Momentum Conservation Chapter 8: Momentum Conservation K = (1/2) m v 2 Work-Energy Theorem Energy Conservation p = m v Impulse-Momentum Theorem Momentum Conservation Work Impulse Distance, l

Momentum Conservation

1D Collision M m m M

Momentum Conservation Elastic Collision

Momentum Conservation Energy Conservation Loss of energy as thermal and other forms of energy

Momentum Conservation Example 2 m v 1 + m v 2 = m v 1 ’ + m v 2 ’ Before collision After collision v 1 ’ = v 2 ’ (totally inelastic collision)

Momentum Conservation

Impulsive Force Very large magnitude Very short time [Example] an impulsive force on a baseball that is struck with a bat has: ~ 5000 N &  t ~ 0.01 s [Note] The “impulse’’ concept is most useful for impulsive forces.

Momentum Conservation Impulse-Momentum Theorem |J | 1D 2D

Momentum Conservation

x y

Example 3 (A) Momentum Conservation (B) Energy Conservation (A) m v = (m+M) v’ (B) K 1 +U g1 = K 2 +U g2 Express v and v’ in terms of m, M, g, and h. 1 2

Momentum Conservation

Example 1 v i = 28 m/s v f = 28 m/s What is the impulse given the wall ? Note: m = kg.   p x, and  p y for the ball  J (on the wall) = - J (on the ball) p x,i p x,f p y,f x y (1) Coordinates (2) J (on the ball)  p x = p x,f - p x,i = - 2 x p x,i  p y = p y,f - p y,i = 0 where: p x,i = m v i sin  1.2 N*s p y,i

Momentum Conservation 1D/2D “Explosion’’ 1  2 (or more)

Momentum Conservation Center of mass Center of Mass (c.m. or CM) The overall motion of a mechanical system can be described in terms of a special point called “center of mass” of the system:

Momentum Conservation

CM Position (2D) m1m1 m 2 + m 3 m 1 + m 2 m3m3 X X y cm = 0.50 m x cm = 1.33 m

Momentum Conservation CM Position and Velocity m v 1 + m v 2 = (m + m) v ’ (totally inelastic collision) 48.0 m x t = -2 s t = 0 s

Momentum Conservation 2D Collision