Unit 2 AP Forces Review Problems



Forces Review Problems

Conceptual Problems

1. A physics book is motionless on the top of a table. If you give it a hard push with your hand (and then remove your hand from the book), it slides across the table and slowly comes to a stop. Use Newton’s 1st and/or 2nd laws of motion to answer the following questions.

a. Why does the book remain motionless before the force is applied?

b. Why does the book move when the hand pushed on it?

c. Why does the book eventually come to a stop?

d. Under what conditions would the book remain in motion at a constant speed?

2. Why do you lunge forward when your car suddenly comes to a halt? Why are you pressed backward against the seat when your car rapidly accelerates? In your explanations, refer to the most appropriate one of Newton’s three laws of motion.

3. Newton’s second law indicates that when a net force acts on an object, it must accelerate. Does this mean that when two or more forces are applied to an object simultaneously, it must accelerate?

4. A father and his much smaller seven-year-old daughter are facing each other on ice skates. With their hands, they push off against one another. (a) Which one, if either, experiences the larger pushing force? (b) Which one, if either, experiences the larger acceleration?

5. Why do you have to push harder on chest of drawers to start it moving than to keep it moving once in motion?

6. Let’s say your textbooks have a total mass of 3.0 kg. What would be the mass of the books if they were taken to Jupiter where the acceleration due to gravity is 10 times that of Earth?

7. Suppose the acceleration of an object is zero. Does this mean there are no forces acting on it?

8. Only one force acts on an object. Can the object have zero acceleration? Can it have zero velocity?

9. When a body is moved from sea level to the top of a mountain, what changes: The body’s mass, its weight, or both?

10. Is the coefficient of friction the same between two identical surfaces in a lab on Earth and in a lab in a space colony on the moon?

11. When you stand still on the ground, how large a force does the ground exert on you? Why doesn’t this force make you rise up into the air?

12. Is a net force being applied to an object when the object is moving downward (a) with a constant acceleration of 9.80 m/s/s directed down and (b) with a constant velocity of 9.80 m/s down?

13. A circus performer hangs stationary from a vertical rope. She then begins to climb upward by pulling herself up, hand-over-hand. When she just begins to start climbing, is the tension in the rope less than, equal to, or greater than it is when she just hangs stationary?

14. A 35-kg crate rests on a horizontal floor. A 65-kg person is standing on the crate. Determine the magnitude of the normal force that (a) the floor exerts on the crate and (b) the crate exerts on the person.

15. What is the weight of a 60-kg astronaut (a) on Earth, (b) on the moon (gmoon = 1.7m/s/s), (c) on Mars (gmars = 3.7 m/s/s)?

16. A box weighing 70 N rests on the floor. A rope that is tied to the top of the box runs vertically upward over a pulley and a weight is hung from the other end of the rope. Determine the force that the floor exerts on the box if the weight hanging on the other side of the pulley weighs (a) 30 N, (b) 60 N, (c) 90 N.

17. A 12.0-kg lantern is suspended from the ceiling by two vertical wires. What is the tension in each wire? (58.8N)

18. What is meant about the forces acting on a book if we state that the book is in a state of equilibrium?

19. Can an object in equilibrium be moving?

20. Can an object ever be in equilibrium if

a. Only one force acts on it?

b. Only two forces that are perpendicular to each other act on it?

c. Only two forces that aren’t perpendicular to each other act on it?

21. What is

a. the largest possible resultant force of two forces with magnitudes of 3 N and 4 N?

b. the smallest possible resultant?

22. Gayle is pushing a lawn mower across her lawn. How can she increase the horizontal component of the force without changing the actual force that she is applying to the spreader handle?

23. Sue and Jenny kick a soccer ball at exactly the same time. Sue's foot exerts a force of 66N at 900. Jenny's foot exerts a force of 88N at 00. What is the magnitude and direction of the resultant force on the ball?

24. A force vector has a magnitude of 720N and acts 380 North of East. Determine the components of the force that point along the N-S line and along the E-W line.

Problems (Draw free-body diagrams for all problems dealing with individual forces acting on an object)

25. 65-kg squirrel jumps off a 10-m tower into the water below.

a. Find the squirrel’s velocity when hitting the water. (14 m/s, down)

b. The squirrel comes to a stop 2 m below the surface. Find the net force exerted by the water on the little rodent to make it stop in 2m. (3.19 E3 N, up)

26. A 0.145-kg baseball traveling 30 m/s strikes the catcher’s mitt, which, in bringing the ball to rest, recoils backward 11 cm. What was the net force applied by the glove on the ball? (-593.05 N)

27. A stuntman is being pulled along a rough road at a constant velocity by a cable attached to a moving truck. The cable is parallel to the ground. The mass of the stuntman is 109 kg, and the coefficient of kinetic friction between the road and him is 0.870. Find the tension in the cable. (929.33 N)

28. A rescue helicopter is lifting an 822N man from a capsized boat by means of a cable and harness.

a. What is the tension in the cable when the man is given an initial upward acceleration of 1.10 m/s/s? (914.27 N)

b. What is the tension during the remainder of the rescue when he is pulled upward at a constant velocity? (822 N)

29. Safety engineers estimate that an elevator can hold 20 people of 75-kg each average mass. The elevator itself has a mass of 500 kg. Tensile strength tests show that the cable supporting the elevator can tolerate a maximum tension force of 2.96 x 104 N. What is the greatest acceleration that the elevator's motor can produce without breaking the cable? (5 m/s/s, up)

30. A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than “30g’s.”

a. Calculate the net force on a 70-kg person accelerating at this rate. (2.06 E4 N, against his motion)

b. What distance is traveled if brought to rest at this rate from 90 km/h? (1.06 m)

31. Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 5-kg projectile from rest to a speed of 4.0E3 m/s. The net force accelerating the projectile is 4.9E5 N. How much time is required for the projectile to come up to speed? (.041s)

32. During a circus performance, a 72-kg human cannonball is shot out of an 18-m-long cannon. If the human cannonball spends 0.95 s in the cannon, determine the average net force exerted on him in the barrel of the cannon. (2.87 E3 N in the direction of his motion)

33. A rock of mass 45-kg accidentally breaks loose from the edge of a cliff and falls straight down. The magnitude of the air resistance that opposes its downward motion is 250 N. What is the acceleration of the rock? (4.24 m/s/s, down)

34. A 92 Kg baseball player slides into second base. The coefficient of kinetic friction between the player and the ground is 0.61.

a. What is the magnitude of the frictional force? (549.98 N, opposite the direction of motion)

b. If the player comes to rest after 1.2 s, what is his initial speed? (7.18 m/s)

35. A block whose weight is 45.0 N rests on a horizontal table. A horizontal force of 36.0 N is applied to the block. The coefficients of static and kinetic friction are 0.650 and 0.420, respectively. Will the block move under the influence of the force, and, if so, what will be its acceleration? Explain your reasoning. (Yes, 3.73 m/s/s)

36. The speed of a bobsled is increasing due to an acceleration of 2.4 m/s/s. At a given instant in time, the total forces resisting the motion, including kinetic friction and air resistance, total 450 N. The mass of the bobsled and its rider is 270 kg.

a. What is the magnitude of the force propelling the bobsled forward? (1.1 E3 N)

b. What is the magnitude of the net force that acts on the bobsled? (648 N)

37. What is the acceleration of a falling sky-diver (mass 60 kg including parachute) when the upward force of air resistance is equal to one fourth of her weight? (7.35 m/s/s, down)

38. After popping open her parachute, the diver in the previous problem descends leisurely to the ground at constant speed. What now is the force of air resistance on her and her parachute? (same magnitude as her weight ( 588 N, up)

39. A 1.14 x 104 kg lunar landing craft is about to touch down on the surface of the moon where the acceleration due to gravity is 1.60 m/s/s, down. At an altitude of 165 m the craft’s downward velocity is 18.0 m/s. To slow down the craft, a retrorocket is fired to provide an upward thrust. Assuming the descent is vertical, find the magnitude of the thrust needed to reduce the velocity to zero at an instant when the craft touches the lunar surface. (2.94 E4 N, up)

40. A 5.20 x 102 N person is trapped at the bottom of a well that is 35.1 m deep. If the person is pulled directly upward by a rope that has a maximum tension of 569 N, what is the shortest time in which the person can be brought out to safety? (8.74 s)

41. A 5-kg paint bucket is hanging from a rope attached to the bottom of another 50-kg paint bucket, also hanging from a rope.

a. If the buckets are at rest, what is the tension in each cord? (539 N, 49 N)

b. If the two buckets are pulled upward with an acceleration of 1.50 m/s/s by the upper cord, calculate the tension in each cord. (621.5 N, 56.5 N)

42. A 5500-kg helicopter accelerates upward at 0.50 m/s/s while lifting a 1200-kg car by a mass-less cable.

a. What is the lift force exerted by the air on the rotors? (6.91 E4 N)

b. What is the tension in the cable that connects the car to the helicopter? (1.24 E4 N)

43. Two objects (45.0 and 21.0 kg) are connected by a massless rope on opposite sides of a massless, frictionless pulley. Find:

a. the acceleration of the objects. (3.56 m/s/s)

b. the tension in the string. (280.56 N)

44. Two masses (3 Kg and 7 Kg), initially at rest, are hanging over a frictionless pulley and are each initially 1.60m above the ground. The top of the pulley is 4.8 m above the ground. What maximum height does the lighter object reach after the system is released? (3.84 m above the ground)

45. What is the minimum pushing force necessary to hold a 20 kg block against a vertical wall without it slipping? The coefficient of friction between the surfaces is 0.23. (852.17 N)

46. Two blocks (m1 = 20 kg, m2 = 35 kg) are connected to each other by a rope and are resting on a horizontal surface (µ 0.13). If someone tugs the front block (m1) with a force of 200N, what will be the block’s acceleration and what will be the tension in the rope connecting m1 to m2? (2.36 m/s/s, 127-ish N)

47. A skater with an initial speed of 7.60 m/s is gliding across the ice. Air resistance is negligible. The coefficient of kinetic friction between the ice and the skate blades is 0.100.

a. Find the deceleration caused by kinetic friction. (-.98 m/s/s)

b. How far will the skater travel before coming to a rest? (29.47 m)

48. Traveling at a speed of 16.1 m/s, the driver of an automobile suddenly locks the wheels by slamming on the brakes. The coefficient of friction between the tires and the road is 0.720. How much time does it take for the car to come to a halt? Ignore the effects of air resistance. (2.28 s)

49. A 65 kg person is in an elevator accelerating upwards at the rate of 2 m/s/s. If the person was standing on a scale in the elevator, what would the scale’s reading show? (767 N)

50. A 50 kg person is in a 600 kg elevator. The elevator starts from rest and reaches a velocity of 10 m/s downward in 3 seconds. If the person is standing on a scale inside the elevator, what would the scale read? (323.5N)

51. A 55 kg person rides in a 550 kg elevator that has 5500 N of tension in the cable. If the person is standing on a scale in the elevator, what would the scale read? (499.95 N)

Vectors and 2-D Problems

52. Three forces are acting on an object (F1= 44N, 280, F2= 26.5N, 1240, F3= 31N, 2700. Determine the resultant force of the three vectors. (26.70N, 260)

53. A 100 kg sign is supported by two separate cables. One cable (T1) makes an angle of 39 degrees to its horizontal and the other cable (T2) makes an angle of 59 degrees to its horizontal. Calculate the tension in each of the cables. (509.70 N, 769.09 N)

54. A person pushes a 21-kg lawn mower at constant speed with a force of 92 N directed along the handle, which is at an angle of 35( to the horizontal.

a. Calculate the friction force on the mower. (75.36N)

b. Find the normal force exerted vertically upward on the mower by the ground. (258.57N)

c. Find μ. (0.29)

d. Find the force the person must exert on the lawn mower handle to accelerate it from rest to 2.5 m/s in 4.0 seconds (assuming the same friction). (108.03N)

55. A 20 Kg sled is being pulled across a horizontal surface at a constant velocity. The pulling force on the handle is 80N directed at a 30-degree angle above the horizontal. What is the coefficient of friction between the sled and the ground? (0.44)

56. Two blocks (#1= 350N, #2= 246N) are connected by a massless rope over a frictionless pulley. Block #1 is resting on a table and Block #2 is hanging from the pulley over the edge of a table. The coefficient of friction between the Block #1 and the table is 0.21. Calculate the acceleration of the system upon release and the tension in the rope. (2.84m/s/s, 174-ish N)

57. A 0.150 Kg wet bar of soap slides freely down a ramp 2.0 m long inclined at 7.3(. Neglect friction.

a. How long does it take to reach the bottom (assume it began from rest)? (1.79s)

b. How would this change if the soap’s mass was 0.250 Kg? (it wouldn’t; mass is independent)

58. An 18-kg box is released on a 37.0( incline and accelerates down the incline at 0.270 m/s2.

a. Find the friction force impeding its motion. (101.3N, up the incline)

b. How large is the coefficient of friction? (0.72)

59. A 205Kg log is pulled up a ramp by means of a rope that is parallel to the surface of the ramp. The ramp is 30 degrees to the horizontal and the coefficient of friction between the ramp and the log is 0.900. If the log has an acceleration of 0.800m/s/s, what is the tension in the rope? (2.73 E3N)

60. A 7.0 kg block lies on a smooth plane tilted at 30( to the horizontal. The coefficient of friction between the block and the plane is 0.15.

a. Determine the acceleration of the block as it slides down the plane. (3.63 m/s/s, down the plane)

b. If the block starts at rest 9.0 m up the plane from its base, what will be the block’s velocity when it reaches the bottom of the incline? (8.08m/s, down the plane)

61. A 12 Kg block is given a quick push so it has an initial speed of 5.0 m/s up a 33( inclined plane. The coefficient of friction between the block and the plane is 0.16.

a. How far up the plane will it go? (1.88m)

b. How much time elapses before it returns to its starting point (be careful here)? (1.72s)

62. A penguin slides at a constant velocity of 1.4 m/s down an icy 6.9 degree incline. At the bottom of the incline the penguin slides onto a horizontal patch of ice with the same coefficient of friction as the incline. How much time is required for the penguin to slide to a halt after entering the horizontal patch of ice? (1.19s)

63. A block (m1) lying on a 250 inclined plane is connected by a massless cord passing over a pulley to another mass (m2) hanging over the edge of the incline. The coefficient of friction between m1 and the plane is 0.15 and m1 = m2 = 2.7Kg. What is the acceleration of the masses when m2 begins to fall? (2.16m/s/s)

64. A 50 kg sign is suspended by two wires. Find the tension in each of the wires. (415.54 N, 388.60 N)

400 350

1 2

65. Find the tension in wire A and the weight of the unknown mass below. (319.48 N, 414N)

A

460

B

400

66. A 5 Kg mass and a 8 Kg mass are attached to a mass-less cord that passes over a frictionless pulley. The masses are free to move.

a. Draw the scenario, showing all forces acting on both masses.

b. What direction does the smaller mass move? (up)

c. What is the acceleration of the system? (2.26 m/s/s)

d. What is the tension in the rope? (60.32 N)

67. Two masses (5 Kg and 8 Kg) connected by a mass-less rope hang over opposite ends of a frictionless pulley. Each mass is initially 2m above the ground, and the top of the pulley is 8 m above the ground. What maximum height does the lighter object reach after the system is released? (4.46 m)

68. A 90.0 kg box (mass 2) rests on a table. The left side of the 90 kg box is attached to a 12.0 kg box (mass 1) by a mass-less string that passes over a frictionless pulley. The right side of the 90 kg box is attached to a 29.0 kg box (mass 3) by a mass-less string that passes over a friction-free pulley. The 12 kg and 29 kg boxes are suspended above the ground. When the system is released, the objects move. The coefficient of kinetic friction between the middle object (mass 2) and the surface of the table is 0.15.

a. What is the acceleration of the three objects? (0.26 m/s/s)

b. Find the tension in each of the two strings. ( T 1-2 = 120.72 N, T 2-3 = 276.66 N)

-----------------------

W = ?

300 N

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download