Momentum. A ball bounces off the floor as shown. The direction of the impulse on the ball, is... straight up straight down to the right to the left

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1 Momentum A ball bounces off the floor as shown. The direction of the impulse on the ball,, is... A: B: C: D: straight up straight down to the right to the left This is also the direction of

2 Momentum A car moves in the + x direction at 55 mph. It makes a u-turn, and is then returning ( x direction) at 55 mph. is... A) zero B) to the right (+ x direction) C) to the left ( x direction) D) not enough information to decide.

3 Momentum A lump of clay is thrown at a wall. A rubber ball of identical mass is thrown with the same speed toward the same wall. Which has a greater change in momentum? a. The clay b. The ball c. They are the same d. It is not possible to know

4 Elastic & Inelastic Collisions Perfectly elastic: kinetic energy conserved

5 Elastic & Inelastic Collisions Inelastic: some kinetic energy lost Some energy stored and released. Some energy is lost in deformation, sound, etc. <

6 Elastic & Inelastic Collisions Perfectly inelastic: some kinetic energy lost

7 Elastic & Inelastic Collisions The two boxes are sliding along a frictionless surface. They collide and stick together. Afterward, the velocity of the two boxes is A. 2 m/s to the left. B. 1 m/s to the left. C. 0 m/s, at rest. D. 1 m/s to the right. E. 2 m/s to the right.

8 Elastic Collisions Collisions between two very hard objects, such as two billiard balls or two steel balls, come close to being perfectly elastic.

9 Head-on Elastic Collisions

10 Head-on Elastic Collisions

11 Head-on Elastic Collisions

12 Head-on Elastic Collisions

13 Head-on Elastic Collisions If neither ball is initially at rest, consider the velocity of one relative to the other.

14 Head-on Elastic Collisions A 200 g ball moves to the right at 2.0 m/s. It has a head-on, perfectly elastic collision with a 100 g ball that is moving toward it at 3.0 m/s. What are the final velocities of both balls?

15 Head-on Elastic Collisions

16 Head-on Elastic Collisions

17 Inelastic Collisions A train car moves to the right with initial speed vi. It collides with a stationary train car of equal mass. After the collision the two cars are stuck together. What is the train cars final velocity? m1 (vfx)1 + m2 (vfx)2 = m1 (vix)1 + m2 (vix)2 mvf + mvf = mvi + 0 vf = ½ v i

18 Explosions Kinetic energy gained. Kf > Ki Momentum conserved.

19 Explosions

20 Explosions

21

22 Momentum Problem Solving

23 Momentum Problem Solving System is ball alone. momentum of the system is not conserved. System is ball+earth. momentum of the system is conserved.

24 Momentum Problem Solving Example: A bomb shell (mass 6m) moving at 10 m/s downward explodes into three parts. Mass m moves at 10 m/s to the right. Mass 2m moves at 50 m/s down. Find the final velocity of the 3m mass. (Compare to HW )

25 Momentum of Many Particles System: N interacting particles. Newton s second law for each individual particle:

26 Momentum of Many Particles Internal interaction forces: The sum of all the interaction forces is zero Internal forces between parts of an object do not affect the motion of the object as a whole.

27 Momentum of Many Particles Newton s 2nd Law for N particles: where M is the total system mass: This is the same as the motion of a single body of mass M and velocity

28 Momentum of Many Particles Newton s 2nd Law for N particles: where If there is no external force: so is constant.

29 Center of Mass CM refers to the Center of Mass of the system The CM is the weighted average of the locations of the masses. In a uniform gravity field, this is the same as the center of gravity (CG).

30 Center of Mass Particles of higher mass count more than particles of lower mass.

31 Center of Mass

32 Center of Mass

33 Center of Mass Slide 12-33

34 Center of Mass of a Solid Divide a solid object into many small cells of mass Δm. As Δm 0 and is replaced by dm, the sums become Before these can be integrated: dm must be replaced by expressions using dx and dy. Integration limits must be established.

35 Center of Mass of a Solid A baseball bat is cut in half at its center of mass. Which end is heavier? A. The handle end (left end) B. The hitting end (right end) C. The two ends weigh the same. Slide 12-35

36 Center of Mass of a Solid A baseball bat is cut in half at its center of mass. Which end is heavier? A. The handle end (left end) B. The hitting end (right end) C. The two ends weigh the same.

37 Momentum of Many Particles Newton s 2nd Law for N particles: where is the velocity of the Center of Mass of the system. is the position of the CM:

38 Momentum of Many Particles

39 Momentum of Many Particles CM follows a parabola

40 Momentum of Many Particles path of CM

41 Momentum of Many Particles The jumper s CM accelerates uniformly at -9.8 m/s2.

The total momentum in any closed system will remain constant.

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