CHAPTER 2. Knowledge. For each question, select the best answer from the four alternatives.

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1 CHAPTER 2 Review K/U Knowledge/Understanding T/I Thinking/Investigation C Communication A Application Knowledge For each question, select the best answer from the four alternatives. 1. When a body is at rest, the net force acting on it is (a) maximum (b) zero (c) minimum (d) constant (2.1) K/U 2. The inertia of an object is directly proportional to its (a) mass (b) velocity (c) acceleration (d) speed (2.2) K/U 3. When a constant net force acts on an object, which quantity remains constant? (2.2) K/U (a) velocity (b) displacement (c) acceleration (d) momentum 4. Action and reaction forces (a) act on two different objects (b) have the same direction (c) have unequal magnitude (d) always cancel each other (2.2) K/U 5. A 5.0 kg object undergoes an acceleration of 2.0 m/s 2. What is the magnitude of the resultant force acting on the object? (2.2) T/I (a) 0 N (b) 2.0 N (c) 5.0 N (d) N 6. The tension in a cable supporting a beam at a construction site is less than the weight of the beam. The beam may be (a) going up or down with non-uniform velocity (b) going up with increasing velocity (c) going down with decreasing velocity (d) going down with increasing acceleration (2.3) K/U 7. A 2.0 kg mass sits at rest on a plane inclined at from the horizontal. The coefficient of static friction is What is the frictional force on the mass? (2.4) T/I (a) 5.9 N (b) 6.9 N (c) 8.5 N (d) 9.8 N 8. A bicyclist brakes suddenly, and the wheels skid across the ground. The force of friction between the wheels and the ground acts (a) backward on the front wheels and forward on the rear wheels (b) forward on the front wheels and backward on the rear wheels (c) backward on both wheels (d) forward on both wheels (2.4) K/U 9. A snowboarder is sliding down a frictionless hill inclined at an angle of θ to the horizontal. What is the acceleration of the skier? (2.4) K/U (a) g tan θ (b) g sin θ (c) g cos θ (d) g Indicate whether each statement is true or false. If you think the statement is false, rewrite it to make it true. 10. If only three forces of equal magnitude act on an object, the object must have a non-zero net force. (2.1) K/U 11. When a non-zero net force acts on an object, the object will speed up in the direction of the net force. (2.2) K/U 12. When you pull up on an object at rest on a horizontal surface, you decrease the normal force on the object but not the weight of the object. (2.2) K/U 13. When a skater bumps into the boards in an arena, first the skater exerts a force on the boards, and then the boards exert an equal and opposite reaction force on the skater. (2.2) K/U 14. In an elevator with an acceleration of 0.20g up, the force exerted on the floor by a passenger of mass m is 1.2mg. (2.3) K/U 15. When a person walks on a rough surface, the frictional force exerted by the surface on the person is opposite to the direction of the person s motion. (2.3) K/U 16. When you are sliding down a hill on a snowboard, the normal force on you is larger in magnitude than the force of gravity. (2.3) K/U 17. When two objects slip over each other, the force of friction between them is called static friction. (2.4) K/U 18. The magnitude of the frictional force depends on the nature of the two surfaces in contact. (2.4) K/U 19. One advantage of a linear actuator over manual labour is that a linear actuator can apply the same force each time. (2.5) K/U 100 Chapter 2 Dynamics NEL

2 Understanding 20. A 75 kg man stands in an elevator. Calculate the force that the floor exerts on him when the elevator starts moving upward with an acceleration of 2.0 m/s 2. (2.1) K/U T/I 21. The airline pilot in Figure 1 is pulling a suitcase at a constant speed with force F > applied to the handle at an angle of θ above the horizontal. A small force of friction resists the motion. (2.1) K/U T/I C A Figure 1 (a) Draw an FBD of the suitcase. (b) Determine the components of the net force. Choose the direction of motion to be the 1x-direction. (c) Determine the components of the forces. Choose the 1x-direction as the direction in which the handle is pointing. (d) Which choice of 1x is more convenient? Explain your answer. (Hint: Did you show the components of all the forces in your diagrams?) 22. Express the magnitude and direction of the net force acting on the following. (2.1) T/I A (a) a drop of rain falling with a constant speed (b) a cork with a mass of 10 g floating on still water (c) a stone with a mass of 0.1 kg just after it is dropped from the window of a stationary train (Neglect air resistance.) (d) the same stone at rest on the floor of a train, which is accelerating at 1.0 m/s Draw an FBD for each of the following objects. (2.1) K/U T/I C A (a) a saucepan hanging from a hook (b) a person standing at rest on the floor (c) a puck sliding in a straight line on the ice to the right (d) a toboggan pulled by a rope at an angle above the horizontal to the right with significant friction on the toboggan 24. An astronaut is separated from his small spacecraft accelerating in interstellar space at a constant rate of 100 m/s 2. Determine the acceleration of the astronaut the instant he is outside the spaceship. (Assume that there are no nearby stars to exert a gravitational force on him.) (2.2) T/I A 25. Explain why action and reaction forces cannot cancel each other, even though they are equal and opposite. (2.2) K/U C 26. A constant horizontal force of magnitude 20.0 N is applied to block A with a mass of 4.0 kg, which pushes against block B with a mass of 6.0 kg. The blocks slide eastward over a frictionless surface. Calculate the acceleration of the blocks. (2.2) T/I 27. A student holding a spring balance in his hand suspends from it an object with a mass of 1.0 kg. The balance slips from his hands and falls down. What is the reading of the balance while it is in the air? (2.3) K/U T/I A 28. Is it always necessary for the coefficient of friction to be less than one? Explain your answer. (2.4) K/U C A 29. Provide one advantage and one disadvantage each of static and kinetic friction in situations involving inclined planes. Explain your reasoning. (2.4) K/U C 30. How are linear actuators used to make the workplace more ergonomic, reducing workdays lost to strain and injury? (2.5) K/U Analysis and Application 31. Describe how a trebuchet applies the principles of linear motion. (2.1) K/U T/I 32. A rope with a mass of 0.53 kg is pulling a block with a mass of 8.6 kg with a force of 31.5 N. Calculate the force of reaction exerted by the block on the rope when the block is resting on a smooth horizontal surface. (2.1) T/I A 33. A helicopter with a mass of kg rises with a vertical acceleration of 12 m/s 2. The crew and the passengers have a total mass of kg. Express the magnitude and direction of the force on the floor by the crew and the passengers. (2.1) T/I A 34. Two forces are acting on a 23 kg object. One force has a magnitude of 45 N and is directed east. The other force has a magnitude of 29 N and is directed north. Determine the object s acceleration. (2.1) T/I A 35. Three forces act on an object: a 47 N force at 318 north of east, a 58 N force at 468 north of east, and a force of magnitude F at an angle of θ south of west. The object is in equilibrium. Calculate F and θ. (2.1) T/I A NEL Chapter 2 Review 101

3 36. Two blocks are connected by a string passing over a frictionless pulley, as shown in Figure 2. When the blocks are in motion, block A experiences a force of kinetic friction of magnitude 5.4 N. The mass of m A is 2.3 kg, and the mass of m B is 3.5 kg. (2.1, 2.2) T/I A m A Figure 2 m B (a) Calculate the magnitude of the acceleration of the blocks. (b) Calculate the magnitude of the tension in the string. 37. A man is floating on an air mattress in a swimming pool. (2.1) K/U T/I C A (a) Draw two FBDs: one for the man and one for the mattress. (b) Identify the reaction forces for all of the forces in your FBDs in (a). (c) The mass of the man is kg, and the mass of the mattress is 7.0 kg. Determine the normal force of the water on the mattress. (d) Determine the normal force of the mattress on the man. 38. Describe how you could use this textbook, a piece of paper, and a desk to demonstrate Newton s first law of motion. (2.2) K/U T/I C A 39. The engines of an airplane exert a force of kn [E] during takeoff. The mass of the airplane is 42 t (1 t kg). (2.2) T/I A (a) Calculate the acceleration produced by the engines. (b) Calculate the minimum length of runway needed if the speed required for takeoff on this runway is 71 m/s. 40. Two masses, 1.3 kg and 2.4 kg, are tied together with a string. The string has negligible mass and does not stretch. The masses are pulled on a frictionless horizontal surface with a force of 8.6 N [W]. (2.2) T/I A (a) Determine the acceleration of the masses. (b) Calculate the force acting on the 1.3 kg mass. 41. A horizontal force of N pulls two masses, 11 kg and 19 kg, which are at rest on a frictionless table and connected by a light string. Calculate the tension in the string (a) when the applied force pulls directly on the 11 kg mass (b) when the applied force pulls directly on the 19 kg mass (2.3) T/I A 42. A sign with a mass of 2.5 kg is supported by a single rope, as shown in Figure 3. A strong horizontal wind exerts a force of 12 N on the sign. Calculate (a) the tension in the rope (b) the angle, u, the rope makes with the horizontal (2.3) T/I A wind Figure 3 Bridge Slippery When Wet 43. A circus performer with a mass of 54 kg hangs from some ropes, as shown in Figure 4. (2.3) T/I A Figure (a) Calculate the tension in each rope. (b) What would happen to the tension in each rope if the horizontal rope were slightly longer and attached to the wall at a higher point? Explain your reasoning. 44. A water skier with a mass of 65 kg is pulled behind a boat that is moving with a constant speed of 25 m/s. The tension in the horizontal rope is N [S]. Calculate the magnitude and direction of the force that the water exerts on the skier s ski. (2.3) T/I A 45. A hockey stick is in contact with a puck for s. The speed of the puck when it leaves the stick is 32 m/s. The hockey puck has a mass of 160 g. Calculate the magnitude of the force applied to the puck. (Assume that this force is constant while the stick and puck are in contact.) (2.3) T/I A 102 Chapter 2 Dynamics NEL

4 46. A spacecraft requires a force of N to accelerate in deep space at 6.9 m/s 2. How much force is required for the same spacecraft to accelerate at the same rate upward from Earth? (2.3) T/I A 47. Three masses are connected by strings, as shown in Figure 5. Assume that the masses of the strings are negligible. Calculate the acceleration of each mass and the tension in the string. (2.3) T/I A string A 6.0 kg Figure kg string B 3.0 kg 48. The tightrope walker in Figure 6 gets tired and decides to stop for a rest. During this rest period, she is in equilibrium. She stops at the middle of the rope and notices that both sides of the rope make an angle of 158 below the horizontal. Calculate the tension in the rope on both sides of the tightrope walker. The mass of the tightrope walker is 60.0 kg. (2.3) K/U T/I C A 52. You are trying to slide a heavy trunk across a horizontal floor. The mass of the trunk is 85 kg, and you need to exert a force of N to make it just begin to move. (2.4) T/I A (a) Determine the coefficient of static friction between the floor and the trunk. (b) After the trunk starts moving, you continue to push with this force. The trunk reaches a speed of 2.0 m/s after 5.0 s. Calculate the coefficient of kinetic friction. 53. A race car driver discovers that she can accelerate at 4.0 m/s 2 without spinning her tires, but if she tries to accelerate more rapidly, she always burns rubber. Determine the coefficient of static friction between the driver s tires and the road. (2.4) T/I A 54. A hockey puck slides along a rough, icy surface. It has an initial speed of 35 m/s and slides to a stop after travelling a distance of 95 m. Calculate the coefficient of kinetic friction between the puck and the ice. (2.4) T/I A 55. A piece of wood with a mass of 2.4 kg is held in a vise sandwiched between two wooden jaws, as shown in Figure 7. A blow from a hammer drives a nail that exerts a force of 450 N on the wood. The coefficient of static friction between the wood surfaces is Calculate the magnitude of the minimum normal force that each jaw of the vise exerts on the wood block to hold the block in place. (2.4) T/I A Figure Your moving company runs out of rope, so you are forced to push two crates along the floor, one in front of the other. The crates have masses of 45 kg and 22 kg, and you push on the 45 kg crate. The crates are moving at constant speed, and the coefficient of kinetic friction between both crates and the floor is Calculate the magnitude of the normal force between the two crates. (2.4) T/I A 50. A person sits on an office chair with wheels on it. A co-worker exerts a force of N [right 358 down] on the chair. The person and the chair accelerate at 0.62 m/s 2 [right]. The force of friction acting on the chair is N [left]. (2.4) K/U T/I (a) Determine the total mass of the chair and person. (b) Calculate the normal force acting on the chair. 51. You are given the job of moving a refrigerator with a mass of kg across a horizontal floor. The coefficient of static friction between the refrigerator and the floor is Calculate the magnitude of the minimum force that is required just to set the refrigerator into motion. (2.4) T/I A Figure Two crates with masses of 15 kg and 35 kg are stacked on the back of a truck, with the lighter crate on top of the heavier. The frictional forces are strong enough that the crates do not slide off the truck. The truck is accelerating at 1.7 m/s 2. Draw FBDs for both crates, and determine the values of all forces in your diagrams. Indicate the direction of the truck s motion in your diagrams. (2.1, 2.4) K/U T/I C A 57. A block with a mass of 2.0 kg is placed on a plane inclined at 328 to the horizontal. The coefficient of friction between the block and the plane is (2.4) T/I A (a) Calculate the force of friction acting on the block. (b) Is the force of friction static or kinetic? Explain. NEL Chapter 2 Review 103

5 58. A chest of drawers with a mass of 66 kg rests on the floor. The coefficient of static friction between the chest and the floor is Calculate the magnitude of the minimum horizontal force that a person must apply to start the chest moving. (2.4) T/I A 59. A block resting at the top of a plane inclined at 268 with the horizontal slides down with an acceleration of g [down the plane]. Calculate the coefficient of 5 kinetic friction. (2.4) T/I A 60. A person is standing without slipping in a train that is accelerating forward. The coefficient of static friction between the passenger and the train floor is (2.4) T/I C A (a) Draw an FBD of the person. (b) Determine the maximum acceleration of the train before the person starts to slip. (c) Describe what the person can do, without changing any of his clothing or grabbing on to anything, to keep from slipping when the acceleration exceeds this value. 61. Determine the maximum acceleration of a train in which a box lying on its floor will remain stationary, given that the coefficient of static friction between the box and the train floor is (2.4) T/I A 62. A block slides down an incline of angle 268 with an acceleration of 2.5 m/s 2. Determine the coefficient of kinetic friction between the block and the incline. (2.4) T/I A 63. A metal block with a mass of 2.2 kg is resting on a table. The coefficient of kinetic friction between the block and the table is Calculate the acceleration of the block when a force of 18 N [E] is applied on it. (2.4) T/I A 64. An object sliding on a rough horizontal plane slows down at 6.6 m/s 2. Calculate the coefficient of kinetic friction between the object and the plane. (2.4) T/I A 65. A box with a mass of 2.2 kg sits on top of another box with a mass of 3.8 kg. The coefficient of friction between the two boxes is 0.25, and the coefficient of kinetic friction between the larger box and the horizontal surface is Determine the largest horizontal force that can be applied to the larger box so that the smaller box does not slip off. (2.4) T/I A Evaluation 66. A student says, If action reaction forces cancel, then the net force must always be zero. How can anyone ever accelerate? Discuss the validity of this statement. (2.2) K/U T/I C 67. You tie a rope to a large crate and try to pull it across a horizontal surface toward a fence, but it will not move. Suggest a way of moving the crate without getting any help from another person. Discuss any limitations of the method. (2.3) T/I C A 68. A person with a mass of 59.2 kg sits on a light seat attached to a rope that runs over a pulley, as shown in Figure 8. The person pulls down on the rope to move herself up at a constant velocity. (2.3) T/I A Figure 8 (a) Explain why this setup provides an advantage over climbing up a rope. (b) What magnitude of force does the person exert on the rope? (c) What assumptions are you making about the setup when calculating the force exerted by the person? 69. The following steps summarize the strategy for solving two-dimensional force problems that require Newton s second law of motion. Place the steps in the correct order. (2.3) K/U T/I C (a) Solve the problem using Newton s second law of motion. (b) Determine the x- and y-components of each force, and write the necessary equations. (c) Identify the given variables and the required variables. (d) Choose a coordinate system, and draw an FBD. Include a label for each force. (e) Identify the object on which the forces act. (f) Read the problem before trying to solve it. 70. A student claims the following about cross-country skiing: I wish there was no friction when I m sliding down those small hills, but I m sure glad there is a little friction when I m trying to go uphill. Why do you think the student would say this? Explain your reasoning. (2.4) K/U T/I A 104 Chapter 2 Dynamics NEL

6 71. The coefficient of static friction between your running shoes and dry pavement is When the pavement is wet, the coefficient of static friction is (2.4) T/I (a) Determine the maximum acceleration you can achieve in both cases. (b) How quickly could you run 100 m if you could sustain these accelerations? Are these times reasonable? 72. Two workers move a 52 kg crate by sliding it across the floor. Worker 1 can exert a force of N, and worker 2 can exert a force of N. One worker must push on the crate below the horizontal and the other must pull at the same angle above the horizontal (Figure 9). Determine the acceleration of the crate. Assume that the coefficient of kinetic friction is 0.52 and u = 258. (2.4) T/I A Figure A driver makes an emergency stop and inadvertently locks up the brakes of the car, which skids to a stop on dry concrete. Consider the effect of heavy rain on this scenario. Using the values in Table 1, determine how much farther the car would skid (expressed as a percentage of the dry-weather skid) if the concrete were wet instead. What does this question imply about driving safely? (2.4) T/I A Table 1 Coeffi cients of Kinetic Friction for Rubber on Concrete Surface rubber on dry concrete 0.85 rubber on wet concrete Two skiers are racing down a hill that is inclined at 238 to the horizontal. Skier 1 has a mass of 59 kg, and skier 2 has a mass of 73 kg. The coefficient of kinetic friction between the skis and the hill is Use the equation below to answer the following questions. (2.6) T/I A a 5 g sin u 2 m K g cos u 2 F air m (a) Compare the accelerations of the skiers if air resistance is negligible. Explain your answer. (b) The air resistance on race day is 82 N. Compare the accelerations of the skiers. (c) Evaluate the difference in accelerations. Does the difference affect the race? m K Reflect on Your Learning 75. How would you explain the common forces experienced in everyday life to a class if you were the teacher and your students had not taken physics? How would you explain FBDs to your class? T/I C A 76. In what areas of your daily experience do you now see the physics concepts that were explored in this chapter? T/I C 77. How did the information you learned in this chapter affect your thinking about frictional forces? T/I C A 78. Identify a situation you have experienced that involves concepts from this chapter. Write a question about it, and share it with a classmate. A 79. What was the most surprising thing you learned in this chapter? C 80. Was there any example in this chapter that you found particularly relevant to your daily life? C Research WEB LINK 81. Research biomechanics. How are the principles of biomechanics used by athletes? Identify the various fields that make use of a force platform and discuss its use. K/U T/I C A 82. Research automobile seat belts. Explain why seat belts are equipped with pre-tensioners and web clamps. Prepare a short oral presentation on automatic belt systems to give to your class. K/U T/I C A 83. Research the effect of belt friction. Describe the various techniques involved in friction management for climbing operations. K/U T/I C A 84. Research the physics of archery. What aspects of the principles of motion are applied in archery (Figure 10)? K/U C A Figure 10 NEL Chapter 2 Review 105