Newton s Third Law. Lecture 9. Chapter 7. Physics I. Course website:

Transcription

1 Lecture 9 Physics I Chapter 7 Newton s Third Law Course website:

2 Today we are going to discuss: Chapter 7: Some leftover (Ch.6) Interacting Objects: Section 7.1 Analyzing Interacting Objects: Section 7.2 (skip Propulsion) Newton s Third Law: Section 7.3 Ropes and Pulleys: Section 7.4

3 ConcepTest A box of weight 100 N is at rest on a floor where s = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move? Will It move? A) moves to the left B) moves to the right C) the box does not move D) moves down E) moves up F N S fr Smg N The static friction force has a maximum of s N = 50 N. The tension in the rope is only 30 N. So the pulling force is not big enough to overcome friction. m T=30N Follow-up: What happens if the tension is 55 N?

4 Demonstration Two Interleaved Books Simply lay the pages of two phone books on top of each other one by one before attempting to pull them apart. It increases max friction When we apply F A force, we create two components F pull and F perp. Since there is no motion, we have a static friction force F fr equal to the F pull. As we increase F pull, F perp gets larger increasing (F fr ) max, which means that our goal moves farther away. So the more we pull the larger goal becomes But luckily F pul grows faster and with two tanks it can be done. F fr F A F perp F pull F fr F pull It pulls books apart NxF fr

5 ConcepTest. Going Sledding Your little sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this? A) pushing her from behind B) pulling her from the front C) both are equivalent D) it is impossible to move the sled E) tell her to get out and walk In case 1, the force F is pushing down (in addition to mg), so the normal force is larger. In case 2, the force F is pulling up, against gravity, so the normal force is lessened. Recall that the frictional force is proportional to the normal force. 2 1

6 Newton s 3 rd Law Forces come from other objects Chapter 7.

7 Newton s Third Law of Motion Whenever one object exerts a force on a second object, the second exerts an equal force in the opposite direction on the first. = For every action force, there is an equal and opposite reaction force NOTE: Action and Reaction forces act on different objects!

8 Let s try to justify N.3 rd law. When a hammer hits a nail, it exerts a forward force on the nail. Is it true that a nail also exerts a force on a hammer (in return)? When a hammer hits a nail, the hammer stops very quickly 0 / 10 / i.e. the hammer changes velocity, i.e. it accelerates (a) If the hammer accelerates (decelerates), there must be a force acting on the hammer from the poor nail, according to the N. 2 nd law. If you still don t believe me, hit the nail with a glass hammer. It s the force of the nail on the hammer that would cause the glass to shatter! Me

9 Action-Reaction Pair of Forces Let s come up with a convention how to denote these pairs of forces F B on A F A on B F BA A B FAB Or simply = Or simply If object A exerts a force on object B, then object B exerts a force on object A. - The pair of forces, as shown, is called an action/reaction pair. Helpful notation: the second subscript is the object that the force is being exerted on; the first is the source. F WS F SW A key to the correct application of the third law is that the forces are exerted on different objects. Make sure you don t use them as if they were acting on the same object. - i.e. If you want to describe a motion of a skater, you have to use a force F WS acting from the wall on the skater - And if you want to describe the wall, use F SW.

10 Newton s Third Law of Motion Rocket propulsion can also be explained using Newton s third law: hot gases from combustion spew out of the tail of the rocket at high speeds. The reaction force is what propels the rocket.

11 Acceleration Constraints If two objects A and B move together, their accelerations are constrained to be equal: a A = a B This equation is called an acceleration constraint. Consider a car being towed by a truck. In this case, the acceleration constraint is a Cx = a Tx = a x. Because the accelerations of both objects are equal, we can drop the subscripts C and T and call both of them a x.

12 Acceleration Constraints Sometimes the acceleration of A and B may have different signs. Consider the blocks A and B in the figure. The string constrains the two objects to accelerate together. But, as A moves to the right in the +x direction, B moves down in the y direction. In this case, the acceleration constraint is a Ax = a By.

13 Internal forces cancel each other!!!!!! Cancel due to Newton s Third Law

14 Two blocks problem We can now forget about the internal forces y x F Treat, m=m 1 +m 2, as the system (one big block) Apply N. 2 nd law to m x component of N. 2 nd law a m=m 1 +m 2 F ma F m m 1 2 F m a F x ma x ( m m ) a 1 2 Given: F, m 1,m 2 Find: a (common acceleration)

15 ConcepTest Crazy Mosquito A mosquito runs head-on into a truck. Which is true during the collision? A) The magnitude of the mosquito s acceleration is larger than that of the truck. B) The magnitude of the truck s acceleration is larger than that of the mosquito. C) The magnitude of the mosquito s acceleration is the same as that of the truck. D) The truck accelerates but the mosquito does not. E) The mosquito accelerates but the truck does not. F MT F TM Newton s 3rd law: Newton s 2nd law: F MT =F TM =F a M >> a T Don t confuse cause and effect! The same force can have very different effects. The same idea can be applied to an interaction of an apple and the Earth in the next slide. But you don t have to read the next slide. Only if you want.

16 Falling ball exerts force on Earth (read if you want)

17 Ropes and Pulleys

18 Tension If a flexible cord pulls an object, the cord is said to be under TENSION Let s assume that the cord is a described object and apply N 2 nd law 0 T 1 m Often in problems the mass of the string or rope is much less than the masses of the objects that it connects. m=0 T 2 massless string approximation: Tension is the same at any point of the rope, For problems in this book, you can assume that any strings or ropes are massless unless it explicitly states otherwise.

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20 Example: Two boxes and a pulley. Two boxes are connected by a cord running over a pulley. The coefficient of kinetic friction between box A and the table is We wish to find the acceleration, a, of the system. As box B moves down, box A moves to the right. F N T F fr T F g =m A g F g =m B g

21 Thank you See you on Wednesday

22 Example: A ramp, a pulley, and two boxes.

23 Example: A ramp, a pulley, and two boxes

24 y Two blocks problem: y-equation F N m Box is a described object x F g =mg F F y ma y mg N ma y a y = 0 (no motion in y direction) F N mg Y equation gives a normal force