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Student _______________ 4 Momentum & WEP Physics Regents Date __________ 1. As shown in the diagram below, an open box and its contents have a combined mass of 5.0 kilograms. A horizontal force of 15 newtons is required to push the box at a constant speed of 1.5 meters per second across a level surface. The inertia of the box and its contents increases if there is an increase in the A) B) C) D) speed of the box mass of the contents of the box magnitude of the horizontal force applied to the box coefficient of kinetic friction between the box and the level surface 2. Cart A has a mass of 2 kilograms and a speed of 3 meters per second. Cart B has a mass of 3 kilograms and a speed of 2 meters per second. Compared to the inertia and magnitude of momentum of cart A, cart B has A) the same inertia and a smaller magnitude of momentum B) the same inertia and the same magnitude of momentum C) greater inertia and a smaller magnitude of momentum D) greater inertia and the same magnitude of momentum 3. A laboratory cart with a mass of 5 kilograms rolls through a distance of 2 meters in 10 seconds. Which of the following mathematical statements can be used to determine the momentum? A) 5 kg × 2m/10s C) 5kg + 2m/l0s B) 5 kg × 10s/2m D) 5 kg + 10s/2m 4. Two rocks weighing 5 Newtons and 10 Newtons, respectively, fall freely from rest near the Earth's surface. After 3 seconds of free-fall, compared to the 5-newton rock, the 10-newton rock has greater A) acceleration C) momentum 5. A 25-kilogram mass travels east with a constant velocity of 40. meters per second. The momentum of this mass is A) B) C) D) 1.0 × 10 3 kg-m/s east 9.8 × 10 3 kg-m/s east 1.0 × 10 3 kg-m/s west 9.8 × 10 3 kg-m/s west 6. A motorcycle being driven on a dirt path hits a rock. Its 60.-kilogram cyclist is projected over the handlebars at 20. meters per second into a haystack. If the cyclist is brought to rest in 0.50 second, the magnitude of the average force exerted on the cyclist by the haystack is A) 6.0 × 10 1 N C) 1.2 ×10 3 N B) 5.9 ×10 2 N D) 2.4 × 10 3 N 7. Which situation will produce the greatest change of momentum for a 1.0-kilogram cart? A) B) C) D) accelerating it from rest to 3.0 m/s accelerating it from 2.0 m/s to 4.0 m/s applying a net force of 5.0 N for 2.0 s applying a net force of 10.0 N for 0.5 s B) height D) speed Page 1 4 Momentum & WEP 8. During a collision, an 84-kilogram driver of a car moving at 24 meters per second is brought to rest by an inflating air bag in 1.2 seconds. The magnitude of the force exerted on the driver by the air bag is approximately A) 7.0 × 10 1 N C) 1.7 × 10 3 N B) 8.2 × 10 2 N D) 2.0 × 10 3 N 9. Two cars having different weights are traveling on a level surface at different constant velocities. Within the same time interval, greater force will always be required to stop the car that has greater A) weight C) velocity B) kinetic energy D) momentum 10. An object is brought to rest by a constant force. Which factor other than the mass and velocity of the object must be known in order to determine the magnitude of the force required to stop the object? A) B) C) D) the time that the force acts on the object the gravitational potential energy of the object the density of the object the weight of the object 11. A 0.025-kilogram bullet is fired from a rifle by an unbalanced force of 200 Newtons. If the force acts on the bullet for 0.1 second, what is the maximum speed attained by the bullet? A) 5 m/s C) 400 m/s B) 20 m/s D) 800 m/s 12. A 1.0-kilogram mass changes speed from 2.0 meters per second to 5.0 meters per second. The change in the object's momentum is A) 9.0 kg-m/sec C) 3.0 kg-m/sec B) 21 kg-m/sec D) 29 kg-m/sec Page 2 4 Momentum & WEP 13. Base your answer to the following question on the information and diagram below. Block A moves with a velocity of 2 meters per second to the right, as shown in the diagram, and then collides elastically with block B, which is at rest. Block A stops moving, and block B moves to the right after the collision. What is the total change in momentum of blocks A and B ? A) B) C) D) 14. Base your answer to the following question on the information and diagram below. The diagram shows a compressed spring between two carts initially at rest on a horizontal frictionless surface. Cart A has a mass of 2 kilograms and cart B has a mass of 1 kilogram. A string holds the carts together. After the string is cut and the two carts move apart, the magnitude of which quantity is the same for both carts? A) momentum B) velocity C) inertia D) kinetic energy 15. A 2-kilogram object traveling 10 meters per second north has a perfect elastic collision with a 5-kilogram object traveling 4 meters per second south. What is the total momentum after collision? A) 0 kg-m/s C) 20 kg-m/s south B) 20 kg-m/s north D) 40 kg-m/s east Page 3 4 Momentum & WEP 16. The diagram below represents two masses before 18. The diagram below shows a 4.0-kilogram cart and after they collide. Before the collision, mass mA moving to the right and a 6.0-kilogram cart moving is moving to the right with speed v, and mass mB is to the left on a horizontal frictionless surface. at rest. Upon collision, the two masses stick together. Which expression represents the speed, v', of the masses after the collision? [Assume no outside forces are acting on mA or mB.] A) B) C) D) 17. In the diagram below, a block of mass initially at rest on a frictionless horizontal surface is struck by a bullet of mass moving with horizontal velocity . When the two carts collide they lock together. The magnitude of the total momentum of the two-cart system after the collision is A) 0.0 kg•m/s C) 15 kg•m/s B) 6.0 kg•m/s D) 30. kg•m/s 19. A 2-kilogram car and a 3-kilogram car are originally at rest on a horizontal frictionless surface as shown in the diagram below. A compressed spring is released causing the cars to separate. The 3-kilogram car reaches a maximum speed of 2 meters per second. What is the maximum speed of the 2-kilogram car? A) 1 m/s B) 2 m/s C) 3 m/s D) 6 m/s What is the velocity of the bullet-block system after the bullet embeds itself in the block? A) B) C) D) 20. A 75-kilogram bicyclist coasts down a hill at a constant speed of 12 meters per second. What is the kinetic energy of the bicyclist? A) 4.5 C) 5.4 10 2 J 10 3 J B) 9.0 D) 1.1 10 2 J l0 4 J 21. Which cart shown below has the greatest kinetic energy? A) B) C) D) Page 4 4 Momentum & WEP 22. If the velocity of a moving object is doubled, the object's kinetic energy is A) unchanged C) doubled B) halved D) quadrupled 23. A shopping cart slows as it moves along a level floor. Which statement describes the energies of the cart? A) The kinetic energy increases and the gravitational potential energy remains the same. B) The kinetic energy increases and the gravitational potential energy decreases. C) The kinetic energy decreases and the gravitational potential energy remains the same. D) The kinetic energy decreases and the gravitational potential energy increases. 24. A car travels at constant speed v up a hill from point A to point B, as shown in the diagram below. 25. A pendulum is pulled to the side and released from rest. Which graph best represents the relationship between the gravitational potential energy of the pendulum and its displacement from its point of release? A) B) C) D) 26. The diagram below shows a 1.5-kilogram kitten jumping from the top of a 1.80-meter-high refrigerator to a 0.90-meter-high counter. As the car travels from A to B, its gravitational potential energy A) increases and its kinetic energy decreases B) increases and its kinetic energy remains the same C) remains the same and its kinetic energy decreases D) remains the same and its kinetic energy remains the same Compared to the kitten's gravitational potential energy on top of the refrigerator, the kitten's gravitational potential energy on top of the counter is A) half as great B) twice as great C) one-fourth as great D) four times as great 27. A vertical spring has a spring constant of 100. newtons per meter. When an object is attached to the bottom of the spring, the spring changes from its unstretched length of 0.50 meter to a length of 0.65 meter. The magnitude of the weight of the attached object is A) 1.1 N B) 15 N C) 50. N D) 65 N Page 5 4 Momentum & WEP 28. A vertical spring 0.100 meters long is elongated to a length of 0.119 meters when a 1.00-kilogram mass is attached to the bottom of the spring. The spring constant of this spring is A) 9.8 N/m C) 98 N/m B) 82 N/m D) 520 N/m 29. The graph below shows elongation as a function of the applied force for two springs, A and B. 31. A 60.-kilogram student climbs a ladder a vertical distance of 4.0 meters in 8.0 seconds. Approximately how much total work is done against gravity by the student during the climb? A) 2.4 × 10 3 J C) 2.4 ×10 2 J B) 2.9 × 10 2 J D) 3.0 × 10 1 J 32. What force is required to do 60 joules of work in sliding an object a distance of 10 meters across a level floor? A) 6 N C) 60 N B) 10 N D) 600 N 33. The graph below represents the relationship between the force exerted on an elevator and the distance the elevator is lifted. Compared to the spring constant for spring A, the spring constant for spring B is A) smaller C) the same B) larger 30. The graph below shows the relationship between the elongation of a spring and the force applied to the spring causing it to stretch. How much total work is done by the force in lifting the elevator from 0.0 m to 9.0 m? A) C) B) D) What is the spring constant for this spring? A) 0.020 N/m C) 25 N/m B) 2.0 N/m D) 50. N/m Page 6 4 Momentum & WEP 34. As shown in the diagram below, a student exerts an average force of 600. newtons on a rope to lift a 50.0-kilogram crate a vertical distance of 3.00 meters. Compared to the work done by the student, the gravitational potential energy gained by the crate is A) exactly the same C) 330 J more B) 330 J less D) 150 J more 35. A box is dragged up an incline a distance of 8 meters with a force of 50 Newtons. If the increase in potential energy of the box is 300 joules, the work done against friction is A) 100 J B) 200 J C) 300 J D) 400 J 36. The graph below represents the work done against gravity by a student as she walks up a flight of stairs at constant speed. Compared to the power generated by the student after 2.0 seconds, the power generated by the student after 4.0 seconds is A) the same C) half as great B) twice as great D) four times as great Page 7 4 Momentum & WEP 37. A 70.-kilogram cyclist develops 210 watts of power while pedaling at a constant velocity of 7.0 meters per second east. What average force is exerted eastward on the bicycle to maintain this constant speed? A) 490 N C) 3.0 N 40. The diagram below shows a 0.1-kilogram apple attached to a branch of a tree 2 meters above a spring on the ground below. B) 30. N D) 0 N 38. A 3.0-kilogram block is initially at rest on a frictionless, horizontal surface. The block is moved 8.0 meters in 2.0 seconds by the application of a 12-newton horizontal force, as shown in the diagram below. What is the average power developed while moving the block? A) 24 W B) 32 W C) 48 W D) 96 W The apple falls and hits the spring, compressing it 0.1 meter from its rest position. If all of the gravitational potential energy of the apple on the tree is transferred to the spring when it is compressed, what is the spring constant of this spring? A) 10 N/m C) 100 N/m B) 40 N/m D) 400 N/m 41. In the diagram below, an average force of 20. Newtons is used to pull back the string of a bow 0.60 meter. 39. The diagram below represents a 155-newton box on a ramp. Applied force F causes the box to slide from point A to point B. As the arrow, leaves the bow, its kinetic energy is A) 3.4 J B) 6.0 J C) 12 J What is the total amount of gravitational potential energy gained by the box? A) 28.4 J C) 868 J B) 279 J D) 2740 J D) 33 J 42. The diagram below shows a moving, 5.00-kilogram cart at the foot of a hill 10.0 meters high. For the cart to reach the top of the hill, what is the minimum kinetic energy of the cart in the position shown? [Neglect energy loss due to friction.] A) 4.91 J C) 250. J B) 50.0 J D) 491 J Page 8 4 Momentum & WEP 43. A wound spring provides the energy to propel a toy car across a level floor. At time t i,the car is moving-at speed v i across the floor and the spring is unwinding, as shown below. At time t f, the spring has fully unwound and the car has coasted to a stop. Which statement best describes the transformation of energy that occurs between the t i and t f? A) Gravitational potential energy at t i is converted to internal energy at t f. B) Elastic potential energy at t i is converted to kinetic energy at t f. C) Both elastic potential energy and kinetic energy at t i are converted to internal energy at t f. D) Both kinetic energy and internal energy at t i are converted to elastic potential energy at t f. 44. The graph below represents the kinetic energy, gravitational potential energy, and total mechanical energy of a moving block. Which best describes the motion of the block? A) B) C) D) accelerating on a flat horizontal surface sliding up a frictionless incline falling freely being lifted at constant velocity 45. A child, starting from rest at the top of a playground slide, reaches a speed of 7.0 meters per second at the bottom of the slide. What is the vertical height of the slide? [Neglect friction.] A) 0.71 m C) 2.5 m B) 1.4 m D) 3.5 m Page 9 4 Momentum & WEP 46. Base your answer to the following question on the diagram below. Which represents a 2.0-kilogram mass placed on a frictionless track at point A and released from rest. Assume the gravitational potential energy of the system to be zero at point E. Compared to the total mechanical energy of the system at point A, the total mechanical energy of the system at point F is A) less B) more C) the same 47. A block slides across a rough, horizontal tabletop. As the block comes to rest, there is an increase in the block-tabletop system's A) B) C) D) gravitational potential energy elastic potential energy kinetic energy internal (thermal) energy 48. When a spring is compressed 2.50 x 10 –2 meter from its equilibrium position, the total potential energy stored in the spring is 1.25 x 10 –2 joule. Calculate the spring constant of the spring. [Show all work, including the equation and substitution with units.] 49. A spring gains 2.34 joules of elastic potential energy as it is compressed 0.250 meter from its equilibrium position. What is the spring constant of this spring? A) 9.36 N/m C) 37.4 N/m B) 18.7 N/m D) 74.9 N/m Page 10 4 Momentum & WEP Base your answers to questions 50 through 53 on the information below. In a laboratory investigation, a student applied various downward forces to a vertical spring. The applied forces and the corresponding elongations of the spring from its equilibrium position are recorded in the data table below. Directions: Construct a graph on the grid below, following the directions below. 50. Using your graph, calculate the spring constant of this spring. [Show all work, including the equation and substitution with units.] Page 11 4 Momentum & WEP 51. Plot the data points for force versus elongation. 52. Mark an appropriate scale on the axis labeled "Force (N)." 53. Draw the best-fit line or curve. Base your answers to questions 54 and 55 on the information and graph below. The graph represents the relationship between the force applied to each of two springs, A and B, and their elongations. 54. What physical quantity is represented by the slope of each line? 55. A 1.0-kilogram mass is suspended from each spring. If each mass is at rest, how does the potential energy stored in spring A compare to the potential energy stored in spring B? Page 12