Chapter 8 Impulse and Momentum

Momentum and Collisions This chapter is concerned with inertia and motion. Momentum helps us understand collisions. Elastic Collisions - objects rebound Inelastic Collisions - object stick together an usually become distorted and generate heat

Momentum Momentum = mass ´ velocity p = mv Momentum is a vector quantity.

Large Momentum Examples Huge ship moving at a small velocity High velocity bullet P = Mv P = mv

Momentum Examples A large truck has more momentum than a car moving at the same speed because it has a greater mass. Which is more difficult to slow down? The car or the large truck?

Impulse Newton’s Second Law can read SF = ma = m(Dv/Dt) = (Dmv)/(Dt) = (Dp/ Dt) Rearranging, Impulse = Dp = FDt

When Force is Limited Apply a force for a long time. Examples: Follow through on a golf swing. Pushing a car. FDt

Make it Bounce Dp = p2 - p1 = -p1 - p1 = -2p1 p1 p2 = -p1

Minimize the Force Increase Dt Catching a ball Bungee jumping FDt

Maximize Momentum Change Apply a force for a short time. Examples: Boxing Karate FDt

Conservation of Momentum This means that the momentum doesn’t change. Recall that SF t = D(mv), so SF = 0 In this equation, F is the "external force." Internal forces cannot cause a change in momentum.

Examples Example 1: a bullet fired from a rifle Example 2: a rocket in space

Collisions Before m1 m2 After m1 m2

Inelastic Collisions v = 10 v = 0 M M Before Collision p = Mv v’ = 5 M After Collision p = 2Mv’ Mv = 2Mv’ v’ = ½ v

Elastic Collisions Conserve Energy and Momentum Before Collision Equal masses Case 1: Case 2: M > M Case 3: M < M

Coefficient of Restitution For perfectly elastic collisions e = 1. If the two object stick together, e = 0. Otherwise 0 < e < 1.

Center of Mass

On to problems...