AP Physics-B Dynamics (Newton s Laws) - The Causes of Motion Introduction: This unit introduces the most basic of all scientific concepts, the interaction between forces and matter. You should understand from the outset that any time two or more objects interact, the interaction causes a force on each object. There are no exceptions. In your earlier science courses, a force was defined as a push or a pull. This is correct but now you need to understand that a force on a body is caused by an interaction between bodies. We isolate and then study the forces acting on one body without regard to the origin of the forces. This gets confusing for the beginning physics student. You need to spend a lot of time thinking about, sorting through, and organizing in your mind the information learned in this unit. Sir Isaac Newton had to go through the same process in developing his laws of motion. You have an advantage you have over three hundred years of the experiences of all of the physics to follow. Force is a vector quantity; it always has direction and magnitude. A force applied to a body can do two things; it can alter the dimension or shape of the body or it can alter the state of motion of the body. Natural forces known to scientists are gravitational, electromagnetic, and nuclear forces. Dynamics is the study of forces which cause motion. Performance Objectives: Upon completion of the readings and activities of this unit and when asked to respond either orally or on a written test, you will: State the first law of motion and display a clear understanding of its universality and implications. Give examples of what happens to an object when no external net force acts on it. Use the words force, mass, weight, and inertia in their correct scientific meanings. State the second law of motion, and display a clear understanding of its universality and implications. Be able to apply the law to determine the results of forces. Solve problems involving this law. Understand the rationale behind the definition of the Newton. Recognize the relationship between the second law and the unit of force. Distinguish between weight and mass. Explain the nature of weight as a force. Use the second law to determine the mass. Demonstrate an understanding of the meaning of new force. Use the concept of net force to solve problems. State the observations regarding sliding friction. Compute the coefficient of friction. Solve problems involving frictional forces. State the third law, and display a clear understanding of its universality and implications. Distinguish between forces applied to a body and forces being applied by the body. Be able to isolate bodies to solve problems. Incorporate the problems solving techniques learned in this unit with ideas learned in the kinematics and the vector units. Textbook Reference: Physics (Sixth Edition): Chapter 4 In the beginning there was Aristotle. And objects at rest tended to remain at rest. And objects in motion tended to come to rest. And soon everything was at rest and God saw that boring. Then God created Newton. - Dr. William Baker, President Bell Laboratories (1978) Answer the following questions and solve the following problems on your own paper. No credit given for work done on this sheet! Introductory Questions: 1. Your weight is the result of a gravitational force of the earth on your body. What is the corresponding reaction force?
2. As you stand on the floor, does the floor exert an upward force against your feet? How much force does it exert? 3. Suppose a brick is suspended from a rigid support by a suitable length of cord. a.) What downward force acts on the brick? b.) If this force is the action force, what is the corresponding reaction force? 4. a.) What upward force acts on the suspended brick in Question 3? b.) If this force is the action force, what is the corresponding reaction force? Conceptual Questions - First Law: 5. A ball is rolled across the top of a table and slowly comes to a stop. Considering Newton s first law of motion, explain why the ball stops. How could the ball have remained in motion? 6. In terms of inertia, what is the disadvantage of a lightweight camera when snapping the shutter? Why do most photographers prefer a massive tripod? 7. Why does the downward motion and sudden stop of the hammer tighten the hammerhead? 8. An astronaut in space has a weightless anvil. Is it more difficult, less difficult or just as difficult to shake the anvil back and forth in space as it is on earth? 9. Many automobile passengers suffer neck injuries when struck by cars from behind. How does Newton=s law of inertia apply here? How do headrests help guard against this type of injury? 10. Most car ads now include mileage ratings, on for highway driving and one for city driving. Why is the city driving rating always less than the highway driving rating? 11. If a ball moving with a velocity of 20 cm/s has no net force act on it, its velocity after 5 seconds will be? Second Law Exercises: 12. A force gives a 2 kg mass an acceleration of 5.0 m/s 2. What is the magnitude of the force? 10 N 13. A force of 30.0 N gives a stone an acceleration of 4.0 m/s 2. What is the mass of the stone? 7.5 kg 14. A net force of 25 N is applied to a 2.0 kg mass. What is the acceleration given to the mass? 12.5 m/s 2 15. Determine the weight of a 4.8 kg mass. 47 N 16. A small yacht weighs 4900 N. What is its mass in kilograms? 500 kg 17. A car has a mass of 1200 kg. What is the weight of the car? What net external force must be applied to the car to accelerate the car along a level highway at the rate of 4.0 m/s 2 (neglecting friction)? What acceleration would this force produce if a 750 N frictional force were present? 11,760 N 4800 N 3.375 m/s 2 More Second Law Problems, but this time the net force is not given: Keep in mind that this is a vector equation and you must keep track of the directions. The applied force is in the direction of the motion and the opposing force is any force acting on the body in a direction opposite to the motion. When moving bodies are in contact, the opposing force is due to friction. When there are relative motions between a fluid and a body that moves through the fluid, the opposing force is called the drag force. If a body falls for enough through the air (which is a fluid), the drag force eventually equals the weight which is the applied force, so the net force and the acceleration on the body are zero. The body then falls at a constant velocity called the terminal velocity. F net = F app + F opp
18. Determine the acceleration that a force of 25.0 N gives to a 4.0 kg mass. The friction force to overcome is 5.0 N. 5.0 m/s 2 19. A rocket weighs 9800.0 N. a.) What is its mass? b.) What applied force gives it a vertical acceleration of 4.00 m/s 2? 1000.0 kg 13,800 N 20. A small rocket weighs 14.7 N. a.) What is its mass? b.) The rocket is fired from a high platform but its engine fails to burn properly. The rocket gains a total upward force of only 10.2 N. At what rate and in what direction is the rocket accelerated? 1.5 kg -3.0 m/s 2 21. A falling bowling ball has a mass of 2.0 kg. The upward force of air resistance is 11.6 N. What is the acceleration of the bowling ball? -4.0 m/s 2 22. An elevator of mass 1000.0 kg is supported by a cable that can sustain a force of 12,000.0 N. What is the greatest upward acceleration that can be given the elevator without breaking the cable? 2.2 m/s 2 23. A person weighing 490.0 N stands on a scale in an elevator. a.) What does the scale read when the elevator is at rest? b.) The elevator starts to ascend and accelerates the person upward at 2.0 m/s 2. What is the reading on the scale now? c.) When the elevator reaches a desirable speed, it no longer accelerates. What is the reading on the scale as the elevator rises uniformly? d.) The elevator begins to slow down as it reaches the proper floor. Do the scale readings increase or decrease? e.) The elevator starts to descend. Does the scale reading increase or decrease? f.) What does the scale read if the elevator descends at a constant speed? g.) If the cable snapped and the elevator fell freely, what would the scale read? 24. The mass of an elevator plus its occupants is 750.0 kg. The tension in the cable is 8950 N. At what rate does the elevator accelerate upward? 2.1 m/s 2 25. A baseball weighs 4.9 N. a.) What is its mass? b.) At what rate is the ball accelerated straight up if a 68.9 N force is applied to it in that direction? 128 m/s 2 26. What applied force accelerates a 20 kg stone straight up at 10.0 m/s 2? 396 N Conceptual Questions - Second Law: 27. If you find a body that is not moving even though we know it to be acted on by a force. What inference can we draw? 28. How does the weight of a falling body compare to the air resistance just before it reaches terminal velocity? After? 29. Suppose you place a ball in the middle of a wagon and then accelerate the wagon forward. Describe the motion of the ball relative to the ground and to the wagon. Friction: Whenever an object moves while in contact with another object, frictional forces oppose the relative motion. If we slide a box across a floor, we find that we must continue to apply a steady horizontal force to cause the box to slide uniformly over the horizontal surface. The opposing force is called friction. If the applied force is just equal to the friction force, the body will move at a constant velocity. If the applied force is greater than the friction force, the body will accelerate.
Some observations regarding sliding (kinetic) friction are: 1.) The frictional force is parallel to the surfaces sliding over one another and in the direction opposite to the motion of the object; 2.) The friction force is proportional to the force which is normal (perpendicular) to the surfaces and which presses them together; 3.) The friction force is roughly independent of the area of the surfaces in contact; 4.) The frictional force is roughly independent of the speed of sliding, provided that the resulting heat does not alter the condition of the surfaces; 5.) The friction force depends open the nature of the substances in contact and the condition of the surface; and 6.) Sliding friction is less than or equal to starting (static) friction. F friction When two bodies, in contact with each other, have some velocity relative µ = to each other, the ratio of the friction force to the normal force is called the coefficient F normal of kinetic friction. The Greek letter mu is the symbol for the coefficient of friction. 30. A 5000 N piano is moved 20 feet across a floor at constant speed by a horizontal force of 750 N. Find the coefficient of friction. 0.15 31. A force of 155 N is required to start a sled whose weight is 800 N; while a force of 54 N is sufficient to keep it moving at constant speed once it is started. Find the coefficient of starting and sliding friction. 0.19 0.0675 32. A horizontal force of 6.0 N is applied to a 1.0 kg block, which rests on a horizontal surface. If the coefficient of friction is 0.40, find the acceleration of the block. 2.1 m/s 2 33. A man holds a block from falling by pushing it horizontally against a vertical wall. If the block weighs 3.0 N and the coefficient of static friction between the block and the wall is 0.4, what force must he exert? 7.5 N Forces at an angle to the motion remember resolution of a vector! 34. A 20.0 kg sled is pulled along level ground. The sled s rope makes an angle of 60.0 degrees with the snowcovered ground and pulls on the sled with a force of 180 N. Find the acceleration of the sled if the friction force to be overcome is 15 N. 3.8 m/s 2 35. A box having a mass of 50.0 kg is dragged across a horizontal floor by means of a rope tied on the front of it. The coefficient of sliding friction between the box and the floor is 0.300. If the angle between the rope and the floor is 30.0 degrees, what force must be exerted on the rope to move the box at constant speed? 145 N 36. A 1200 N sled is pulled along a horizontal surface at a uniform speed by means of a rope that makes an angle of 30 degrees above the horizontal. If the force on the rope is 100 N, what is the coefficient of friction? 0.0753 37. A 50 kg box is placed on an inclined plane making an angle of 30 degrees with the horizontal. If the coefficient of kinetic friction is 0.30, find the acceleration of the block down the plane. 2.4 m/s 2 Now is the time to remember those kinematic formulas: 38. An artillery shell has a mass of 8.0 kg. The shell is fired from the muzzle of a gun with a speed of 700.0 m/s. The gun barrel is 3.5 m long. What is the average force on the shell while it is in the gun barrel? 5.6 x 10 5 N 39. A racing car has a mass of 700.0 kg. It starts from rest and travels 120 m in 2.0 seconds. What is the force applied to it? (Ignore friction) 4.2 x 10 4 N 40. A car weighing 9800.0 N travels at 30.0 m/s. a.) What braking force brings it to rest in 100.0 m? b.) in 10.0m? 4500 N 45000 N
41. A rocket that weighs 7840 N on earth is fired. The force of propulsion is 10,440 N. Determine a.) the mass of the rocket. b.) the upward acceleration of the rocket. c.) the velocity of the rocket at the end of 10 seconds. 800 kg 3.25 m/s 2 32.5 m/s 42. A 60.0 kg sled is coasting with a constant velocity of 10.0 m/s over smooth ice. It enters a rough stretch of ice 6.0 m long in which the force of friction is 120 N. With what speed does the sled emerge from the rough stretch of ice. 8.7 m/s 43. An object which is given an initial speed of 10.0 m/s on level ice comes to rest in 100.0 m. What is the coefficient of kinetic friction between the object and the ice? 0.051 Two Body Problems: Although two bodies are moving, the two bodies are attached and therefore move with the same speed and the same acceleration. The two bodies are treated as one system. Usually it is necessary to determine the acceleration of the system first. To find the tension in the cord connecting the bodies, isolate one body and solve for the tension using Newton s Second Law. F net a system = m total 44. Objects of mass 5.0 kg and 2.0 kg are connected by a light cord that passes over a horizontal frictionless rod. a.) What is the acceleration of the system? b.) What is the tension in the cord on the 5.0 kg side? c.) What is the tension in the cord on the 2.0 kg side? 4.2 m/s 2 b = c = 28 N 45. A cord connecting objects of mass 10.0 kg and 5.0 kg passes over a light frictionless pulley. a.) What is the acceleration of the system? b.) What is the tension in the cord? 3.27 m/s 2 65.3 N 46. Bob and Joe, two construction workers on the roof of a building, are about to raise a bucket of nails from the ground by means of a rope passing over a pulley 16 m above the ground. Bob has a mass of 100.0 kg and Joe has a mass of 80.0 kg. The bucket s mass is 40.0 kg and the mass of the nails is 80.0 kg. They slip off the roof and the following unfortunate sequence of events takes place: Bob and Joe, hanging on the same rope, strike the ground just as the bucket of nails hits the pulley. Un-nerved by his fall, Bob lets go of the rope, and the falling bucket of nails pulls Joe up to the roof where he cracks his head against the pulley but manages to hang on. However, the bottom falls out of the bucket when it struck the ground, and the empty bucket rises as Joe returns to the ground. Finally, Joe has had enough and lets go of the rope and remains on the ground only to be hit in the head by the empty bucket. Ignoring the possible mid-air collisions which merely add insult to injury, how long did it take for this little drama to unfold? (To make calculations easier, use g = -10 m/s s ) 47. A block of mass 6.0 kg resting on a horizontal frictionless surface is connected to a hanging 4.0 kg block by a cord passing over a frictionless pulley. Find the tension in the cord and the acceleration of the blocks. 3.92 m/s 2 23.52 N 48. A 0.350 kg block of wood on a horizontal plane is fastened to a cord passing over a frictionless pulley and attached to a 0.265 kg mass. The coefficient of kinetic friction between the block and the plane is 0.45. a.) Determine the acceleration of the system after it is set in motion. b.) What is the tension in the cord? 1.72 m/s 2 2.14 N Newton s Third Law of Motion states: Whenever one body exerts a force on another, the second body exerts on the first a force of equal magnitude in the opposite direction. This is also known as the law of action and reaction or the law of interaction. According to this law, there is no such thing as a single force. A body can produce a force only if there is some other body to exert its force upon. FORCES ALWAYS OCCUR IN PAIRS! an action force and a reaction force. The action and reaction forces are not on the same body.