1. Newton’s Laws Examples Physics 6A Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Newton’s Laws of Motion These three rules govern the motion of any object. 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force. 2: This is the formula we will use to calculate the effect of forces on objects. 3: Forces always come in action-reaction pairs. You have probably heard this as “for every action there is an equal and opposite reaction”.

3. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0v0

4. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0v0 You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v 0 indefinitely. Does the eraser do this?

5. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0v0 You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v 0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated?

6. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0v0 Here it is again – does the motion of the eraser follow this rule? 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force. You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v 0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated?

7. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0v0 There must some net force acting on the eraser since it changed its velocity You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v 0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated? Here it is again – does the motion of the eraser follow this rule? 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force.

8. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0v0 There must some net force acting on the eraser since it changed its velocity You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v 0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated? Here it is again – does the motion of the eraser follow this rule? 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force. What force(s) are exerted on the eraser?

9. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. v0v0 There must some net force acting on the eraser since it changed its velocity You may think that Newton’s first law (inertia) would tell us that the eraser should continue forward at speed v 0 indefinitely. Does the eraser do this? No, of course it slows down and then stops. So is Newton’s first law violated? Here it is again – does the motion of the eraser follow this rule? 1: Law of Inertia The velocity of an object will not change unless it is acted upon by a nonzero net force. What force(s) are exerted on the eraser? We can draw a picture of the eraser and all the forces that act on it. This is one of your most important tools – we call it a “free-body diagram”

10. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Here is the force diagram for the eraser weight Normal force friction

11. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Here is the force diagram for the eraser weight Normal force friction Assuming that the normal force and the weight are the same magnitude, which direction is the net force on the eraser? ‘Normal’ means perpendicular

12. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Here is the force diagram for the eraser weight Normal force friction Assuming that the normal force and the weight are the same magnitude, which direction is the net force on the eraser? The net force is to the left (in the direction of the friction force). What does this tell you about the acceleration of the eraser? ‘Normal’ means perpendicular

13. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Here is the force diagram for the eraser weight Normal force friction Assuming that the normal force and the weight are the same magnitude, which direction is the net force on the eraser? The net force is to the left (in the direction of the friction force). What does this tell you about the acceleration of the eraser? Yes, the acceleration is also to the left. This will always happen – the acceleration will be the same direction as the net force (this is from Newton’s 2 nd law) ‘Normal’ means perpendicular

14. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. Here is the force diagram for the eraser weight Normal force friction Assuming that the normal force and the weight are the same magnitude, which direction is the net force on the eraser? The net force is to the left (in the direction of the friction force). What does this tell you about the acceleration of the eraser? Yes, the acceleration is also to the left. This will always happen – the acceleration will be the same direction as the net force (this is from Newton’s 2 nd law) At this point it should be clear why the eraser slowed down and stopped. The acceleration was to the left – opposite the velocity, so the speed decreased. We will return to this example and do some calculations after we learn more about friction. ‘Normal’ means perpendicular

15. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? weight Normal force friction

16. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Let’s think about the friction force first. What objects are interacting to make the friction force happen? weight Normal force friction

17. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Let’s think about the friction force first. What objects are interacting to make the friction force happen? It is the rough surface of the eraser rubbing against the metal chalk rail. How would you describe the ‘reaction’ to this force? weight Normal force F rail on eraser

18. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Let’s think about the friction force first. What objects are interacting to make the friction force happen? It is the rough surface of the eraser rubbing against the metal chalk rail. How would you describe the ‘reaction’ to this force? The ‘reaction’ is always the same 2 objects, with their roles reversed. So we can consider the force that the eraser exerts on the rail as the corresponding reaction. This was not in our free-body diagram because our diagram only had forces on the eraser. weight Normal force F rail on eraser F eraser on rail,x

19. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? weight Normal force F rail on eraser F eraser on rail,x

20. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? weight Normal force F rail on eraser F eraser on rail,x

21. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? The weight is the force of gravity exerted on the eraser by the earth. F earth on eraser Normal force F rail on eraser F eraser on rail,x

22. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? The weight is the force of gravity exerted on the eraser by the earth. So how would you describe the reaction force? Is it the normal force? F earth on eraser Normal force F rail on eraser F eraser on rail,x

23. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? The weight is the force of gravity exerted on the eraser by the earth. So how would you describe the reaction force? Is it the normal force? NO (why not??) F earth on eraser Normal force F rail on eraser F eraser on rail,x

24. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? What about the weight? What is the reaction to that force? What objects are interacting to make the weight of the eraser? The weight is the force of gravity exerted on the eraser by the earth. So how would you describe the reaction force? Is it the normal force? NO (why not??) The reaction has to be the same objects with their roles reversed. The weight was the earth pulling downward on the eraser, so the reaction should be the eraser pulling upward on the earth. (same 2 objects, opposite direction) F earth on eraser Normal force F rail on eraser F eraser on rail,x EARTH (not to scale) F eraser on earth

25. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Ok, last one – what is the reaction that corresponds to the normal force? First identify which 2 objects are interacting. F earth on eraser Normal force F rail on eraser F eraser on rail,x EARTH (not to scale) F eraser on earth

26. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Ok, last one – what is the reaction that corresponds to the normal force? First identify which 2 objects are interacting. This time it is the eraser and the chalk rail, but in the vertical (y) direction. F earth on eraser F rail on eraser,y F rail on eraser,x F eraser on rail,x EARTH (not to scale) F eraser on earth

27. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail The eraser in the diagram is pushed giving it an initial velocity v 0, then released and allowed to slide until it stops. We will put some numbers in later. For now, we will consider what Newton’s Laws tell us about this motion. One more idea with this eraser example: How does Newton’s 3 rd law apply here? Does each force in our diagram have an ‘equal and opposite’ reaction force? Ok, last one – what is the reaction that corresponds to the normal force? First identify which 2 objects are interacting. This time it is the eraser and the chalk rail, but in the vertical (y) direction. The opposite to this force is a downward force on the chalk rail due to the eraser. F earth on eraser F rail on eraser,y F rail on eraser,x F eraser on rail,x EARTH (not to scale) F eraser on earth F eraser on rail,y

28. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration.

29. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. 120 N weight Normal force y x

30. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. 120 N weight Normal force We can use Newton’s 2 nd law to calculate the acceleration. y x

31. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. 120 N weight Normal force We can use Newton’s 2 nd law to calculate the acceleration. We can write down separate equations for the x- and y-directions: y x

32. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. 120 N weight Normal force We can use Newton’s 2 nd law to calculate the acceleration. We can write down separate equations for the x- and y-directions: y x

33. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: Pushing a box across the floor. A 60 kg box is at rest on a frictionless horizontal floor. It is pushed to the right by a 120-Newton force. Draw a free-body diagram for the box. Find the resulting acceleration. 120 N weight Normal force We can use Newton’s 2 nd law to calculate the acceleration. We can write down separate equations for the x- and y-directions: y x Notice that we could determine that the normal force equals the weight, but in this problem we don’t really care (if there were friction we would need this fact)

34. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser.

35. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser. weight Normal force friction Here is the free-body diagram again. Notice that the only horizontal force is friction.

36. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser. weight Normal force friction Here is the free-body diagram again. Notice that the only horizontal force is friction. We can write down Newton’s 2 nd law for the x-direction:

37. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser. weight Normal force friction Here is the free-body diagram again. Notice that the only horizontal force is friction. We can write down Newton’s 2 nd law for the x-direction: We can use kinematics to find the acceleration:

38. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Example: An eraser sliding on the chalk rail. A 0.1kg eraser is given an initial velocity of 4 m/s along the chalk rail. It slows down and comes to rest in a distance of 3 m. Find the magnitude of the friction force that acts on the eraser. weight Normal force friction Here is the free-body diagram again. Notice that the only horizontal force is friction. We can write down Newton’s 2 nd law for the x-direction: We can use kinematics to find the acceleration: Put this value in to find the friction force: