Conceptual Physics Newton s Laws Outline Hewitt: Chapter 4, 5, 6 Exercises: 3 Forces Fill in the Charts completely Variables introduced or used in chapter: Quantity Symbol Units Force Mass Accelerated Weight Pressure Summation Add Σ None Formula Chart* *In Class, we will use x for horizontal motion, and y for vertical motion instead of d Force Weight Friction Newton s 1 st Law ΣF = 0 Newton s 2 nd Law ΣF = ma Newton s 3 rd Law F 12 = - F 21 Page 45
Define the following terms using COMPLETE SENTENCES: Inertia Weight Gravitational Force Normal Force Friction Static Friction Kinetic/Sliding Friction Rolling Friction Fluid Friction Equilibrium Pressure Newton s 1 st Law Newton s 2 nd Law Newton s 3 rd Law Net Force Air Resistance Terminal Velocity/Terminal Speed Action Force Page 46
Reaction Force Unit 5 Newton s Laws Homework FBD s: Draw FBD for the 1-8 1. A book is at rest on a table top. 2. A horizontal bar hangs from the ceiling suspended from two ropes. If a girl is holding on to the bar with one hand and is hanging motionless below the bar, diagram the forces acting on the girl and then diagram the forces acting on the bar. 3. An egg is free-falling from a nest in a tree. Neglect air resistance. 4. A flying squirrel is gliding (no wing flaps) from a tree to the ground at constant velocity. Consider air resistance. 5. A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance. 6. A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder. Diagram the vertical forces acting on the backpack. 7. A force is applied to the right to drag a sled with a rightward acceleration across loosely-packed snow, which has a coefficient of friction. 8. A football is moving upwards towards its peak after having been booted by the punter. Neglect air resistance. Diagram the forces acting upon the football as it rises upward towards its peak. 9. Free body diagrams for four situations are shown below. In each case, the net force is known. However the magnitude of some of the individual forces is not known. Analyze each situation individually to determine the magnitude of the unknown forces. (the last object has a mass of 10 kg) Problems: Use GUESS to solve each 10. Different masses are hung on a spring scale calibrated in Newtons. a) The force exerted by gravity on 1 kg = 9.8 N. b) The force exerted by gravity on 5 kg = N. c) The force exerted by gravity on kg = 98 N. d) The force exerted by gravity on 70 kg = N. 11. What acceleration will result when a 12-N net force is applied to the right on a 3-kg object? What would the acceleration be if the same force is applied to a 6-kg object? [4 m/s 2, 2 m/s 2 ] 12. A net force of 16 N causes a mass to accelerate to the left at the rate of 5 m/s 2. Determine the mass of the object. [3.2 kg] 13. An object is accelerating at 2 m/s 2. If the net force is tripled and the mass of the object is doubled, what is the new acceleration? [3 m/s 2 ] 14. An object is accelerating at 2 m/s 2. If the net force is tripled and the mass of the object is halved, what is the new acceleration? [12 m/s 2 ] Page 47
15. A crate with a mass of 50.0 kg experiences an acceleration to the right with a magnitude of 3.5 m/s 2. Find the magnitude of the net force on the crate. [175 N] 16. A boy pushes a 0.50 kg book across a table by exerting a net force of 2.00 N on it. Calculate the magnitude of the acceleration that the book will experience. [4m/s 2 ] 17. An applied force of 50 N is used to accelerate a 100 N object to the right across a frictional surface. The object encounters 10 N of friction. Determine the normal force, the net force, the mass, and the acceleration of the object. (Neglect air resistance.) [F N = 100 N, F net = 40 N, a = 3.92 m/s 2, m = 10.2 kg] 18. What is the frictional force when a 750 kilogram car travels on a road (coefficient of friction of 0.4)? [2940 N] 19. A 52 Newton sled is pulled across a cement sidewalk at a constant velocity. A horizontal force of 36 Newtons is applied. What is the coefficient of sliding friction between the sled and the cement? [0.69] 20. Suppose the 52 Newton sled is now pulled on snow. The coefficient of friction drops to 0.12. If a person weighing 650 Newtons sits on the sled, what force is needed to sled across the snow at a constant velocity? [84.24 N] 21. An applied force of 20 N is used to accelerate a 20 kg object to the right across a frictional surface. The object encounters 10 N of friction. Determine the normal force, the net force, the coefficient of friction (µ) between the object and the surface, the force of gravity, and the acceleration of the object. (Neglect air resistance.) [F N = 196 N, F g = 196 N, F net = 10 N, a = 0.5 m/s 2, µ = 0.051] 22. A 5 kg object is sliding to the right and encountering a friction force which slows it down. The coefficient of friction between the object and the surface is 0.1. Determine the force of gravity, the normal force, the force of friction, the net force and the acceleration. (Neglect air resistance). [F g = 49 N, F N = 49 N, F FR = 4.9 N, F net = -4.9 N, a = -0.98 m/s 2 ] 23. A rightward force is applied to a 6 kg object to move it across a rough surface at constant velocity. The object encounters 15 N of frictional force. Determine the gravitational force, normal force, net force, applied force and coefficient of friction. Neglect air resistance. [F g = 58.8 N, F N = 58.8 N, F net = 0 N, F a = 15 N, µ = 0.255] 24. A rightward force is applied to a 10 kg object to move it across a rough surface at constant velocity. The coefficient of friction between the object and the surface is 0.2. Draw an FBD and determine the weight of the object, the normal force, applied force, frictional force and net force. Neglect air resistance. [F g = 98 N, F N = 98 N, F a = 19.6 N, F FR = 19.6 N, F net = 0 N] 25. A rightward force of 25 N is applied to a 4 kg object to move it across a rough surface with a rightward acceleration of 2.5 m/s 2. Draw an FBD and determine the weight of the object, normal force, frictional force, net force and coefficient of friction between the object and the surface. Neglect air resistance. [F g = 39.2 N, F N = 39.2 N, F FR = 15 N, F net = 10 N, µ = 0.383] 26. A box weighs 60 N and needs an applied force of 50 Newtons in order to overcome friction and move at a constant velocity. What is the coefficient of static friction? [0.833] 27. A metal crate has a mass of 50 kg and a coefficient of static friction of 0.4. a. How much force must be applied to get the crate moving? [196 N] b. Once it is moving, the coefficient of friction changes to 0.32. What force is needed to keep the box moving with constant velocity? [156.8 N] Diagrams 28. Which one(s) of the following force diagrams depict an object moving to the right with a constant speed? List all that apply. Page 48
For the 29-33 consider the velocity-time plot below for the motion of an object along a horizontal surface. The motion is divided into several time intervals, each labeled with a letter. 29. During which time interval(s), if any, are there no forces acting upon the object? List all that apply. 30. During which time interval(s), if any, are the forces acting upon the object balanced? List all that apply. 31. During which time interval(s), if any, is there a net force acting upon the object? List all that apply. 32. During which time interval(s), if any, is the net force acting upon the object directed toward the right? List all that apply. 33. During which time interval(s), if any, is the net force acting upon the object directed toward the left? List all that apply. For the 34-38, consider the dot diagram below for the motion of an object along a horizontal surface. The motion is divided into several time intervals, each labeled with a letter. 34. During which time interval(s), if any, are there no forces acting upon the object? List all that apply. 35. During which time interval(s), if any, are the forces acting upon the object balanced? List all that apply. 36. During which time interval(s), if any, is there a net force acting upon the object? List all that apply. 37. During which time interval(s), if any, is the net force acting upon the object directed toward the right? List all that apply. 38. During which time interval(s), if any, is the net force acting upon the object directed toward the left? List all that apply. For the 39-43, consider the trajectory diagram shown below for a projectile thrown at an angle to the horizontal. The vector arrows represent the horizontal and vertical components of the projectile's velocity. Use the trajectory diagram to answer the next several questions. (Consider air resistance to be negligible.) 39. At which point(s), if any, are there no forces acting upon the object? List all that apply. 40. At which point(s), if any, are the forces acting upon the object balanced? List all that apply. 41. At which point(s), if any, is there a net force acting upon the object? List all that apply. 42. At which point(s), if any, is the net force acting upon the object directed toward the right? 43. At which point(s), if any, is the net force acting upon the object directed upward? List all that apply. Page 49
Newton s 3 Laws 44. Newton s 1 st Law is also known as the Law of. 45. Mathematically, Newton s 1 st Law states: 46. Mathematically, Newton s 2 nd Law states: 47. Mathematically, Newton s 3 rd Law states: 48. Newton s 3 rd Law is also known as the Law 49. Imagine a place in the cosmos far from all gravitational and frictional influences. Suppose an astronaut in that place throws a rock. The rock will: 50. An 2-kg object is moving horizontally with a speed of 4 m/s. How much net force is required to keep the object moving with the same speed and in the same direction? 51. Mac and Tosh are arguing in the cafeteria. Mac says that if he throws his jello with a greater speed it will have a greater inertia. Tosh argues that inertia does not depend upon speed, but rather upon mass. With whom do you agree? Why? 52. Mr. Wegley spends most Sunday afternoons at rest on the sofa, watching pro football games and consuming large quantities of food. What effect (if any) does this practice have upon his inertia? Explain. 53. Ben Tooclose is being chased through the woods by a bull moose which he was attempting to photograph. The enormous mass of the bull moose is extremely intimidating. Yet, if Ben makes a zigzag pattern through the woods, he will be able to use the large mass of the moose to his own advantage. Explain this in terms of inertia and Newton's first law of motion. 54. You are standing on the floor. a) What is the reaction force to your feet pushing on the floor? b) What is the reaction force to your weight? 55. You are pulling on a rope. What is the reaction force? Which Law: Each one of Newton's Laws can play a role in any one particular situation. Pick which of Newton's most governs the situations described below. a. First Law (inertia) b. Second Law (F = ma) c. Third Law (action-reaction) 56. A helicopter must have two sets of blades in order to fly with stability. 57. If you were in an elevator and the cable broke, jumping up just before the elevator hit the ground would not save you. Sorry. 58. You usually jerk a paper towel from a roll in order to tear it instead of pulling it smoothly. 59. A student desk changes the amount of force it puts on other objects throughout a school day. 60. Heavy objects are not easier to move around in a horizontal fashion on the Moon than on the Earth. 61. The stronger, heavier team in a tug-of-war does not create a larger tension in the rope than the weaker, lighter team. 62. You are in a car that is traveling on I-10. Your backpack: a) Sits while traveling at 75 mph. b) Slides forward when someone cuts you off and the driver hits the brakes. c) Slides back when the driver is accelerating to merge. d) Slides back and forth while the driver swerves quickly through traffic. 63. You are in your seat, napping during class. 64. You stand on a scale to read your weight. 65. Your hand hurts when you catch a fastball with no glove. Page 50
Review Sheet - Newton s Laws Complete this review sheet as a study aid for your test over Newton s Laws. It is due the day of the test. Make sure to study your notes key words to be familiar with force, contact forces, action-at-a-distance forces, inertia, Newton s 3 laws, mass, balanced vs. unbalanced forces, friction, force of gravity, normal force, tension, air resistance, spring force, static friction, kinetic friction 1. The resistance of an object to change its state of motion is a. velocity b. inertia c. force d. acceleration 2. True/False Mass is the measure of an object s inertia. 3. A push or pull on an object caused by an interaction with another object. a. velocity b. force c. acceleration d. resistance 4. True/False An object in motion tends to change its motion when an unbalanced force acts on it. 5. The amount of inertia of an object depends on the object s a. force b. weight c. acceleration d. mass 6. Force is measured in a. Newtons b. watts c. joules d. kg / m 7. Two forces that oppose the motion of an object are a. normal force and friction force b. air resistance and friction force c. friction force and applied force d. tension force and force of air 8. True/False Force is a vector quantity. 9. True/False The normal force (F N ) is the support force a surface exerts upwards on an object. 10. An archer shoots an arrow. Consider the action force to be the bow string against the arrow. The reaction to this force is the. a. arrow's push against the bowstring. b. air resistance against the bow. c. weight of the arrow. d. grip of the archer's hand on the bow. e. friction of the ground against the archer's feet. 11. True or False For Newton s 3 rd law to occur, there must be 2 objects involved each exerting a force on the other. 12. A player hits a ball with a bat. The action force is the impact of the bat against the ball. What is the reaction to this force? a. The force of the ball against the bat b. Air resistance on the ball c. The grip of the player's hand against the bat d. The weight of the ball Page 51
13. A woman weighing 500 N sits on the floor. She exerts a force on the floor of. a. 500 N. b. 50 N c. 250 N d. 1000 N. e. 5 N 14. As the 500 N woman sits on the floor, the floor exerts a force on her of. a. 5 N. b. 1000 N. c. 500 N. d. 50 N. e. 250 N. 15. Identify which law goes with the following examples. a. A child coasting on ice has to use a tree to come to a stop. b. When stepping off of a boat the boat moves backwards c. A car with a large load drives more sluggishly. d. It takes a full elevator longer to reach the top than and empty elevator. e. The Paris gun (a big gun used in WWI) moves backwards when fired. f. All of the papers on the front seat fall off when the brakes are slammed on. 16. A force of 750 N is applied to slide a mass of 110 kg to the right. The force of friction that opposes this motion is 150 N. Find the weight of the object, the normal force, and the acceleration of the object. [F g = 1078 N, F N = 1078 N, a = 5.455 m/s 2 ] 17. A force of 300 N is sufficient to keep a 100 kg wooden crate moving at constant velocity across a wooden floor. What is the coefficient of sliding friction? [0.306] 18. Choose the best answer: Kinetic friction: a. increases as the normal force increases b. is less than or equal to static friction c. is the force to overcome when an object is moving at a constant velocity. d. all of the above 19. According to Newton s Law, an object with no net force acting on it can move with a constant velocity. 20. Newton s law states that the larger the force the larger the acceleration and the larger the mass the smaller the acceleration. 21. Two teams in a tug of war exert the same amount of force on each other and the rope does not move. Newton s law explains why the rope doesn t move. 22. Mr. Physics buys a 20 kg sheet of plywood at Home Depot. How much force is required to pull the top sheet off the pile if the coefficient of friction is 0.23 and the board accelerates at 2.2 m/s 2? [89.08 N] 23. A 35 kg box is sliding on a rough table. If the applied force is 122.2 N and the coefficient of friction is 0.225, what is the net force? [45 N] 24. If you start with an acceleration of 10 m/s 2, what would your new acceleration be if you multiply the mass by three and multiply the force by four? [13.33 m/s 2 ] 25. A 1500 kg car can accelerate uniformly at 4 m/s 2. What will its acceleration be if it accelerates while pulling another car of the same mass (the mass has doubled)? Explain why. [2 m/s 2 ] Page 52
26. A force of 750 N is applied to slide a mass of 110 kg to the right. The coefficient of kinetic friction is 0.23. Find the force of friction, normal force, force of gravity, net force and acceleration. [F FR = 247.94 N, F N = 1078 N, F g = 1078 N, F net = 502.06, a = 4.564 m/s 2 ] 27. An applied force of 50 N is used to accelerate an 80 N object to the right across a frictional surface. The object encounters 10 N of friction. Determine the mass, the normal force, the net force in both directions and the acceleration of the object. [m = 8.16 kg; F N = 80 N; F net x = 40 N; F net y = 0 N; a = 4.9 m/s 2 ] 28. A rightward force is applied to a 6 kg object to move it across a rough surface at constant velocity. The object encounters 15 N of frictional force. Determine the force of gravity, the normal force, the net force in both directions, the coefficient of friction (µ) and the applied force. [F net x = 0 N; F net y = 0 N; F N = 58.8 N; F g = 58.8 N; µ = 0.26; F a = 15 N] 29. A rightward force of 25 N is applied to a 4 kg object to move it across a rough surface with a rightward acceleration of 2.5 m/s 2. Determine the gravitational force, the normal force, the net force in both directions, the frictional force, and the coefficient of friction between the object and the surface. [F FR = 15 N; F N = 39.2 N; F g = 39.2 N; F net x = 10 N; F net y = 0 N; µ = 0.383] 30. The coefficient of static friction between a 100 kg box and a surface is 0.30. What is the maximum force that can be applied to the box horizontally before it will move? [294 N] 31. A cart is pulled with a net force of 200 N to the right. If the acceleration of the cart is 3 m/s 2, what is the mass of the cart? [66.7 kg] Page 53
Lab: Skateboard Project 1. Weigh you and your skateboard in pounds: Fg = 2. Convert pounds to kg: Using: 1 kg = 2.2 lbs M = (1kg) = (this is your MASS) (2.2 lbs) 3. Calculate your WEIGHT: Fg = mg 4. Draw a FBD of you on the skateboard being pulled with no acceleration 5. Calculate your NORMAL FORCE: a. Sum forces in Y direction = 0 (You are not moving in Y) b. Solve for Fn 6. Standing on the skateboard, see how much force is needed to get your STARTED: This is your STATIC friction: Fstatic = 7. Calculate Coefficient of static friction: Fs = µsfn 8. Now, pull at a CONSTANT SPEED. This is your Kinetic 9. Friction: Fk = 10. Calculate the Coefficient of kinetic Friction: Fk = µkfn 11. Which is greater? Coefficient of kinetic friction of static? Page 54