Warm-up A 0.6kg groundball approaches a player horizontally with a velocity of 20 m/s to the south. The player then brings the ball to a stop. What impulse was delivered to the ball by the player?

Conservation of Momentum

Conservation of Momentum can be observed when two or more objects are interacting with each other.

Momentum in a Collison The following data was collected. Calculate the momentum of both billiard balls before and after the collision.

Conservation of Momentum The Law of Conservation of Momentum: for an isolated system, the total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects. Total initial momentum = Total final momentum 𝑝 𝐴, 𝑖 + 𝑝 𝐵,𝑖 = 𝑝 𝐴,𝑓 + 𝑝 𝐵,𝑓 Ignore Friction!

Conservation of Momentum Examples Billiard Balls Jumping Pushing away from each other

Practice A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat?

Force and Change in Momentum Newton’s Third Law: For every action there is an equal and opposite reaction. Newton’s Third Law leads to conservation of momentum 𝑭 𝟏 = −𝑭 𝟐 𝐹 1 =𝑓𝑜𝑟𝑐𝑒 𝑜𝑛 𝑚 1 𝐹 2 =𝑓𝑜𝑟𝑐𝑒 𝑜𝑛 𝑚 2 The impulse on 𝑚 1 is equal and opposite to the impulse on 𝑚 2 𝑱 𝟏 =− 𝑱 𝟐 𝑭 𝟏 ∆𝒕=− 𝑭 𝟐 ∆𝒕 𝒎 𝟏 𝒗 𝟏,𝒇 − 𝒎 𝟏 𝒗 𝟏,𝒊 =− 𝒎 𝟐 𝒗 𝟐,𝒇 − 𝒎 𝟐 𝒗 𝟐,𝒊

Force During Real Collisions During a collision, the forces may vary in time in a complicated way. At all times during the collision, the forces on the two cars are equal in magnitude and opposite in direction. In this class: Use average force for impulse. Assume the forces involved in a collision are constant