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University of the Philippines College of Science

Physics 71 Set A Second Long Exam First Semester AY 2011-2012

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Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

Instructions: Choose the letter of the best answer. Ignore air resistance unless stated otherwise. The acceleration due to gravity is: g = 9.81 sm2 .

1. Push it. Leslie pushes a 10.0 [kg] cabinet horizontally on a level surface with an applied force of 25.0 [N]. If the cabinet slides on the surface by 5.00 [m], what is the work done by gravity on the cabinet? (a) 491 [J] (b) 125 [J] (c) -491 [J] (d) - 125 [J] (e) 0 2. Cable. A 10. [kg] object is hoisted by a cable whose tension is 140[N]. What is the total work done on the object as it moves 2.0[m]upward? (a) 42 [J]

(b) 84 [J]

(c) 130 [J]

(d) 260 [J]

(e) 280 [J]

3. Crash Collision. Two cars were moving in a collision course with each other, but Superman prevented the collision by stopping both cars with km his hands. Car A has a mass of 2000 [kg] and was moving with a speed of 200 h . Car B, which has a mass of 4000 [kg] , was approaching car A from the opposite direction with a speed km of 150 h . To which car did Superman do greater work? (a) car A (b) car B

(c) Equal amount of work will be done to both cars.

4. Falling. Romeo dropped a 0.0150 [kg] ring from rest at a 22.0-m high building. Juliet, who is directly below the falling ring, placed her hands on the ground. What is the speed of the ring just before it reaches Juliet’s hands? (a) 0 (b) 14.7 ms (c) 20.8 ms (d) 216 ms (e) 432 ms

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

5. Area under the curve. A force F is applied to a box of mass 2.0 [kg] parallel to the x-axis as it moves along a straight line. The x - component of the force varies with the x - coordinates of the box as shown below, with the force given in Newtons and the position in meters. What is the work done on the box by F as it moves from x = 1.0 to x = 5.0? (a) 0 [J]

(b) 4.0 [J]

(c) 10. [J]

(d) 20. [J]

(e) 25. [J]

6. Moving particle. A particle experiences a force, which acts along the x-axis, as described in the force vs. position plot shown. What is the work done by this force if it starts at x=2.0 m and ends at position x=0? (a) 0 J (b) 0.5 J (c) 1.0 J (d) -0.5 J (e) -1.0 J 7. K+U. You throw a rock straight up with initial speed v from the ground. Which of the following graphs can represent the rock’s mechanical energy, E, as a function of time while the rock is in air?

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

8. K-U. At time t = 0, you throw a rock straight up with initial speed v from the ground. Let K and U be the kinetic and potential energies of the particle, respectively, and let U=0 when the rock is on the ground. Which of the following graphs show the quantity K − U as a function of time?

9. Pellet Gun. A 0.10-kg pellet is launched straightup from a pellet gun, which N . Right before launching, contains a spring of spring constant k = 5.0 × 102 m the spring is compressed a distance 0.050 m, and the pellet is at rest. From this initial position, the pellet is observed to reach its maximum height at 0.40 m above its starting point. Find the work done by air resistance as the pellet goes from its starting point to its maximum height. (a) -0.23 [J] (b) -1.0 [J] (c) 0 [J] (d) 0.23 [J] (e) 1.0 [J] 10. Glider. A 0.45 [kg] glider that sits on a frictionless air track is connected to a spring with spring constant 2.5 [N/m]. Initially, the spring is unstretched so that the glider is in equilibrium. Patty then stretches the glider by a distance of 0.25 [m]. What is the work done by the spring on the glider? (a) -0.16 [J] (b) 0.16 [J] (c) -0.078 [J] (d) 0.078 [J] (e) 0 11. Conservative. If the only forces that do work on a system are conservative, which of the following quantities must remain constant? (a) Kinetic Energy (b) Gravitational Potential Energy

(c) Elastic Potential Energy (d) Total Mechanical Energy

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

12. Cellphone. Jone’s cellphone with mass of 0.150 [kg] is placed on top of a table. Ana slid the cellphone to the right by a distance of 3.00 [m]. After seeing this, Jone immediately returned the cellphone back to its initial position by sliding it to the left by a distance of 3.00 [m]. If the coefficient of kinetic friction between the table and the cellphone is 0.0100, what is the total work done by kinetic friction on the cellphone? (a) 0 (b) 0.0441 [J] (c) 0.0883 [J] (d) -0.0441 [J] (e) -0.0883 [J] 13. Energy diagram. How many stable and unstable equilibrium points can you find in the figure? (a) 0 stable equilibrium points, 1 unstable equilibrium point (b) 1 stable equilibrium point, 0 unstable equilibrium points (c) 0 stable equilibrium points, 0 unstable equilibrium points (d) 2 stable equilibrium points, 1 unstable equilibrium point (e) 1 stable equilibrium point, 2 unstable equilibrium points 14. Axes. You throw a ball from the ground at an angle above the horizontal such that it follows the trajectory as shown at the right. Which of the following statements correctly describes the ball at the peak of its trajectory, point P? (a) It is in stable equilibrium. (b) It is in unstable equilibrium. (c) It is in neutral equilibrium. (d) It is not in equilibrium. 15. Thanks to Dobby. Remember that Harry was once unable to get to Platform 9 and3/4. If Harry weighed 491[N] then, and he was running towards the barrier at m 1.0 s , what is the magnitude of the average force that the barrier must m exert on him such that the contact time is just 0.010 [s]and he rebounds at 3.5 s ?

Physics 71/Second Long Exam A

(a) 2.3×104 [N]

(b) 1.3×104 [N]

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(c) 2.2×103 [N]

(d) 4.0 [N]

1st Sem AY 2011-2012

(e) 1.3 [N]

m 16. Impulse. The speed of a pitched baseball of mass 0.10 [kg] is 90. s . Right after m the ball is batted, it moves with a speed of 100. s in the direction opposite to its original velocity. What is the magnitude of the impulse of the net force on the ball during the collision? (a) 1.0 [N · s]

(b) 10 [N · s]

(c) 19 [N · s]

(d) 190 [N · s]

(e) 19,000 [N · s]

17. Conservation of Momentum. Which of the following statements regarding the law of conservation of momentum is FALSE? (a) It is valid only when internal forces in the system are conservative (b) It is valid even when internal forces in the system are non-conservative (c) It is valid only in inertial frames of reference (d) It is valid if vector sum of external forces is zero (e) It is valid if total rate of change of momentum of the entire system is zero 18. Skaters. In a figure skating competition, an 80.0-kg boy and a 60.0-kg girl collide and grab on to each other on very smooth ice so that both move with the same velocity afterwards. Before the collision, the boy was m moving to the right at 1.80 m s , while the girl was moving to the left at 2.50 s . What is their velocity just after the collision? (a) 4.29 × 10−2 [m/s] to the left (b) 4.29 × 10−2 [m/s] to the right (c) 2.1 [m/s] to the left

(d) 2.1 [m/s] to the right (e) 0

19. Gunman. A gunman holds a rifle tightly against his shoulder and fires the rifle horizontally using a 5.00 [g] bullet with an initial velocity of 350 [m/s]. The combined mass of the gunman and the rifle is 115 [kg] . What is the recoil velocity of the gunman with the rifle? (a) −1.52 × 10−2 ms (c) −1.64 × 10−2 ms (b) +1.52 × 10−2 ms (d) +1.64 × 10−2 ms

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

20. Ballistic Pendulum. A 5.00-[kg] box is suspended from the ceiling by a cord that is 50.0 [cm] long. A 10.0-[g] bullet was fired horizontally with speed at 350 [m/s] into the box. By how much will the vertical height of the pendulum change? (a) 2.48 [cm]

(b) 2.56 [cm]

(c) 3.12 [cm]

(d) 3.98 [cm]

(e) 4.21 [cm]

21. Standard collision. An object B of mass 2.0[kg]moving at 5.0 ms to the left strikes a stationary object A. A completely inelastic collision occurs and the composite object moves at 2.0 ms to the left. What is the mass of object A? (a) 1.0[kg]

(b) 2.0[kg]

(c) 3.0[kg]

(d) 4.0[kg]

(e) 5.0[kg]

22. Elastic Collision. A 1.00-[kg] m block is moving on a frictionless, horizontal air track with a speed of 0.800 s to the right. It makes a collision with another glider m that has a mass of 0.800-[kg] that is moving to the left with a speed of 2.50 s . What is the final velocity of the 0.800-[kg] glider after the elastic collision? (a) 1.17 ms to the right (d) 2.14 ms to the left (b) 1.17 ms to the left (e) 3.30 ms to the right (c) 2.14 ms to the right 23. Vectors. A point mass m is revolving with uniform speed in the clockwise direction along the circular path of radius R. The center of the circle coincides with the origin of the threedimensional rectangular coordinate system. At the instant shown in the figure, what is the correct order of the directions for the following vector quantities: net force on the mass, instantaneous velocity, and angular velocity of the mass? (a) Net force is zero; ˆj; ˆj (d) ˆi; ˆj; kˆ (b) Net force is zero; ˆj; −kˆ (e) ˆi; ˆj; −kˆ (c) ˆi; ˆj; ˆj

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

24. Constant speed. Anna and Bob are on a merry-go-round of radius R which rotates with constant angular speed. Anna is standing a distance R/2 from the center, while Bob is standing a distance 3R/4 from the center. Which of the following statements is/are TRUE? I. Bob and Anna have the same acceleration. II. Bob and Anna have the same linear speed. III. Bob and Anna have the same angular acceleration. (a) I only

(b) II only

(c) III only

(d) I and II only (e) I and III only

25. Circular Motion angular accel radconstant rad A body moving in a circular path has eration of 1.0 s2 . If its initial angular velocity is 5.0 s , what is its angular velocity after 2.0 [s]? rad rad rad rad (b) 7.0 (c) 2.0 (d) 3.0 (e) 1.0 (a) 9.0 rad s s s s s 26. Revolution. A rotating disk experiencing uniform angular acceleration starts from rest to an angular speed of 3.14 rad/s in 30.0 s. What is the magnitude of the angular acceleration of the disk? rad rad rad rad (a) 0.100 rad (b) 0.105 (c) 0.314 (d) 30.0 (e) 94.2 s2 s2 s2 s2 s2 27. Weight training. For the same total mass M of each given object, which has the greatest rotational kinetic energy if they both rotate with the same angular velocity about an axis perpendicular to its shaft? (a) A barbell with mass M concentrated near the ends of its 1.0-meter length rotating about the middle of its shaft. (b) A dumbbell with mass M concentrated near the ends of its 1.0-ft length rotating about the middle of its shaft. 28. Rotational Motion. A solid sphere, a ring and a spherical shell of the same masses and radii are made to roll without slipping along an incline with the same initial velocity v0 and the same initial height. Which of the following quantities are equal for all objects at the moment that each object reaches the bottom of the incline? (a) Translational kinetic energy (b) Rotational kinetic energy (c) Total kinetic energy (d) Time of descent

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

29. Solid cylinder. What is the moment of inertia of a uniform solid cylinder with a radius of 1.5[m]and mass 3.0[kg]about an axis along the edge of the cylinder and running parallel to its length? (a) 6.8 kg · m2 (d) 20. kg · m2 (b) 10. kg · m2 (e) 41 kg · m2 (c) 14. kg · m2 30. Parallel axis theorem. When a net external torque of magnitude 64.0 [N · m] is applied to a long uniform rod of mass 10.0 kg, it will rotate about its center of mass with angular acceleration rad of magnitude 1.57 s2 . If a torque of the same magnitude is applied to the same rod about a parallel axis 1.00m away from the original axis, what is the new magnitude of the angular acceleration? rad (a) 1.26 rad (d) 50.8 2 s s2 rad rad (b) 1.57 s2 (e) 74.0 s2 (c) 11.6 rad s2 31. Torque. Object B moves with constant speed in a circular path with radius R. It is acted upon by a single force Fa . What is the magnitude of the torque about the center of the circular path? (a) RFa . (b) zero (c) Cannot be obtained because the speed of the object is not given. 32. Seesaw. A 50.0-[kg] girl and a 60.0-[kg] boy sit on the opposite sides of a seesaw, each child a distance of 2.00[m]from the fulcrum. The boy sits on the side that is initially higher, so that the seesaw swings about the fulcrum. At the moment when the seesaw is horizontal, what is the net torque on the seesaw? (a) 20.0 [N · m]into the page (b) 20.0 [N · m]out of the page (c) 10.0 [N · m]into the page

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

(d) 10.0 [N · m]out of the page (e) The net torque is zero since the seesaw is horizontal. 33. Sleeping Beauty. Aurora is trying to spin thread on a wheel. She applies a force tangent to the wheel, giving it a torque of 2.0 [N · m]. If the wheel has a moment of inertia equal to 1.0 kg · m2 , what is the wheel’s angular acceleration? rev rev rad rad (b) 0.50 (d) 2.0 (c) 1.0 (e) 2.0 (a) 0.50 rad 2 2 2 2 s s s s s2 34. Angular dynamics. A disk of radius 0.120[m]and moment of inertia 1.44×10−4 kg · m2 is initially rad spinning with uniform angular speed of 21.0 s about a fixed axis perpendicular to its plane and passing through its center. You tried to stop it by applying a force of magnitude 0.100 [N]perpendicular to the thickness of the disk, as shown in the figure. If the coefficient of kinetic friction between your hand and the disk surface is 0.200, how long will it take before the disk comes to a full stop? (a) 2.40 × 10−3 s (b) 1.20 × 10−2 s (c) 0.252 s

(d) 1.26 s (e) 16.7 s

35. Keep ’em rollin’. The same amount of work is done on three identical disks, R, S, and T , all of which are initially at rest. R slides on top of a frictionless surface, S rotates about its stationary center of mass, and T rolls without slipping. Which disk gained the highest total kinetic energy? (a) R (b) S (c) T

(d) R and T (e) All have the same total kinetic energy.

36. Rolling Cylinder. A solid cylinder starts from rest and rolls without slipping down a hill. After its center of mass drops a total vertical distance of 2.0[m], what is the speed of the center of mass of the cylinder? (a) 3.1 ms (d) 5.1 ms (b) 3.8 ms (e) 6.3 ms (c) 4.4 ms

Physics 71/Second Long Exam A

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37. Weaker. A torque τ resulted in an angular speed ω with power P. If the torque is doubled, how much power will be measured when the resulting angular speed is half of the original value? (a) P/4 (b) P/2 (c) P (d) 2P (e) 4P 38. Energy DVD. Consider two very thin discs A and B. Disc A has twice the radius and half the mass of disc B. Each disc, initially at rest, is made to rotate about an axis through its center of mass perpendicular to the plane of the disc. Which disc requires greater energy in order to complete 1 revolution after 1 second? (a) Disc A (b) Disc B

(c) Both require the same amount of power

39. Angular momentum. A thin uniform rod of mass 1.12 [kg] and length 0.750 [m]that is initially at rest is pivoted at its center of mass. A constant net torque of magnitude 4.20 [N · m]is applied to the rod. After 2.00 [s], what is the angular momentum of the rod? i h i h kg·m2 kg·m2 (d) 160. s (a) 0.0525 s h i h i 2 kg·m2 (b) 8.40 kg·m (e) 212 s s h i 2 (c) 80.0 kg·m s 40. Collide. Two discs A and B, with moments of inertia Ia and Ib respectively, are attached to a horizontal rod through their centers of mass. A is rotating at an angular speed ωa while B is at rest. If we bring the two discs together by applying a force very near the axis (thereby applying negligible torque), what will be the resulting angular speed ω of the two discs? (a) ω = Ia ωa /(Ia + Ib ) (b) ω = Ia ωa /(Ia − Ib )

(c) ω = Ib ωa /(Ia + Ib ) (d) ω = Ib ωa /(Ia − Ib )

41. Conservative and nonconservative. A small box of mass 1.20 [kg] starts from rest at a height 4.25 [m]on top of a ramp inclined at 60◦ with respect to the horizontal. Upon release, the box slides down to a level surface of length 3.50 [m]before ascending again at another ramp inclined at 45◦ with respect to the horizontal. If all surfaces have constant coefficient of kinetic friction µ = 0.250, what is the maximum height h that the box can reach in the other incline? (a) 1.11 [m] (b) 2.21 [m] (c) 2.91 [m] (d) 3.50 [m] (e) 4.25 [m]

Physics 71/Second Long Exam A

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42. Loop-the-loop. A stunt man rides a sled through a loop-the-loop track of radius R. He is initially at a height h above the ground, as shown in the figure. Assuming that the track is frictionless, what is the minimum value of the height h for the stunt man to go through the loop-the-loop safely? (a) R/2

(b) R

(c) 3R/2

(d) 2R

End of Second Long Exam

(e) 5R/2

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Physics 71 Set A Second Long Exam First Semester AY 2011-2012

Name:

Instructor:

Section/Class Schedule:

Student Number:

Course:

College

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

Instructions: Choose the letter of the best answer. Ignore air resistance unless stated otherwise. The acceleration due to gravity is: g = 9.81 sm2 .

1. Push it. Leslie pushes a 10.0 [kg] cabinet horizontally on a level surface with an applied force of 25.0 [N]. If the cabinet slides on the surface by 5.00 [m], what is the work done by gravity on the cabinet? (a) 491 [J] (b) 125 [J] (c) -491 [J] (d) - 125 [J] (e) 0 2. Cable. A 10. [kg] object is hoisted by a cable whose tension is 140[N]. What is the total work done on the object as it moves 2.0[m]upward? (a) 42 [J]

(b) 84 [J]

(c) 130 [J]

(d) 260 [J]

(e) 280 [J]

3. Crash Collision. Two cars were moving in a collision course with each other, but Superman prevented the collision by stopping both cars with km his hands. Car A has a mass of 2000 [kg] and was moving with a speed of 200 h . Car B, which has a mass of 4000 [kg] , was approaching car A from the opposite direction with a speed km of 150 h . To which car did Superman do greater work? (a) car A (b) car B

(c) Equal amount of work will be done to both cars.

4. Falling. Romeo dropped a 0.0150 [kg] ring from rest at a 22.0-m high building. Juliet, who is directly below the falling ring, placed her hands on the ground. What is the speed of the ring just before it reaches Juliet’s hands? (a) 0 (b) 14.7 ms (c) 20.8 ms (d) 216 ms (e) 432 ms

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

5. Area under the curve. A force F is applied to a box of mass 2.0 [kg] parallel to the x-axis as it moves along a straight line. The x - component of the force varies with the x - coordinates of the box as shown below, with the force given in Newtons and the position in meters. What is the work done on the box by F as it moves from x = 1.0 to x = 5.0? (a) 0 [J]

(b) 4.0 [J]

(c) 10. [J]

(d) 20. [J]

(e) 25. [J]

6. Moving particle. A particle experiences a force, which acts along the x-axis, as described in the force vs. position plot shown. What is the work done by this force if it starts at x=2.0 m and ends at position x=0? (a) 0 J (b) 0.5 J (c) 1.0 J (d) -0.5 J (e) -1.0 J 7. K+U. You throw a rock straight up with initial speed v from the ground. Which of the following graphs can represent the rock’s mechanical energy, E, as a function of time while the rock is in air?

Physics 71/Second Long Exam A

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1st Sem AY 2011-2012

8. K-U. At time t = 0, you throw a rock straight up with initial speed v from the ground. Let K and U be the kinetic and potential energies of the particle, respectively, and let U=0 when the rock is on the ground. Which of the following graphs show the quantity K − U as a function of time?

9. Pellet Gun. A 0.10-kg pellet is launched straightup from a pellet gun, which N . Right before launching, contains a spring of spring constant k = 5.0 × 102 m the spring is compressed a distance 0.050 m, and the pellet is at rest. From this initial position, the pellet is observed to reach its maximum height at 0.40 m above its starting point. Find the work done by air resistance as the pellet goes from its starting point to its maximum height. (a) -0.23 [J] (b) -1.0 [J] (c) 0 [J] (d) 0.23 [J] (e) 1.0 [J] 10. Glider. A 0.45 [kg] glider that sits on a frictionless air track is connected to a spring with spring constant 2.5 [N/m]. Initially, the spring is unstretched so that the glider is in equilibrium. Patty then stretches the glider by a distance of 0.25 [m]. What is the work done by the spring on the glider? (a) -0.16 [J] (b) 0.16 [J] (c) -0.078 [J] (d) 0.078 [J] (e) 0 11. Conservative. If the only forces that do work on a system are conservative, which of the following quantities must remain constant? (a) Kinetic Energy (b) Gravitational Potential Energy

(c) Elastic Potential Energy (d) Total Mechanical Energy

Physics 71/Second Long Exam A

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12. Cellphone. Jone’s cellphone with mass of 0.150 [kg] is placed on top of a table. Ana slid the cellphone to the right by a distance of 3.00 [m]. After seeing this, Jone immediately returned the cellphone back to its initial position by sliding it to the left by a distance of 3.00 [m]. If the coefficient of kinetic friction between the table and the cellphone is 0.0100, what is the total work done by kinetic friction on the cellphone? (a) 0 (b) 0.0441 [J] (c) 0.0883 [J] (d) -0.0441 [J] (e) -0.0883 [J] 13. Energy diagram. How many stable and unstable equilibrium points can you find in the figure? (a) 0 stable equilibrium points, 1 unstable equilibrium point (b) 1 stable equilibrium point, 0 unstable equilibrium points (c) 0 stable equilibrium points, 0 unstable equilibrium points (d) 2 stable equilibrium points, 1 unstable equilibrium point (e) 1 stable equilibrium point, 2 unstable equilibrium points 14. Axes. You throw a ball from the ground at an angle above the horizontal such that it follows the trajectory as shown at the right. Which of the following statements correctly describes the ball at the peak of its trajectory, point P? (a) It is in stable equilibrium. (b) It is in unstable equilibrium. (c) It is in neutral equilibrium. (d) It is not in equilibrium. 15. Thanks to Dobby. Remember that Harry was once unable to get to Platform 9 and3/4. If Harry weighed 491[N] then, and he was running towards the barrier at m 1.0 s , what is the magnitude of the average force that the barrier must m exert on him such that the contact time is just 0.010 [s]and he rebounds at 3.5 s ?

Physics 71/Second Long Exam A

(a) 2.3×104 [N]

(b) 1.3×104 [N]

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(c) 2.2×103 [N]

(d) 4.0 [N]

1st Sem AY 2011-2012

(e) 1.3 [N]

m 16. Impulse. The speed of a pitched baseball of mass 0.10 [kg] is 90. s . Right after m the ball is batted, it moves with a speed of 100. s in the direction opposite to its original velocity. What is the magnitude of the impulse of the net force on the ball during the collision? (a) 1.0 [N · s]

(b) 10 [N · s]

(c) 19 [N · s]

(d) 190 [N · s]

(e) 19,000 [N · s]

17. Conservation of Momentum. Which of the following statements regarding the law of conservation of momentum is FALSE? (a) It is valid only when internal forces in the system are conservative (b) It is valid even when internal forces in the system are non-conservative (c) It is valid only in inertial frames of reference (d) It is valid if vector sum of external forces is zero (e) It is valid if total rate of change of momentum of the entire system is zero 18. Skaters. In a figure skating competition, an 80.0-kg boy and a 60.0-kg girl collide and grab on to each other on very smooth ice so that both move with the same velocity afterwards. Before the collision, the boy was m moving to the right at 1.80 m s , while the girl was moving to the left at 2.50 s . What is their velocity just after the collision? (a) 4.29 × 10−2 [m/s] to the left (b) 4.29 × 10−2 [m/s] to the right (c) 2.1 [m/s] to the left

(d) 2.1 [m/s] to the right (e) 0

19. Gunman. A gunman holds a rifle tightly against his shoulder and fires the rifle horizontally using a 5.00 [g] bullet with an initial velocity of 350 [m/s]. The combined mass of the gunman and the rifle is 115 [kg] . What is the recoil velocity of the gunman with the rifle? (a) −1.52 × 10−2 ms (c) −1.64 × 10−2 ms (b) +1.52 × 10−2 ms (d) +1.64 × 10−2 ms

Physics 71/Second Long Exam A

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20. Ballistic Pendulum. A 5.00-[kg] box is suspended from the ceiling by a cord that is 50.0 [cm] long. A 10.0-[g] bullet was fired horizontally with speed at 350 [m/s] into the box. By how much will the vertical height of the pendulum change? (a) 2.48 [cm]

(b) 2.56 [cm]

(c) 3.12 [cm]

(d) 3.98 [cm]

(e) 4.21 [cm]

21. Standard collision. An object B of mass 2.0[kg]moving at 5.0 ms to the left strikes a stationary object A. A completely inelastic collision occurs and the composite object moves at 2.0 ms to the left. What is the mass of object A? (a) 1.0[kg]

(b) 2.0[kg]

(c) 3.0[kg]

(d) 4.0[kg]

(e) 5.0[kg]

22. Elastic Collision. A 1.00-[kg] m block is moving on a frictionless, horizontal air track with a speed of 0.800 s to the right. It makes a collision with another glider m that has a mass of 0.800-[kg] that is moving to the left with a speed of 2.50 s . What is the final velocity of the 0.800-[kg] glider after the elastic collision? (a) 1.17 ms to the right (d) 2.14 ms to the left (b) 1.17 ms to the left (e) 3.30 ms to the right (c) 2.14 ms to the right 23. Vectors. A point mass m is revolving with uniform speed in the clockwise direction along the circular path of radius R. The center of the circle coincides with the origin of the threedimensional rectangular coordinate system. At the instant shown in the figure, what is the correct order of the directions for the following vector quantities: net force on the mass, instantaneous velocity, and angular velocity of the mass? (a) Net force is zero; ˆj; ˆj (d) ˆi; ˆj; kˆ (b) Net force is zero; ˆj; −kˆ (e) ˆi; ˆj; −kˆ (c) ˆi; ˆj; ˆj

Physics 71/Second Long Exam A

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24. Constant speed. Anna and Bob are on a merry-go-round of radius R which rotates with constant angular speed. Anna is standing a distance R/2 from the center, while Bob is standing a distance 3R/4 from the center. Which of the following statements is/are TRUE? I. Bob and Anna have the same acceleration. II. Bob and Anna have the same linear speed. III. Bob and Anna have the same angular acceleration. (a) I only

(b) II only

(c) III only

(d) I and II only (e) I and III only

25. Circular Motion angular accel radconstant rad A body moving in a circular path has eration of 1.0 s2 . If its initial angular velocity is 5.0 s , what is its angular velocity after 2.0 [s]? rad rad rad rad (b) 7.0 (c) 2.0 (d) 3.0 (e) 1.0 (a) 9.0 rad s s s s s 26. Revolution. A rotating disk experiencing uniform angular acceleration starts from rest to an angular speed of 3.14 rad/s in 30.0 s. What is the magnitude of the angular acceleration of the disk? rad rad rad rad (a) 0.100 rad (b) 0.105 (c) 0.314 (d) 30.0 (e) 94.2 s2 s2 s2 s2 s2 27. Weight training. For the same total mass M of each given object, which has the greatest rotational kinetic energy if they both rotate with the same angular velocity about an axis perpendicular to its shaft? (a) A barbell with mass M concentrated near the ends of its 1.0-meter length rotating about the middle of its shaft. (b) A dumbbell with mass M concentrated near the ends of its 1.0-ft length rotating about the middle of its shaft. 28. Rotational Motion. A solid sphere, a ring and a spherical shell of the same masses and radii are made to roll without slipping along an incline with the same initial velocity v0 and the same initial height. Which of the following quantities are equal for all objects at the moment that each object reaches the bottom of the incline? (a) Translational kinetic energy (b) Rotational kinetic energy (c) Total kinetic energy (d) Time of descent

Physics 71/Second Long Exam A

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29. Solid cylinder. What is the moment of inertia of a uniform solid cylinder with a radius of 1.5[m]and mass 3.0[kg]about an axis along the edge of the cylinder and running parallel to its length? (a) 6.8 kg · m2 (d) 20. kg · m2 (b) 10. kg · m2 (e) 41 kg · m2 (c) 14. kg · m2 30. Parallel axis theorem. When a net external torque of magnitude 64.0 [N · m] is applied to a long uniform rod of mass 10.0 kg, it will rotate about its center of mass with angular acceleration rad of magnitude 1.57 s2 . If a torque of the same magnitude is applied to the same rod about a parallel axis 1.00m away from the original axis, what is the new magnitude of the angular acceleration? rad (a) 1.26 rad (d) 50.8 2 s s2 rad rad (b) 1.57 s2 (e) 74.0 s2 (c) 11.6 rad s2 31. Torque. Object B moves with constant speed in a circular path with radius R. It is acted upon by a single force Fa . What is the magnitude of the torque about the center of the circular path? (a) RFa . (b) zero (c) Cannot be obtained because the speed of the object is not given. 32. Seesaw. A 50.0-[kg] girl and a 60.0-[kg] boy sit on the opposite sides of a seesaw, each child a distance of 2.00[m]from the fulcrum. The boy sits on the side that is initially higher, so that the seesaw swings about the fulcrum. At the moment when the seesaw is horizontal, what is the net torque on the seesaw? (a) 20.0 [N · m]into the page (b) 20.0 [N · m]out of the page (c) 10.0 [N · m]into the page

Physics 71/Second Long Exam A

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(d) 10.0 [N · m]out of the page (e) The net torque is zero since the seesaw is horizontal. 33. Sleeping Beauty. Aurora is trying to spin thread on a wheel. She applies a force tangent to the wheel, giving it a torque of 2.0 [N · m]. If the wheel has a moment of inertia equal to 1.0 kg · m2 , what is the wheel’s angular acceleration? rev rev rad rad (b) 0.50 (d) 2.0 (c) 1.0 (e) 2.0 (a) 0.50 rad 2 2 2 2 s s s s s2 34. Angular dynamics. A disk of radius 0.120[m]and moment of inertia 1.44×10−4 kg · m2 is initially rad spinning with uniform angular speed of 21.0 s about a fixed axis perpendicular to its plane and passing through its center. You tried to stop it by applying a force of magnitude 0.100 [N]perpendicular to the thickness of the disk, as shown in the figure. If the coefficient of kinetic friction between your hand and the disk surface is 0.200, how long will it take before the disk comes to a full stop? (a) 2.40 × 10−3 s (b) 1.20 × 10−2 s (c) 0.252 s

(d) 1.26 s (e) 16.7 s

35. Keep ’em rollin’. The same amount of work is done on three identical disks, R, S, and T , all of which are initially at rest. R slides on top of a frictionless surface, S rotates about its stationary center of mass, and T rolls without slipping. Which disk gained the highest total kinetic energy? (a) R (b) S (c) T

(d) R and T (e) All have the same total kinetic energy.

36. Rolling Cylinder. A solid cylinder starts from rest and rolls without slipping down a hill. After its center of mass drops a total vertical distance of 2.0[m], what is the speed of the center of mass of the cylinder? (a) 3.1 ms (d) 5.1 ms (b) 3.8 ms (e) 6.3 ms (c) 4.4 ms

Physics 71/Second Long Exam A

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37. Weaker. A torque τ resulted in an angular speed ω with power P. If the torque is doubled, how much power will be measured when the resulting angular speed is half of the original value? (a) P/4 (b) P/2 (c) P (d) 2P (e) 4P 38. Energy DVD. Consider two very thin discs A and B. Disc A has twice the radius and half the mass of disc B. Each disc, initially at rest, is made to rotate about an axis through its center of mass perpendicular to the plane of the disc. Which disc requires greater energy in order to complete 1 revolution after 1 second? (a) Disc A (b) Disc B

(c) Both require the same amount of power

39. Angular momentum. A thin uniform rod of mass 1.12 [kg] and length 0.750 [m]that is initially at rest is pivoted at its center of mass. A constant net torque of magnitude 4.20 [N · m]is applied to the rod. After 2.00 [s], what is the angular momentum of the rod? i h i h kg·m2 kg·m2 (d) 160. s (a) 0.0525 s h i h i 2 kg·m2 (b) 8.40 kg·m (e) 212 s s h i 2 (c) 80.0 kg·m s 40. Collide. Two discs A and B, with moments of inertia Ia and Ib respectively, are attached to a horizontal rod through their centers of mass. A is rotating at an angular speed ωa while B is at rest. If we bring the two discs together by applying a force very near the axis (thereby applying negligible torque), what will be the resulting angular speed ω of the two discs? (a) ω = Ia ωa /(Ia + Ib ) (b) ω = Ia ωa /(Ia − Ib )

(c) ω = Ib ωa /(Ia + Ib ) (d) ω = Ib ωa /(Ia − Ib )

41. Conservative and nonconservative. A small box of mass 1.20 [kg] starts from rest at a height 4.25 [m]on top of a ramp inclined at 60◦ with respect to the horizontal. Upon release, the box slides down to a level surface of length 3.50 [m]before ascending again at another ramp inclined at 45◦ with respect to the horizontal. If all surfaces have constant coefficient of kinetic friction µ = 0.250, what is the maximum height h that the box can reach in the other incline? (a) 1.11 [m] (b) 2.21 [m] (c) 2.91 [m] (d) 3.50 [m] (e) 4.25 [m]

Physics 71/Second Long Exam A

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42. Loop-the-loop. A stunt man rides a sled through a loop-the-loop track of radius R. He is initially at a height h above the ground, as shown in the figure. Assuming that the track is frictionless, what is the minimum value of the height h for the stunt man to go through the loop-the-loop safely? (a) R/2

(b) R

(c) 3R/2

(d) 2R

End of Second Long Exam

(e) 5R/2

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