Lecture 6 Newton ’ s Laws of Motion

1. Lecture 6 Newton’s Laws of Motion

2. Exam #1 - next Thursday! • 20 multiple-choice problems • No notes allowed; equation sheet provided • A calculator will be needed. • CHECK YOUR BATTERIES! • NO equations or information may be stored in your calculator. This is part of your pledge on the exam. • Scratch paper will be provided, to be turned in at the end of the exam.

3. Cart on Track I a) slowly come to a stop b) continue with constant acceleration c) continue with decreasing acceleration d) continue with constant velocity e) immediately come to a stop Consider a cart on a horizontal frictionless table. Once the cart has been given a push and released, what will happen to the cart?

4. Cart on Track I a) slowly come to a stop b) continue with constant acceleration c) continue with decreasing acceleration d) continue with constant velocity e) immediately come to a stop Consider a cart on a horizontal frictionless table. Once the cart has been given a push and released, what will happen to the cart? After the cart is released, there is no longer a force in the x-direction. This does not mean that the cart stopsmoving!! It simply means that the cart will continuemoving with the same velocity it had at the moment of release. The initial push got the cart moving, but that force is not needed to keep the cart in motion.

5. a2 = 2a1 m1 m2 m1 a1 F a3 m2 F F F = m1 a1 Force and Two Masses a) ¾a1 b) 3/2a1 c) ½a1 d) 4/3a1 e) 2/3a1 A force Facts on mass m1giving acceleration a1. The same force acts on a different mass m2 giving acceleration a2= 2a1. If m1 and m2 are glued together and the same force F acts on this combination, what is the resulting acceleration? F = m2 a2 = a3 = ?

6. a2 = 2a1 m1 m2 m1 a1 F a3 m2 F F F = m1 a1 F = (3/2)m1 a3 => a3 = (2/3) a1 Force and Two Masses a) ¾a1 b) 3/2a1 c) ½a1 d) 4/3a1 e) 2/3a1 A force Facts on mass m1giving acceleration a1. The same force acts on a different mass m2 giving acceleration a2= 2a1. If m1 and m2 are glued together and the same force F acts on this combination, what is the resulting acceleration? Mass m2 must be ( m1)because its acceleration was 2a1 with the same force. Adding the two masses together gives ( )m1, leading to an acceleration of ( )a1 for the same applied force. F = m2 a2 = (1/2 m1 )(2a1 )

7. Weight Apparent weight: Your perception of your weight is based on the contact forces between your body and your surroundings. If your surroundings are accelerating, your apparent weight may be more or less than your actual weight. In this case the “apparent weight” is the sum of the gravitational attaction (actual weight) and the force required to accelerate the body, as specified

8. Newton’s Third Law of Motion Forces always come in pairs, acting on different objects: If object 1 exerts a force on object 2, then object 2 exerts a force – on object 1. These forces are called action-reaction pairs.

9. Some action-reaction pairs

10. Newton’s 3rd: F12 = - F21 action-reaction pairs are equal and opposite, but they act on different bodies Action-reaction pair? a) Yes b) No

11. Newton’s Third Law of Motion Although the forces are the same, the accelerations will not be unless the objects have the same mass. Q: When skydiving, do you exert a force on the earth? Does the earth accelerate towards you? Is the magnitude of the acceleration of the earth the same as the magnitude of your acceleration?

13. F m 2m Contact Force a) 2F b) F c) ½F d) 1/3F e) ¼F Two blocks of masses 2mand mare in contact on a horizontal frictionless surface. If a force F0 is applied to mass 2m, what is the force on mass m?

14. F m 2m Contact Force a) 2F b) F c) ½ F d) 1/3 F e) ¼ F Two blocks of masses 2mand mare in contact on a horizontal frictionless surface. If a force F0 is applied to mass 2m, what is the force on mass m? The force F0 leads to a specific acceleration of the entire system. In order for mass mto accelerate at the same rate, the force on it must be smaller! For the two blocks together, F0 = (3m)a. Since a is the same for both blocks, Fm = ma

15. Newton’s Third Law of Motion Contact forces: The force exerted by one box on the other is different depending on which one you push. Assume the mass of the two objects scales with size, and the forces pictured are the same. In which case is the magnitude of the force of box 1 on box 2 larger?

16. (a) (b) The lighter box will require less net force than the heavier box did (for the same acceleration). If the external force is instead applied to the heavier box, the contact force must be less than it was before: Two boxes sit side-by-side on a smooth horizontal surface. The lighter box has a mass of 5.2 kg, the heavier box has a mass of 7.4 kg. (a) Find the contact force between these boxes when a horizontal force of 5.0 N is applied to the light box. (b) If the 5.0-N force is applied to the heavy box instead, is the contact force between the boxes the same as, greater than, or less than the contact force in part (a)? Explain. (c) Verify your answer to part (b) by calculating the contact force in this case. The boxes will remain in contact, so must have the same acceleration. Use Newton’s second law to determine the magnitude of the contact forces

17. A small car collides with a large truck. Which experiences the greater impact force? Collision Course I a) the car b) the truck c) both the same d) it depends on the velocity of each e) it depends on the mass of each

18. A small car collides with a large truck. Which experiences the greater impact force? Collision Course I a) the car b) the truck c) both the same d) it depends on the velocity of each e) it depends on the mass of each According to Newton’s Third Law, both vehicles experience the same magnitude of force.

19. Forces in Two Dimensions The easiest way to handle forces in two dimensions is to treat each dimension separately, as we did for kinematics.

20. y ax = Fx/m = 33N / 19 kg = 1.7 m/s2 ay = 0 Σ Fy = 0 Fmom,y 35o Fmom,x x mass of child + sled = 19 kg

21. Normal Forces The normal force is the force exerted by a surface on an object, to keep an object above the surface. The normal force is always perpendicular to the surface.

22. The normal force may be equal to, greater than, or less than the weight.

23. No vertical motion, so

24. Case 1 Case 2 Normal Force a) case 1 b) case 2 c) it’s the same for both d) depends on the magnitude of the force F e) depends on the ice surface Below you see two cases: a physics student pulling or pushing a sled with a force F that is applied at an angle θ. In which case is the normal force greater?

25. Case 1 Case 2 Normal Force a) case 1 b) case 2 c) it’s the same for both d) depends on the magnitude of the force F 5) depends on the ice surface Below you see two cases: a physics student pulling or pushing a sled with a force F that is applied at an angle θ. In which case is the normal force greater? In case 1, the force F is pushing down (in addition to mg), so the normal force needs to be larger. In case 2, the force F is pulling up, against gravity, so the normal force is lessened.

26. A B On an Incline a) case A b) case B c) both the same (N = mg) d) both the same (0 < N < mg) e) both the same (N = 0) Consider two identical blocks, one resting on a flat surface and the other resting on an incline. For which case is the normal force greater?

27. A B On an Incline a) case A b) case B c) both the same (N = mg) d) both the same (0 < N < mg) e) both the same (N = 0) Consider two identical blocks, one resting on a flat surface and the other resting on an incline. For which case is the normal force greater? In case A, we know that N = W. In case B, due to the angle of the incline, N < W. In fact, we can see that N = W cos(θ). y x N f θ Wy W θ

28. In order to change the velocity of an object – magnitude or direction – a net force is required. Newton’s third law: If object 1 exerts a force on object 2, then object 2 exerts a force – on object 1. (I) (II) (III) Newton’s Laws

29. Ftop A weight on a string with identical string hanging from bottom … if I pull the bottom string down, which string will break first? W Fbot a) top string b) bottom string c) there is not enough information to answer this question

30. When you lift a bowling ball with a force of 82 N, the ball accelerates upward with an acceleration a. If you lift with a force of 92 N, the ball’s acceleration is 2a. Find (a) the weight of the bowling ball, and (b) the acceleration a.

31. b) a) When you lift a bowling ball with a force of 82 N, the ball accelerates upward with an acceleration a. If you lift with a force of 92 N, the ball’s acceleration is 2a. Find (a) the weight of the bowling ball, and (b) the acceleration a.

32. On vacation, your 1300-kg car pulls a 540-kg trailer away from a stoplight with an acceleration of 1.9 m/s2 (a) What is the net force exerted by the car on the trailer? (b) What force does the trailer exert on the car? (c) What is the net force acting on the car?

34. A 71-kg parent and a 19-kg child meet at the center of an ice rink. They place their hands together and push. (a) Is the force experienced by the child more than, less than, or the same as the force experienced by the parent? (b) Is the acceleration of the child more than, less than, or the same as the acceleration of the parent? Explain. (c) If the acceleration of the child is 2.6 m/s2 in magnitude, what is the magnitude of the parent’s acceleration?

36. Before practicing his routine on the rings, a 67-kg gymnast stands motionless, with one hand grasping each ring and his feet touching the ground. Both arms slope upward at an angle of 24° above the horizontal. (a) If the force exerted by the rings on each arm has a magnitude of 290 N, and is directed along the length of the arm, what is the magnitude of the force exerted by the floor on his feet? (b) If the angle his arms make with the horizontal is greater that 24°, and everything else remains the same, is the force exerted by the floor on his feet greater than, less than, or the same as the value found in part (a)? Explain.

37. N

38. An archer shoots a 0.022-kg arrow at a target with a speed of 57 m/s. When it hits the target, it penetrates to a depth of 0.085 m. (a) What was the average force exerted by the target on the arrow? (b) If the mass of the arrow is doubled, and the force exerted by the target on the arrow remains the same, by what multiplicative factor does the penetration depth change? Explain.