force does the ring push on her at the bottom of the ride? Express your answer with the appropriate units. ANSWER: Correct Part C What is the longest rotation period of the wheel that will prevent the riders from falling off at the top? Express your answer with the appropriate units. ANSWER: Correct Conceptual Question 9.9 A 2 object is moving to the right with a speed of 1 when it experiences an impulse of 6 . Part A What is the object’s speed after the impulse? Express your answer as an integer and include the appropriate units. ANSWER: s kg 1270 N 5.68 s kg m/s i ^ Ns i ^ v = 4 ms Typesetting math: 100% Correct Part B What is the object’s direction after the impulse? ANSWER: Correct Conceptual Question 9.10 A 2 object is moving to the right with a speed of 2 when it experiences an impulse of -6 . Part A What is the object’s speed after the impulse? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B What is the object’s direction after the impulse? to the right to the left kg m/s i ^ Ns i ^ v = 1 ms Typesetting math: 100% ANSWER: Correct Problem 9.5 Part A In the figure , what value of gives an impulse of 6.4 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct to the right to the left Fmax Ns Fmax = 1.6×103 N Typesetting math: 100% Impulse on a Baseball Learning Goal: To understand the relationship between force, impulse, and momentum. The effect of a net force acting on an object is related both to the force and to the total time the force acts on the object. The physical quantity impulse is a measure of both these effects. For a constant net force, the impulse is given by . The impulse is a vector pointing in the same direction as the force vector. The units of are or . Recall that when a net force acts on an object, the object will accelerate, causing a change in its velocity. Hence the object’s momentum ( ) will also change. The impulse-momentum theorem describes the effect that an impulse has on an object’s motion: . So the change in momentum of an object equals the net impulse, that is, the net force multiplied by the time over which the force acts. A given change in momentum can result from a large force over a short time or a smaller force over a longer time. In Parts A, B, C consider the following situation. In a baseball game the batter swings and gets a good solid hit. His swing applies a force of 12,000 to the ball for a time of . Part A Assuming that this force is constant, what is the magnitude of the impulse on the ball? Enter your answer numerically in newton seconds using two significant figures. ANSWER: Correct We often visualize the impulse by drawing a graph of force versus time. For a constant net force such as that used in the previous part, the graph will look like the one shown in the figure. (F J J = F) t J N * s kg * m/s p = mv )p = J = F) t N 0.70 × 10−3 s J J = 8.4 N * s Typesetting math: 100% Part B The net force versus time graph has a rectangular shape. Often in physics geometric properties of graphs have physical meaning. ANSWER: Correct The assumption of a constant net force is idealized to make the problem easier to solve. A real force, especially in a case like the one presented in Parts A and B, where a large force is applied for a short time, is not likely to be constant. A more realistic graph of the force that the swinging bat applies to the baseball will show the force building up to a maximum value as the bat comes into full contact with the ball. Then as the ball loses contact with the bat, the graph will show the force decaying to zero. It will look like the graph in the figure. For this graph, the length height area slope of the rectangle corresponds to the impulse. Typesetting math: 100% Part C If both the graph representing the constant net force and the graph representing the variable net force represent the same impulse acting on the baseball, which geometric properties must the two graphs have in common? ANSWER: maximum force area slope Typesetting math: 100% Correct When the net force varies over time, as in the case of the real net force acting on the baseball, you can simplify the problem by finding the average net force acting on the baseball during time . This average net force is treated as a constant force that acts on the ball for time . The impulse on the ball can then be found as . Graphically, this method states that the impulse of the baseball can be represented by either the area under the net force versus time curve or the area under the average net force versus time curve. These areas are represented in the figure as the areas shaded in red and blue respectively. The impulse of an object is also related to its change in momentum. Once the impulse is known, it can be used to find the change in momentum, or if either the initial or final momentum is known, the other momentum can be found. Keep in mind that . Because both impulse and momentum are vectors, it is essential to account for the direction of each vector, even in a one-dimensional problem. Part D Assume that a pitcher throws a baseball so that it travels in a straight line parallel to the ground. The batter then hits the ball so it goes directly back to the pitcher along the same straight line. Define the direction the pitcher originally throws the ball as the +x direction. ANSWER: F avg )t )t J = F )t avg J = )p = m(vf − vi ) Typesetting math: 100% Correct Part E Now assume that the pitcher in Part D throws a 0.145- baseball parallel to the ground with a speed of 32 in the +x direction. The batter then hits the ball so it goes directly back to the pitcher along the same straight line. What is the ball’s velocity just after leaving the bat if the bat applies an impulse of to the baseball? Enter your answer numerically in meters per second using two significant figures. ANSWER: Correct The negative sign in the answer indicates that after the bat hits the ball, the ball travels in the opposite direction to that defined to be positive. Problem 9.9 A 2.6 object is moving to the right with a speed of 1.0 when it experiences the force shown in the figure. The impulse on the ball caused by the bat will be in the positive negative x direction. kg m/s −8.4 N * s v = -26 m/s kg m/s Typesetting math: 100% Part A What is the object’s speed after the force ends? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the object’s direction after the force ends? ANSWER: Correct Enhanced EOC: Problem 9.27 A tennis player swings her 1000 g racket with a speed of 11.0 . She hits a 60 g tennis ball that was approaching her at a speed of 19.0 . The ball rebounds at 41.0 . You may want to review ( pages 226 – 232) . For help with math skills, you may want to review: v = 0.62 ms to the right to the left m/s m/s m/s Typesetting math: 100% Solving Algebraic Equations Part A How fast is her racket moving immediately after the impact? You can ignore the interaction of the racket with her hand for the brief duration of the collision. Express your answer with the appropriate units. Hint 1. How to approach the problem Given that you can ignore the interaction of the racket with her hand during the collision, what is conserved during the collision? Draw a picture indicating the direction of the racket and ball before the collision and a separate picture for after the collision. Place a coordinate system on your pictures, indicating the positive x direction. Keeping in mind that velocity can be either positive or negative in your coordinate system, what is the initial momentum of the ball–racket system? What is the final momentum of the ball–racket system in terms of the velocity of the racket after the collision? Using conservation of momentum, what are the velocity and speed of the racket after the collision? ANSWER: Correct Part B If the tennis ball and racket are in contact for 8.00 , what is the average force that the racket exerts on the ball? Express your answer with the appropriate units. Hint 1. How to approach the problem How is the impulse on the ball related to the change in momentum of the ball? What is the change in momentum of the ball? How are the impulse on the ball and the collision time related to the average force on the ball? 7.40 ms ms Typesetting math: 100% ANSWER: Correct Problem 9.14 A 2.00×104 railroad car is rolling at 6.00 when a 6000 load of gravel is suddenly dropped in. Part A What is the car’s speed just after the gravel is loaded? Express your answer with the appropriate units. ANSWER: Correct Problem 9.17 A 330 bird flying along at 5.0 sees a 9.0 insect heading straight toward it with a speed of 34 (as measured by an observer on the ground, not by the bird). The bird opens its mouth wide and enjoys a nice lunch. Part A What is the bird’s speed immediately after swallowing? Express your answer to two significant figures and include the appropriate units. ANSWER: 450 N kg m/s kg 4.62 ms g m/s g m/s Typesetting math: 100% Correct Problem 9.20 A 50.0 archer, standing on frictionless ice, shoots a 200 arrow at a speed of 200 . Part A What is the recoil speed of the archer? Express your answer with the appropriate units. ANSWER: Correct Problem 9.25 A 40.0 ball of clay traveling east at 4.50 collides and sticks together with a 50.0 ball of clay traveling north at 4.50 . Part A What is the speed of the resulting ball of clay? Express your answer with the appropriate units. ANSWER: v = 4.0 ms kg g m/s 0.800 ms g m/s g m/s 3.20 ms Typesetting math: 100% Correct Problem 9.32 A particle of mass is at rest at . Its momentum for is given by , where is in . Part A Find an expression for , the force exerted on the particle as a function of time. Express your answer in terms of the given quantities. ANSWER: Correct Problem 9.37 Most geologists believe that the dinosaurs became extinct 65 million years ago when a large comet or asteroid struck the earth, throwing up so much dust that the sun was blocked out for a period of many months. Suppose an asteroid with a diameter of 2.0 and a mass of 1.2×1013 hits the earth with an impact speed of 4.5×104 . Part A What is the earth’s recoil speed after such a collision? (Use a reference frame in which the earth was initially at rest.) Assume that . Express your answer to two significant figures and include the appropriate units. ANSWER: m t = 0 t > 0 px = 6t2 kgm/s t s Fx(t) Fx = 12t N km kg m/s MEarth= 5.98 × 1024 kg = 9.0×10−8 v ms Typesetting math: 100% Correct Part B What percentage is this of the earth’s speed around the sun? (Use the astronomical data in the textbook.) Express your answer using two significant figures. ANSWER: Correct Problem 9.42 One billiard ball is shot east at 1.8 . A second, identical billiard ball is shot west at 1.2 . The balls have a glancing collision, not a head-on collision, deflecting the second ball by 90 and sending it north at 1.50 . Part A What is the speed of the first ball after the collision? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the direction of the first ball after the collision? Give the direction as an angle south of east. = 3.0×10−10 of v % the earth’s speed m/s m/s 1 m/s v = 1.6 ms Typesetting math: 100% Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 9.49 Two 490 blocks of wood are 2.0 apart on a frictionless table. A 12 bullet is fired at 420 toward the blocks. It passes all the way through the first block, then embeds itself in the second block. The speed of the first block immediately afterward is 5.6 . Part A What is the speed of the second block after the bullet stops? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 99.5%. You received 156.21 out of a possible total of 157 points. = 68 1 g m g m/s m/s v = 4.6 ms Typesetting math: 100%

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## Assignment 2 Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 2.6 Part A The figure shows the position-versus-time graph for a moving object. At which lettered point or points: Is the object moving the slowest? Is the object moving the fastest? Is the object at rest? Drag the appropriate items to their respective bins. ANSWER: Correct Part B At which lettered point or points is the object moving to the negative direction? ANSWER: Correct Conceptual Question 2.7 The figure shows the position-versus-time graph for a moving object. At which lettered point or points: Part A Is the object moving the fastest? ANSWER: A B C D E Correct Part B Is the object speeding up? ANSWER: Correct Part C Is the object moving to the left and turning around? ANSWER: A B C D E F A B C D E F Correct Kinematic Vocabulary One of the difficulties in studying mechanics is that many common words are used with highly specific technical meanings, among them velocity, acceleration, position, speed, and displacement. The series of questions in this problem is designed to get you to try to think of these quantities like a physicist. Answer the questions in this problem using words from the following list: A. position B. direction C. displacement D. coordinates E. velocity F. acceleration G. distance H. magnitude I. vector J. scalar K. components Part A Velocity differs from speed in that velocity indicates a particle’s __________ of motion. Enter the letter from the list given in the problem introduction that best completes the sentence. ANSWER: Correct Part B Unlike speed, velocity is a __________ quantity. Enter the letter from the list given in the problem introduction that best completes the sentence. ANSWER: Correct Part C A vector has, by definition, both __________ and direction. Enter the letter from the list given in the problem introduction that best completes the sentence. ANSWER: Correct Part D Once you have selected a coordinate system, you can express a two-dimensional vector using a pair of quantities known collectively as __________. Enter the letter from the list given in the problem introduction that best completes the sentence. ANSWER: Correct Part E Speed differs from velocity in the same way that __________ differs from displacement. Enter the letter from the list given in the problem introduction that best completes the sentence. Hint 1. Definition of displacement Displacement is the vector that indicates the difference of two positions (e.g., the final position from the initial position). Being a vector, it is independent of the coordinate system used to describe it (although its vector components depend on the coordinate system). ANSWER: Correct Part F Consider a physical situation in which a particle moves from point A to point B. This process is described from two coordinate systems that are identical except that they have different origins. The __________ of the particle at point A differ(s) as expressed in one coordinate system compared to the other, but the __________ from A to B is/are the same as expressed in both coordinate systems. Type the letters from the list given in the problem introduction that best complete the sentence. Separate the letters with commas. There is more than one correct answer, but you should only enter one pair of comma-separated letters. For example, if the words “vector” and “scalar” fit best in the blanks, enter I,J. ANSWER: Correct The coordinates of a point will depend on the coordinate system that is chosen, but there are several other quantities that are independent of the choice of origin for a coordinate system: in particular, distance, displacement, direction, and velocity. In working physics problems, unless you are interested in the position of an object or event relative to a specific origin, you can usually choose the coordinate system origin to be wherever is most convenient or intuitive. Note that the vector indicating a displacement from A to B is usually represented as . Part G Identify the following physical quantities as scalars or vectors. ANSWER: rB A = rB − rA Correct Problem 2.4 The figure is the position-versus-time graph of a jogger. Part A What is the jogger’s velocity at = 10 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Answer Requested Part B What is the jogger’s velocity at = 25 ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C What is the jogger’s velocity at = 35 ? Express your answer to two significant figures and include the appropriate units. ANSWER: t s v = 1.3 ms t s v = 0 ms t s v = -5.0 ms Correct Analyzing Position versus Time Graphs: Conceptual Question Two cars travel on the parallel lanes of a two-lane road. The cars’ motions are represented by the position versus time graph shown in the figure. Answer the questions using the times from the graph indicated by letters. Part A At which of the times do the two cars pass each other? Hint 1. Two cars passing Two objects can pass each other only if they have the same position at the same time. ANSWER: Correct Part B Are the two cars traveling in the same direction when they pass each other? ANSWER: Correct Part C At which of the lettered times, if any, does car #1 momentarily stop? Hint 1. Determining velocity from a position versus time graph The slope on a position versus time graph is the “rise” (change in position) over the “run” (change in time). In physics, the ratio of change in position over change in time is defined as the velocity. Thus, the slope on a position versus time graph is the velocity of the object being graphed. ANSWER: A B C D E None Cannot be determined yes no Correct Part D At which of the lettered times, if any, does car #2 momentarily stop? Hint 1. Determining velocity from a position versus time graph The slope on a position versus time graph is the “rise” (change in position) over the “run” (change in time). In physics, the ratio of change in position over change in time is defined as the velocity. Thus, the slope on a position versus time graph is the velocity of the object being graphed. ANSWER: A B C D E none cannot be determined A B C D E none cannot be determined Correct Part E At which of the lettered times are the cars moving with nearly identical velocity? Hint 1. Determining Velocity from a Position versus Time Graph The slope on a position versus time graph is the “rise” (change in position) over the “run” (change in time). In physics, the ratio of change in position over change in time is defined as the velocity. Thus, the slope on a position versus time graph is the velocity of the object being graphed. ANSWER: Correct Problem 2.6 A particle starts from 10 at = 0 and moves with the velocity graph shown in the figure. A B C D E None Cannot be determined m t0 Part A Does this particle have a turning point? ANSWER: Correct Part B If so, at what time? Express your answer using two significant figures and include the appropriate units. ANSWER: Correct Part C What is the object’s position at = 2, 3, 4 ? Yes No t = 1.0 s t s Express your answers using two significant figures separated by commas. ANSWER: Correct Overcoming a Head Start Cars A and B are racing each other along the same straight road in the following manner: Car A has a head start and is a distance beyond the starting line at . The starting line is at . Car A travels at a constant speed . Car B starts at the starting line but has a better engine than Car A, and thus Car B travels at a constant speed , which is greater than . Part A How long after Car B started the race will Car B catch up with Car A? Express the time in terms of given quantities. Hint 1. Consider the kinematics relation Write an expression for the displacement of Car A from the starting line at a time after Car B starts. (Note that we are taking this time to be .) Answer in terms of , , , and for time, and take at the starting line. Hint 1. What is the acceleration of Car A? The acceleration of Car A is zero, so the general formula has at least one term equal to zero. ANSWER: Hint 2. What is the relation between the positions of the two cars? x2 , x3 , x4 = 10,16,26 m DA t = 0 x = 0 vA vB vA t t = 0 vA vB DA t x = 0 x(t) = x0 + v0t + (1/2)at2 xA(t) = DA + vAt The positions of the two cars are equal at time . Hint 3. Consider Car B’s position as a function of time Write down an expression for the position of Car B at time after starting. Give your answer in terms of any variables needed (use for time). ANSWER: ANSWER: Correct Part B How far from Car B’s starting line will the cars be when Car B passes Car A? Express your answer in terms of known quantities. (You may use as well.) Hint 1. Which expression should you use? Just use your expression for the position of either car after time , and substitute in the correct value for (found in the previous part). ANSWER: Correct tcatch t t xB(t) = vBt tcatch = DA vB−vA tcatch t = 0 tcatch dpass = vBDA vB−vA Problem 2.11 The figure shows the velocity graph of a particle moving along the x-axis. Its initial position is at . At = 2 , what are the particle’s (a) position, (b) velocity, and (c) acceleration? Part A Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Express your answer to two significant figures and include the appropriate units. ANSWER: x0 = 2 m t0 = 0 t s x = 6.0 m vx = 4.0 ms Correct Part C Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 2.13 A jet plane is cruising at 300 when suddenly the pilot turns the engines up to full throttle. After traveling 3.9 , the jet is moving with a speed of 400 . Part A What is the jet’s acceleration, assuming it to be a constant acceleration? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 2.20 A rock is tossed straight up with a velocity of 22 When it returns, it falls into a hole deep. You may want to review ( pages 51 – 54) . ax = 2.0 m s2 m/s km m/s a = 9.0 m s2 m/s 10 m For help with math skills, you may want to review: Quadratic Equations For general problem-solving tips and strategies for this topic, you may want to view a Video Tutor Solution of Time in the air for a tossed ball. Part A What is the rock’s velocity as it hits the bottom of the hole? Express your answer with the appropriate units. Hint 1. How to approach the problem Start by drawing a picture of the path of the rock, including its launch point, initial direction, and end point in the hole. Choose a coordinate system, and indicate it on your picture. Where is ? What is the positive direction? What is the position of the launch point and the bottom of the hole? In this coordinate system, what is the sign of the initial velocity and the sign of the acceleration? Calling the launch time , what is the equation for as a function of time? What is the position at the bottom of the hole? This will lead to a quadratic equation for the time when the rock hits the bottom of the hole. The quadratic equation has two solutions for the time. Not all mathematical solutions make sense physically. Which solution makes sense physically in terms of the picture that you drew at the beginning? Keeping the same coordinate system, what is the velocity in the direction as a function of time? What is the velocity when the rock hits the bottom of the hole? ANSWER: Correct Part B How long is the rock in the air, from the instant it is released until it hits the bottom of the hole? Express your answer with the appropriate units. y = 0 m y t = 0 y y t y y v = -26.1 ms Hint 1. How to approach the problem How is the time the rock was in the air related to the time at which the rock hit the ground in Part A? ANSWER: Correct Enhanced EOC: Problem 2.23 A particle moving along the x-axis has its position described by the function 2.00 5.00 5.00 , where is in s. At = 4.00, what are the particle’s (a) position, (b) velocity, and (c) acceleration? You may want to review ( pages 38 – 42) . For help with math skills, you may want to review: Differentiation of Polynomial Functions t = 4.90 s x = ( t3 − t + ) m t t Part A Express your answer with the appropriate units. Hint 1. How to approach the problem Evaluate the position at time = 4.00 . ANSWER: Correct Part B Express your answer with the appropriate units. Hint 1. How to approach the problem How do you determine the velocity as a function of time, , from the position, ? What calculus operation do you have to perform? Once you have , how do you determine at a particular time? ANSWER: Correct Part C Express your answer with the appropriate units. t s 113 m v(t) x(t) v(t) v 91.0 ms Hint 1. How to approach the problem How do you determine the acceleration as a function of time, , from the velocity, ? What calculus operation do you have to perform? Once you have , how do you determine the acceleration at a particular time? ANSWER: Correct Problem 2.26 A particle’s position on the x-axis is given by the function 6.00 6.00 , where is in s. Part A Where is the particle when = 4.00 ? Express your answer with the appropriate units. ANSWER: Correct Problem 2.30 A particle’s velocity is described by the function = , where is in . a(t) v(t) a(t) 48.0 m s2 x = (t2 − t + ) m t vx m/s 1.00 m vx t2 − 7t + 7 m/s t s Part A How many turning points does the particle reach. Express your answer as an integer. ANSWER: Correct Part B At what times does the particle reach its turning points? Express your answers using two significant figures separated by a comma. ANSWER: Correct Part C What is the particle’s acceleration at each of the turning points? Express your answers using two significant figures separated by a comma. ANSWER: Correct 2 t1 , t2 = 5.8,1.2 s a1 , a2 = 4.6,-4.6 m/s2 Problem 2.49 A 200 weather rocket is loaded with 100 of fuel and fired straight up. It accelerates upward at 35 for 30 , then runs out of fuel. Ignore any air resistance effects. Part A What is the rocket’s maximum altitude? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How long is the rocket in the air? Express your answer to two significant figures and include the appropriate units. ANSWER: Answer Requested Problem 2.52 A hotel elevator ascends with maximum speed of . Its acceleration and deceleration both have a magnitude of . Part A How far does the elevator move while accelerating to full speed from rest? kg kg m/s2 s h = 72 km t = 260 s 200 m 5 m/s 1.0 m/s2 Express your answer with the appropriate units. ANSWER: Correct Part B How long does it take to make the complete trip from bottom to top? Express your answer with the appropriate units. ANSWER: Answer Requested Components of Vectors Shown is a 10 by 10 grid, with coordinate axes x and y . The grid runs from -5 to 5 on both axes. Drawn on this grid are four vectors, labeled through . This problem will ask you various questions about these vectors. All answers should be in decimal notation, unless otherwise specified. 12.5 m 45.0 s A D Part A What is the x component of ? Express your answer to two significant figures. Hint 1. How to derive the component A component of a vector is its length (but with appropriate sign) along a particular coordinate axis, the axes being specfied in advance. You are asked for the component of that lies along the x axis, which is horizontal in this problem. Imagine two lines perpendicular to the x axis running from the head (end with the arrow) and tail of down to the x axis. The length of the x axis between the points where these lines intersect is the x component of . In this problem, the x component is the x coordinate at which the perpendicular from the head of the vector hits the origin (because the tail of the vector is at the origin). ANSWER: Correct Part B What is the y component of ? Express your answer to the nearest integer. ANSWER: Correct A A A A Ax = 2.5 A Ay = 3 Part C What is the y component of ? Express your answer to the nearest integer. Hint 1. Consider the direction Don’t forget the sign. ANSWER: Correct Part D What is the component of ? Express your answer to the nearest integer. Hint 1. How to find the start and end points of the vector components A vector is defined only by its magnitude and direction. The starting point of the vector is of no consequence to its definition. Therefore, you need to somehow eliminate the starting point from your answer. You can run two perpendiculars to the x axis, one from the head (end with the arrow) of , and another to the tail, with the x component being the difference between x coordinates of head and tail (negative if the tail is to the right of the head). Another way is to imagine bringing the tail of to the origin, and then using the same procedure you used before to find the components of and . This is equivalent to the previous method, but it might be easier to visualize. ANSWER: B By = -3 x C C C A B Cx = -2 Correct The following questions will ask you to give both components of vectors using the ordered pairs method. In this method, the x component is written first, followed by a comma, and then the y component. For example, the components of would be written 2.5,3 in ordered pair notation. The answers below are all integers, so estimate the components to the nearest whole number. Part E In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Correct Part F In ordered pair notation, write down the components of vector . Express your answers to the nearest integer. ANSWER: Correct Part G What is true about and ? Choose from the pulldown list below. A B Bx, By = 2,-3 D Dx, Dy = 2,-3 B D ANSWER: Correct Problem 3.6 Find x- and y-components of the following vectors. Part A Express your answers using two significant figures. Enter your answers numerically separated by a comma. ANSWER: Correct Part B Express your answers using two significant figures. Enter your answers numerically separated by a comma. ANSWER: They have different components and are not the same vectors. They have the same components but are not the same vectors. They are the same vectors. = (r 430m, 60& below positive x − axis) rx, ry = 210,-370 m v = (610m/s, 23& above positive x − axis) Correct Part C Express your answers using two significant figures. Enter your answers numerically separated by a comma. ANSWER: Correct Problem 3.10 Part A Draw . Draw the vector with its tail at the origin. ANSWER: vx, vy = 560,240 m/s a = (7.3m/s2 , negative y − direction) ax, ay = 0,-7.3 m/s2 B = −4 + 4 ı ^ ^ Correct Part B Find the magnitude of . Express your answer using two significant figures. ANSWER: Correct B B = 5.7 Part C Find the direction of . Express your answer using two significant figures. ANSWER: Correct Part D Draw . Draw the vector with its tail at the origin. ANSWER: B = 45 above the B negative x-axis & = (−2.0 − 1.0 ) cm r ı ^ ^ Correct Part E Find the magnitude of . Express your answer using two significant figures. ANSWER: Correct r r = 2.2 cm Part F Find the direction of . ANSWER: Correct Part G Draw . Draw the vector with its tail at the origin. ANSWER: r = 26.6 below the r negative x-axis & = (−10 − 100 ) m/s v ı ^ ^ Correct Part H Find the magnitude of . Express your answer using four significant figures. ANSWER: Correct v v = 100.5 m/s Part I Find the direction of . ANSWER: Correct Part J Draw . Draw the vector with it’s tail at the origin. ANSWER: v = 84.3 below the v negative x-axis & = (20 + 10 ) m/ a ı ^ ^ s2 Correct Part K Find the magnitude of . ANSWER: Correct Part L a a = 22.4 m/s2 Find the direction of . ANSWER: Correct Problem 3.14 Let , , and . Part A What is the component form of vector ? ANSWER: Correct Part B What is the magnitude of vector ? ANSWER: a = 26.6 above the a positive x-axis & A = 5 − 2 ı ^ ^ B = −2 + 6 ı ^ ^ D = A − B D D = 7 − 8 ı ^ ^ D = −7 − 5 ı ^ ^ D = 7 + 8 ı ^ ^ D = 4 + 5 ı ^ ^ D Correct Part C What is the direction of vector ? Express your answer using two significant figures. ANSWER: Correct Problem 3.15 Let , , and . Part A Write vector in component form. ANSWER: D = 10.6 D = 49 & below positive x-axis A = 4 − 2 ı ^ ^ B = −3 + 5 ı ^ ^ E = 4A + 2B E E = 10 + 2 ı ^ ^ E = + 10 ı ^ ^ E = −10 ^ E = 10 − 2 ı ^ ^ Correct Part B Draw vectors , , and . Draw the vectors with their tails at the origin. ANSWER: Correct Part C A B E What is the magnitude of vector ? Express your answer using two significant figures. ANSWER: Correct Part D What is the direction of vector ? Express your answer using two significant figures. ANSWER: Correct Problem 3.24 Part A What is the angle between vectors and in the figure? Express your answer with the appropriate units. E E = 10.0 E = 11 & counterclockwise from positive direction of x-axis E F ANSWER: Correct Part B Use components to determine the magnitude of . ANSWER: Correct Part C Use components to determine the direction of . Express your answer with the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 91.3%. = 71.6 & G = E + F G = 3.00 G = E + F = 90.0 & You received 129.62 out of a possible total of 142 points.

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## Assignment 8 Due: 11:59pm on Friday, April 4, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 10.3 Part A If a particle’s speed increases by a factor of 5, by what factor does its kinetic energy change? ANSWER: Correct Conceptual Question 10.11 A spring is compressed 1.5 . Part A How far must you compress a spring with twice the spring constant to store the same amount of energy? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct = 25 K2 K1 cm x = 1.1 cm Problem 10.2 The lowest point in Death Valley is below sea level. The summit of nearby Mt. Whitney has an elevation of 4420 . Part A What is the change in potential energy of an energetic 80 hiker who makes it from the floor of Death Valley to the top of Mt.Whitney? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 10.3 Part A At what speed does a 1800 compact car have the same kinetic energy as a 1.80×104 truck going 21.0 ? Express your answer with the appropriate units. ANSWER: Correct Problem 10.5 A boy reaches out of a window and tosses a ball straight up with a speed of 13 . The ball is 21 above the ground as he releases it. 85m m kg U = 3.5×106 J kg kg km/hr vc = 66.4 km hr m/s m Part A Use energy to find the ball’s maximum height above the ground. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Use energy to find the ball’s speed as it passes the window on its way down. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C Use energy to find the speed of impact on the ground. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Hmax = 30 m v = 13 ms v = 24 ms Problem 10.8 A 59.0 skateboarder wants to just make it to the upper edge of a “quarter pipe,” a track that is one-quarter of a circle with a radius of 2.30 . Part A What speed does he need at the bottom? Express your answer with the appropriate units. ANSWER: Correct Problem 10.12 A 1500 car traveling at 12 suddenly runs out of gas while approaching the valley shown in the figure. The alert driver immediately puts the car in neutral so that it will roll. Part A kg m 6.71 ms kg m/s What will be the car’s speed as it coasts into the gas station on the other side of the valley? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Ups and Downs Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational field of the earth. In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy. In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The energy transformations that take place involve the object’s kinetic energy and its gravitational potential energy . The law of conservation of energy for such cases implies that the sum of the object’s kinetic energy and potential energy does not change with time. This idea can be expressed by the equation , where “i” denotes the “initial” moment and “f” denotes the “final” moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem. First, let us consider an object launched vertically upward with an initial speed . Neglect air resistance. Part A As the projectile goes upward, what energy changes take place? ANSWER: v = 6.8 ms K = (1/2)mv2 U = mgh Ki + Ui = Kf + Uf v Correct Part B At the top point of the flight, what can be said about the projectile’s kinetic and potential energy? ANSWER: Correct Strictly speaking, it is not the ball that possesses potential energy; rather, it is the system “Earth-ball.” Although we will often talk about “the gravitational potential energy of an elevated object,” it is useful to keep in mind that the energy, in fact, is associated with the interactions between the earth and the elevated object. Part C The potential energy of the object at the moment of launch __________. ANSWER: Both kinetic and potential energy decrease. Both kinetic and potential energy increase. Kinetic energy decreases; potential energy increases. Kinetic energy increases; potential energy decreases. Both kinetic and potential energy are at their maximum values. Both kinetic and potential energy are at their minimum values. Kinetic energy is at a maximum; potential energy is at a minimum. Kinetic energy is at a minimum; potential energy is at a maximum. Correct Usually, the zero level is chosen so as to make the relevant calculations simpler. In this case, it makes good sense to assume that at the ground level–but this is not, by any means, the only choice! Part D Using conservation of energy, find the maximum height to which the object will rise. Express your answer in terms of and the magnitude of the acceleration of gravity . ANSWER: Correct You may remember this result from kinematics. It is comforting to know that our new approach yields the same answer. Part E At what height above the ground does the projectile have a speed of ? Express your answer in terms of and the magnitude of the acceleration of gravity . ANSWER: is negative is positive is zero depends on the choice of the “zero level” of potential energy U = 0 hmax v g hmax = v2 2g h 0.5v v g h = 3 v2 8g Correct Part F What is the speed of the object at the height of ? Express your answer in terms of and . Use three significant figures in the numeric coefficient. Hint 1. How to approach the problem You are being asked for the speed at half of the maximum height. You know that at the initial height ( ), the speed is . All of the energy is kinetic energy, and so, the total energy is . At the maximum height, all of the energy is potential energy. Since the gravitational potential energy is proportional to , half of the initial kinetic energy must have been converted to potential energy when the projectile is at . Thus, the kinetic energy must be half of its original value (i.e., when ). You need to determine the speed, as a multiple of , that corresponds to such a kinetic energy. ANSWER: Correct Let us now consider objects launched at an angle. For such situations, using conservation of energy leads to a quicker solution than can be produced by kinematics. Part G A ball is launched as a projectile with initial speed at an angle above the horizontal. Using conservation of energy, find the maximum height of the ball’s flight. Express your answer in terms of , , and . Hint 1. Find the final kinetic energy Find the final kinetic energy of the ball. Here, the best choice of “final” moment is the point at which the ball reaches its maximum height, since this is the point we are interested in. u (1/2)hmax v g h = 0 v (1/2)mv2 h (1/2)hmax (1/4)mv2 h = (1/2)hmax v u = 0.707v v hmax v g Kf Express your answer in terms of , , and . Hint 1. Find the speed at the maximum height The speed of the ball at the maximum height is __________. ANSWER: ANSWER: ANSWER: Correct Part H A ball is launched with initial speed from ground level up a frictionless slope. The slope makes an angle with the horizontal. Using conservation of energy, find the maximum vertical height to which the ball will climb. Express your answer in terms of , , and . You may or may not use all of these quantities. v m 0 v v cos v sin v tan Kf = 0.5m(vcos())2 hmax = (vsin())2 2g v hmax v g ANSWER: Correct Interestingly, the answer does not depend on . The difference between this situation and the projectile case is that the ball moving up a slope has no kinetic energy at the top of its trajectory whereas the projectile launched at an angle does. Part I A ball is launched with initial speed from the ground level up a frictionless hill. The hill becomes steeper as the ball slides up; however, the ball remains in contact with the hill at all times. Using conservation of energy, find the maximum vertical height to which the ball will climb. Express your answer in terms of and . ANSWER: Correct The profile of the hill does not matter; the equation would have the same terms regardless of the steepness of the hill. Problem 10.14 A 12- -long spring is attached to the ceiling. When a 2.2 mass is hung from it, the spring stretches to a length of 17 . Part A What is the spring constant ? Express your answer to two significant figures and include the appropriate units. hmax = v2 2g v hmax v g hmax = v2 2g Ki + Ui = Kf + Uf cm kg cm k ANSWER: Correct Part B How long is the spring when a 3.0 mass is suspended from it? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 10.17 A 6.2 mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in . You may want to review ( pages 255 – 257) . For help with math skills, you may want to review: Solving Algebraic Equations = 430 k Nm kg y = 19 cm kg Part A What does the spring scale read just before the mass touches the lower spring? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces acting on the mass before it touches the scale. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? ANSWER: Correct Part B The scale reads 22 when the lower spring has been compressed by 2.7 . What is the value of the spring constant for the lower spring? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces acting on the mass. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? Use these to determine the force on the mass by the spring, taking note of the directions from your picture. How is the spring constant related to the force by the spring and the compression of the spring? Check your units. ANSWER: F = 61 N N cm k = 1400 k Nm Correct Part C At what compression length will the scale read zero? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces on the mass. When the scale reads zero, what is the force on the mass due to the scale? What is the gravitational force on the mass? What is the force on the mass by the spring? How is the compression length related to the force by the spring and the spring constant? Check your units. ANSWER: Correct Problem 10.18 Part A How far must you stretch a spring with = 800 to store 180 of energy? Express your answer to two significant figures and include the appropriate units. ANSWER: y = 4.2 cm k N/m J Correct Problem 10.22 A 15 runaway grocery cart runs into a spring with spring constant 230 and compresses it by 57 . Part A What was the speed of the cart just before it hit the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Spring Gun A spring-loaded toy gun is used to shoot a ball straight up in the air. The ball reaches a maximum height , measured from the equilibrium position of the spring. s = 0.67 m kg N/m cm v = 2.2 ms H Part A The same ball is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the ball go this time? Neglect friction. Assume that the spring is ideal and that the distance by which the spring is compressed is negligible compared to . Hint 1. Potential energy of the spring The potential energy of a spring is proportional to the square of the distance the spring is compressed. The spring was compressed half the distance, so the mass, when launched, has one quarter of the energy as in the first trial. Hint 2. Potential energy of the ball At the highest point in the ball’s trajectory, all of the spring’s potential energy has been converted into gravitational potential energy of the ball. ANSWER: Correct A Bullet Is Fired into a Wooden Block A bullet of mass is fired horizontally with speed at a wooden block of mass resting on a frictionless table. The bullet hits the block and becomes completely embedded within it. After the bullet has come to rest within the block, the block, with the bullet in it, is traveling at speed . H height = H 4 mb vi mw vf Part A Which of the following best describes this collision? Hint 1. Types of collisions An inelastic collision is a collision in which kinetic energy is not conserved. In a partially inelastic collision, kinetic energy is lost, but the objects colliding do not stick together. From this information, you can infer what completely inelastic and elastic collisions are. ANSWER: Correct Part B Which of the following quantities, if any, are conserved during this collision? Hint 1. When is kinetic energy conserved? Kinetic energy is conserved only in perfectly elastic collisions. ANSWER: perfectly elastic partially inelastic perfectly inelastic Correct Part C What is the speed of the block/bullet system after the collision? Express your answer in terms of , , and . Hint 1. Find the momentum after the collision What is the total momentum of the block/bullet system after the collision? Express your answer in terms of and other given quantities. ANSWER: Hint 2. Use conservation of momentum The momentum of the block/bullet system is conserved. Therefore, the momentum before the collision is the same as the momentum after the collision. Find a second expression for , this time expressed as the total momentum of the system before the collision. Express your answer in terms of and other given quantities. ANSWER: kinetic energy only momentum only kinetic energy and momentum neither momentum nor kinetic energy vi mw mb ptotal vf ptotal = (mw + mb)vf ptotal vi ptotal = mbvi ANSWER: Correct Problem 10.31 Ball 1, with a mass of 150 and traveling at 15.0 , collides head on with ball 2, which has a mass of 340 and is initially at rest. Part A What are the final velocities of each ball if the collision is perfectly elastic? Express your answer with the appropriate units. ANSWER: Correct Part B Express your answer with the appropriate units. ANSWER: Correct Part C vf = mb vi mb+mw g m/s g (vfx) = -5.82 1 ms (vfx) = 9.18 2 ms What are the final velocities of each ball if the collision is perfectly inelastic? Express your answer with the appropriate units. ANSWER: Correct Part D Express your answer with the appropriate units. ANSWER: Correct Enhanced EOC: Problem 10.43 A package of mass is released from rest at a warehouse loading dock and slides down the = 2.2 – high, frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass , from the bottom of the chute. You may want to review ( pages 265 – 269) . For help with math skills, you may want to review: Solving Algebraic Equations (vfx) = 4.59 1 ms (vfx) = 4.59 2 ms m h m 2m Part A Suppose the packages stick together. What is their common speed after the collision? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem There are two parts to this problem: the block sliding down the frictionless incline and the collision. What conservation laws are valid in each part? In terms of , what are the kinetic and potential energies of the block at the top of the incline? What is the potential energy of the same block at the bottom just before the collision? What are the kinetic energy and velocity of block just before the collision? What is conserved during the collision? What is the total momentum of the two blocks before the collision? What is the momentum of the two blocks stuck together after the collision? What is the velocity of the two blocks after the collision? ANSWER: Correct Part B Suppose the collision between the packages is perfectly elastic. To what height does the package of mass rebound? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem There are three parts to this problem: the block sliding down the incline, the collision, and mass going back up the incline. What conservation laws are valid in each part? m m v = 2.2 ms m m What is an elastic collision? For an elastic collision, how are the initial and final velocities related when one of the masses is initially at rest? Using the velocity of just before the collision from Part A, what is the velocity of just after the collision in this case? What are the kinetic and potential energies of mass just after the collision? What is the kinetic energy of mass at its maximum rebound height? Using conservation of energy, what is the potential energy of mass at its maximum height? What is the maximum height? ANSWER: Correct Problem 10.35 A cannon tilted up at a 35.0 angle fires a cannon ball at 79.0 from atop a 21.0 -high fortress wall. Part A What is the ball’s impact speed on the ground below? Express your answer with the appropriate units. ANSWER: Correct Problem 10.45 A 1000 safe is 2.5 above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 48 . m m m m m h = 24 cm $ m/s m vf = 81.6 ms kg m cm Part A What is the spring constant of the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 10.49 A 100 block on a frictionless table is firmly attached to one end of a spring with = 21 . The other end of the spring is anchored to the wall. A 30 ball is thrown horizontally toward the block with a speed of 6.0 . Part A If the collision is perfectly elastic, what is the ball’s speed immediately after the collision? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the maximum compression of the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: = 2.5×105 k Nm g k N/m g m/s v = 3.2 ms Correct Part C Repeat part A for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D Repeat part B for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 99.4%. You received 120.28 out of a possible total of 121 points. x = 0.19 m v = 1.4 ms x = 0.11 m

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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 =

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