# PHYS 101 Previous Exam Problems. Force & Motion I

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1 PHYS 101 Previous Exam Problems CHAPTER 5 Force & Motion I Newton s Laws Vertical motion Horizontal motion Mixed forces Contact forces Inclines General problems 1. A 5.0-kg block is lowered with a downward acceleration of.8 m/s by means of a rope. What is the force of the block on the rope? (Ans: 35 N, down). An elevator of mass 480 kg is designed to carry a maximum load of 3000 N. What is the tension in the elevator cable at the maximum load when the elevator moves down accelerating at 9.8 m/s? (Ans: 0) 3. A.00-kg mass is hanging from the ceiling of an elevator accelerating upward at a =.50 m/s (see figure 1). What is the tension T in the string? (Ans: 4.6 N) 4. An object is hung from a spring balance attached to the ceiling of an elevator. The balance reads 70 N when the elevator is at rest. What is the reading of the spring balance when the elevator is moving upward with an acceleration of 4.9 m/s? (Ans: 105 N) 5. A 70-kg man stands on a spring scale in an elevator that has a downward acceleration of.8 m/s. What will the scale read? (Ans: 490 N) 6. A monkey hangs vertically from a rope in a descending elevator that decelerates at.4 m/s. If the tension in the rope is 400 N, find the mass of the monkey. (Ans: 33 kg) 7. Two students are dragging a box (m = 100 kg) across a horizontal frozen lake. The first student pulls with force F1 = 50.0 N, while the second one pulls with force F. The box is moving in the x direction with acceleration a (see figure ). Assuming that friction is negligible, what is F? (Ans: 86.6 N) 8. Only two forces act upon a 5.0-kg box. One of the forces is F1 = 6.0 î ĵ (N). If the box moves with a constant velocity of v = 1.6 î +1. ĵ (m/s), what is the magnitude of the second force? (Ans: 10 N) 9. Three forces act on a particle of mass 1.0 kg that moves with constant velocity v = (5.0 î ĵ ) (m/s). Two of the forces are F 1 (Ans:.0 î ĵ kˆ N) = (6.0 î ĵ.0 kˆ ) (N) and F = (-8.0 î ĵ 5.0 kˆ ) (N). What is the third force? 10. A car of mass 1000 kg is initially at rest. It moves along a straight road for 0 s and then comes to rest again. The velocity time graph for the movement is given in figure 4. What is the magnitude of the net force that acts on the car while it is slowing down to stop from t = 15 s to t = 0 s? (Ans: 000N) 11. A 0.0-kg block is resting on a frictionless horizontal table. A horizontal string pulls the block. If the tension in the string is 0.0 N, what is the speed of the block after moving.0 m? (Ans:.0 m/s) Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 1

2 1. A block of mass.0 kg is being pushed by a force parallel to the ground, as shown in figure 5. The block is observed to have an acceleration of 1.0 m/s down the incline. Assume the incline is frictionless. Calculate the magnitude of the force. (Ans: 9.0 N) 13. In figure 6, a 5-kg box is pushed across a frictionless horizontal floor with a force of 0 N, directed at an angle of 0 o below the horizontal. What is the magnitude of the acceleration of the box? (Ans: 0.75 m/s ) 14. A.0-kg box slides down a frictionless vertical wall while you push on it with a force F at a 30 with the vertical (see figure 7). What is the magnitude of the normal force of the wall on the box if it is to slide down at constant speed? (Ans: 11.3 N) 15. A.3-N weight is suspended by a string from a ceiling and held at an angle θ from the vertical by a 4.0-N horizontal force F, as shown in figure 8. What is the magnitude of the tension in the string? (Ans: 4.6 N) 16. The weight of an astronaut on Earth is 800 N. What is his weight on planet Mars, where g = 3.76 m/s? (Ans: 307 N) 17. A constant force F of magnitude 0 N is applied to block A of mass m = 4.0 kg, which pushes block B, as shown in figure 9. The block slides over a frictionless flat surface with an acceleration of.0 m/s. What is the net force on block B? (Ans:1 N, to the right) 18. Three equal mass blocks each of mass.0 kg move together over a horizontal frictionless surface. Two forces, F o angle 1 = 40 î (N) and F = 10 î (N) are applied on the three-mass system (see figure 10). What is the net force on the middle mass? (Ans: 10 î N) 19. Figure 11 shows block A of mass 6.0 kg and block B of mass 8.0 kg connected by a rigid rod of negligible mass. Force F a = 16 î (N) acts on block A and force F b = 30 î (N) acts on block B. What is the tension in the rod? (Neglect friction) (Ans: N) 0. Two blocks are in contact on a frictionless table. A horizontal force is applied to block m, as shown in figure 1. If m 1 = 3 kg, m = kg, and F = 5 N, find the magnitude of the force between the two blocks. (Ans: 3 N) 1. Two blocks of masses m 1 =.0 kg and m = 3.0 kg are connected as shown in figure 13. Find the tension T if T 1 = 50 N. (Ans: 30 N). In the system shown in figure 14, a horizontal force F acts on the 8.0-kg object. The horizontal surface is frictionless. What is the magnitude of F if the 5.0-kg object has a downward acceleration of 1.0 m/s? (Ans: 54 N) 3. A.0-kg mass has a velocity of (.0 î +.0 ĵ ) m/s at one instant. Four seconds later, its velocity is (.0 î +14 ĵ ) m/s. Assuming that the object is under the influence of a single constant force, find this force. (Ans: 6.0 ĵ N) 4. Three books (X, Y, and Z) rest on a table as shown in figure 16. The weight of each book is also indicated in the figure. What is the magnitude of the force of book Z on book Y? (Ans: 9 N) 5. A 4.0-kg block is pushed up a 30 inclined frictionless plane with a constant horizontal force F (figure 17). If the block moves with constant speed, find the magnitude of the force F. (Ans: 3 N) 6. A 3.0-kg block slides on a frictionless 37 incline plane. A vertical force of 15 N is applied to the block (see figure 18). What is the acceleration of the block? (Ans:.9 m/s down the incline) Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page

3 7. A block with m 1 = 5.7 kg on a frictionless 30 inclined plane is connected by a cord over a massless frictionless pulley to a second block with m = 3.5 kg hanging vertically as shown in figure 19. What is the acceleration of m? (Ans: 0.69 m/s downward) 8. When a 40-N force, parallel to an incline and directed up the incline, is applied to a crate on a frictionless incline that is 30 o above the horizontal, the acceleration of the crate is.0 m/s, down the incline. Find the mass of the crate. (Ans: 14 kg) 9. Two boxes, one of mass m = 5.00 kg and the other with an unknown mass M, are connected with a string passing over a massless frictionless pulley and are placed on frictionless planes, as shown in figure 0.What must be the mass M, if it goes down the plane with an acceleration of a =.45 m/s? (Ans: 19.1 kg) 30. Two equal-mass blocks rest on frictionless surfaces, as in figure 1. Assuming the pulleys to be light and frictionless, find the time required for block A to move 0.5 m down the incline, starting from rest. (Ans: 0.64 s) 31. Two blocks of masses m 1 = 4.00 kg and m =.00 kg are connected by a string passing over a massless and frictionless pulley and placed on a frictionless horizontal table, as shown in figure. A force of F = 10.0 N at an angle of 60.0 with the horizontal is applied to m 1. What is the magnitude of the acceleration of the system? (Ans:.43 m/s ) 3. Two blocks of masses m1 = 5.0 kg and m = 10 kg are connected by a massless rod and slide on a frictionless 30 incline as shown in figure 3. What is the tension in the rod? (Ans: zero) 33. Two masses m1 = kg and m = 4 kg are connected by a light string that passes over a frictionless and massless pulley (see figure 4). Find the magnitude of the acceleration of the masses. (Ans: 3.7 m/s ) 34. Two forces, F1 and F, are acting on a 3.0-kg box in the xy plane. Figure 5 shows only F 1 and the acceleration a of the box. Find F. (Ans: -7 î +4 ĵ N) 35. A 5.0-kg crate is pushed across a frictionless horizontal floor with a force of 00 N, directed 0 below the horizontal. What is the magnitude of the normal force of the floor on the crate? (Ans: 313 N) 36. Figure 7 shows the force versus time graph of a force acting on a 5.0-kg object moving in the x direction along a frictionless one-dimensional track. At t = 0, the object is moving in the negative direction of the x axis with a speed of.0 m/s. What are the speed and direction of the object at t = 7.0 s? (Ans: 7.0 m/s in the positive x direction) 37. A force F = 10 N is applied to block 1, as shown in figure 9. The masses of blocks 1,, and 3 are 5 kg, 3 kg, and kg, respectively. What is the magnitude of the force exerted by block on block 1? Assume the surface is frictionless. (Ans: 5 N) 38. A mass is suspended by a string from the ceiling of a train accelerating horizontally at.5 m/s. What is the angle that the string makes with the vertical? (Ans: 14 o ) 39. Two horizontal forces perpendicular to each other act at the same time on a 5.0-kg box on a horizontal frictionless floor. One force is 6.0 N and the other is 8.0 N in magnitude. What is the magnitude of the acceleration of the box? (Ans:.0 m/s ) 40. A constant force in the xy-plane pushes a.0-kg object across a horizontal frictionless floor on which an x-y coordinate system is drawn. The x and y components of the velocity of the object as a function of time are shown in figure 30. What is the magnitude of the force? (Ans: 4.5 N) 41. The system shown in figure 31 is in equilibrium. If the spring scale is calibrated in N, what does it read? (Ans: 49) Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 3

4 4. With what force will the feet of a person of mass 60.0 kg press downward on an elevator floor when the elevator has an upward acceleration of 1.0 m/s? (Ans: 660 N) 43. The system shown in figure 33 is released from rest and is moving with an acceleration of 4.00 m/s. Find the magnitude of the tension T shown in the figure. (Assume that the pulley and the cords are massless). (Ans: 11.6 N) 44. A -kg object is initially at rest. At time t = 0, a force F 1 = î + ĵ (N) is applied to the object. At time t = 1 s, an additional force F (Ans: ( î + ĵ ) m/s) = î ĵ (N) is applied to the object. Find the velocity of the object at t = s. 45. Figure 36 shows box 1 (m 1 = 4.0 kg) on a frictionless plane inclined at angle θ 1 = 30 o. The box is connected via a cord of negligible mass to box (m = 3.0 kg) on a frictionless plane inclined at angle θ = 60 o. The pulley is frictionless and has negligible mass. What is the acceleration of Box 1? (Ans: 0.84 m/s, up along the incline) 46. A 4.80-kg object is accelerated upward by a cord of negligible mass. The maximum tension that the cord can take before breaking is 75.0 N. Find the maximum upward acceleration that can be given to the object. (Ans: 5.83 m/s ) 47. An 800-N person is standing on a scale inside an elevator at rest. Suddenly the elevator cable breaks and the elevator is in free fall. What is the weight of the person as indicated by the reading on the scale? (Ans: 0 N) 48. A 75 kg person lowers himself from rest to the ground by means of a rope that passes over a frictionless pulley and is attached to a 60 kg box, as shown in figure 37. The person and the box move along vertical lines. What is the magnitude of the acceleration of the person? (Ans: 1.1 m/s ) 49. As shown in figure 39, a man is pulling a 60.0 N box up an inclined frictionless plane with a force F = 3.7 N whose direction makes an angle 30.0 o with inclined plane. The inclined plane makes an angle of 0.0 o with the horizontal. Find the magnitude of the acceleration of the box along the incline. (Ans: zero) 50. Two boxes A and B, are connected to the ends of a light vertical cord, as shown in figure 40. A constant upward force F = 80.0 N is applied to box A. Starting from rest, box B descends 1.0 m in 4.00 s. Find the mass of box B if the tension in the cord between the boxes is 36.0 N. (Ans: 4.34 kg) 51. As shown in figure 4, a block with mass M = 3.00 kg is lying on a smooth surface and is attached to another block of mass m =.00 kg by means of a light, inextensible string which passes over a massless pulley. What force F acting on the block M at angle θ = 60 o above the horizontal will hold both objects at rest? (Ans: 39. N) Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 4

5 A B C D E Conceptual Problems 1. An object of mass M = 10 kg, moving on a frictionless horizontal surface, is subjected to two applied forces as shown in figure 3. In which situation is the object accelerating to the right? A. d B. b C. a D. e E. c. Three blocks, (A,B,C), each having mass M, are connected by strings, as shown in figure 15. Block C is pulled to the right by a force F that causes the entire system to accelerate. Neglecting friction, what is the tension T 1 between blocks B and C? A. F/3 B. F/ C. F/3 D. F E. 4F/3 3. Acceleration is always in the direction: A. of the net force. B. of the initial velocity. C. of the final velocity. D. of the displacement. E. opposite to the frictional force. 4. Which of the following is NOT an example of accelerated motion? A. The horizontal component of a projectile motion. B. The vertical component of a projectile motion. C. A circular motion at constant speed. D. A swinging pendulum. E. The Earth's rotation about the sun. 5. Consider a particle in motion while the net external force on it is zero. Which of the following statements is correct in this case? A. The particle must be moving at a constant velocity. B. The particle must be moving at a constant speed in a circle. C. The particle will come to rest after some time. D. The velocity of the particle is always perpendicular to the direction of the motion. E. The particle has an acceleration of 9.8 m/s. 6. To measure your weight, you stand on a spring scale on the floor of an elevator. Among the following situations, select the one that gives the highest reading on the scale: A. The elevator moves upward with increasing speed. B. The elevator moves upward with decreasing speed. C. The elevator remains stationary. D. The elevator moves downward with increasing speed. E. The elevator moves downward at constant speed. Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 5

6 7. Two boxes A and B (m A = 3.0 kg, and m B =1.0 kg) are in contact on a horizontal frictionless surface, and move along the x axis (see figure 6). A horizontal force F = 10.0 î (N) is applied on box A. The net force acting on A is F 1 and on B is F. Which one of the following statements is correct? 8. A 1000-kg airplane moves in straight horizontal flight at constant speed. The force of air resistance is 1800 N. The net force on the plane is: A. zero B N C N D N E. none of these 9. An object is being accelerated in the absence of friction by a 100-N force. A second force of 100-N is then applied to the object in a direction opposite to the direction of motion. The object with these two forces acting on it will A. Move at a constant velocity B. Slow down C. Move in a circle D. Stop rapidly E. Move backward 10. A 13-N weight and a 1-N weight are connected by a massless string over a massless, frictionless pulley. The 13-N weight has a downward acceleration equal to: A. g/5 B. g/1 C. g/13 D. g E. (13/5)g 11. Figure 8 shows four possible choices for the direction of ONE force of magnitude F to be applied to a block on an inclined plane of angle 30. The directions are either horizontal or vertical. (for all choices, we assume that the block remains on the inclined plane). Rank the choices according to the magnitude of the normal force on the block from the plane, greatest first. A. choice 4, choice 3, choice 1, choice B. choice 3, choice 4, choice 1, choice C. choice 1, choice 3, choice 4, choice D. choice, choice 3, choice 1, choice 4 E. (choice 3 and choice 4) tie, (choice 1 and choice ) tie 1. A 100-kg man standing on a scale in a moving elevator reads his weight as 490 N. The acceleration of the elevator is: A. 4.9 m/s downward B. 4.9 m/s upward C. 9.8 m/s upward D. 9.8 m/s downward E. zero Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 6

7 13. A 500-N man is riding in an elevator. At a certain instant his feet push against the floor with a force greater than 500 N. At this instant, the elevator may be (Choose the CORRECT Answer): A. Moving downward but decreasing in speed B. Moving upward but decreasing in speed C. Moving downward but increasing in speed D. Not moving (Standing still) E. Moving at a constant speed 14. As shown in figure 3, a.0-n rock slides down on a frictionless inclined plane. Which one of the following statements is TRUE concerning the magnitude of the normal force that the plane exerts on the rock? A. The normal force is less than.0 N. B. The normal force is zero. C. The normal force is.0 N. D. The normal force is greater than.0 N. E. The normal force increases as the angle of inclination, θ, is increased. 15. Figure 34 shows four blocks connected with three cords, being pulled to the right on a horizontal frictionless floor by a horizontal force F. Rank the cords according to their tension, greatest to least. A. 3,,1 B. All tie C.,1,3 D. 1 and tie then 3 E. 1,3, 16. A 16-kg fish is weighed with two identical, massless, spring scales, each of negligible weight, as shown in figure 35. What will be the readings on the scales? A. The sum of the two readings will be 3 kg B. The bottom scale will read 16 kg, and the top scale will read zero C. The top scale will read 16 kg, and the bottom scale will read zero. D. Each scale will show a reading greater than zero and less than 16 kg, but the sum of the two readings will be 16 kg E. Each scale will read 8 kg. 17. Consider a particle in motion. Which of the following statements is correct? A. If the sum of the external forces acting on the particle is zero, then the particle is moving with constant velocity. B. If the particle is moving with constant speed, then the sum of the external forces acting on it must always be zero. C. If the sum of the external forces acting on the particle is zero, then it will come to rest after some time. D. The velocity of the particle is always in the direction of the resultant external force. E. If the sum of the external forces acting on the particle is zero, then it has an acceleration of 9.8 m/s. 18. A book is resting on a horizontal table. The reaction force to the weight of the book is A. The force with which the book is pulling on Earth B. The normal force from the table on the book C. The support force from the floor on the table D. The force with which the book is pushing on the table E. The force with which the table is pushing on the floor Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 7

8 19. Consider the following two situations: (I) A box does not move while you are pushing on it, and (II) the box moves with increasing speed while you are pushing on it. Which of the following statements is TRUE about the magnitudes of your force on the box and the force of the box on you? A. They are equal in both situations B. They are equal in situation (I) only C. They are equal in situation (II) only D. The force of the box on you is smaller than your force on the box in situation (II) E. The force of the box on you is larger than your force on the box in situation (I) 0. A block of mass M is hung by ropes as shown in figure 38. The system is in equilibrium. Which of the following statements is CORRECT concerning the magnitudes of the three forces? A. F 1 = F = F B. F = F C. F < F D. F1 = F = F 3 / E. F1 > F A 0.15 kg ball is thrown at an angle of 30 3 o above the horizontal with an initial speed of 1 m/s. At its highest point, the net force on the ball is: A. 1.5 N, down B. 9.8 N, 30 o below horizontal C. 0 D. 9.8N, up E. 9.8 N, down. Three blocks are placed on a table as shown in figure 41. The table exerts a normal force: A. only on block C. B. only on block A. C. upward on block B and downward on block C. D. upward on block A and downward on block C. E. only on block B. 3. Acceleration is always in the direction: A. of the net force. B. of the displacement. C. of the initial velocity. D. of the final velocity. E. opposite to the frictional force. Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 8

9 Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 9

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11 Figure 30 Figure 31 Figure 3 Figure 33 Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Figure 39 Figure 40 Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 11

12 Figure 41 Figure 4 Dr. M. F. Al-Kuhaili PHYS 101 Chapter 5 Page 1

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