Momentum and ImpulseMomentum = mass x velocity

p = mv units: kg·m/s***momentum is a vector quantity

Conceptually, momentum is a characteristic of motion that reflects how difficult it would be to stop the moving object

Impulse(change in momentum) = Force x time: Δp = FΔt units: N·s

A net force applied for a given time interval will result in a change in momentum…this is really Newton’s Second Law: F = ma F = mΔv/ Δt F Δt = Δ mv

Sample Problem

• A 1400 kg car moving westward with a velocity of 15 m/s collides with a utility pole and is brought to rest in 0.30 s. Find the force exerted on the car during the collision.

Conservation of Momentum• Keep in mind…– The individual objects in a collision can, and do,

change momentum– Two objects colliding experience equal force for

equal time, thus the magnitude of impulse, or change in momentum, must be the same for both objects

– When there are no external influences, momentum gained by one object must equal the momentum lost by another and the total momentum of the system is constant

Conservation of Momentum

• Whenever objects interact in the absence of external forces, the net momentum of the objects before the interaction equals the net momentum of the objects after the interaction.

Σp before = Σp after

***This general relationship will take on different appearances when applied to different situations

Types of collisions

• Perfectly Inelastic Collision (Sticky): A collision in which two objects stick together and move with a common velocity after colliding

• For 2 objects colliding inelastically…Σp before = Σp after

m1v1+m2v2=(m1+m2)vf

In these collisions, some kinetic energy is lost in the form of heat and sound as the objects deform during the collision

Types of collisions• Perfectly Elastic Collision (bouncy) : A collision in

which the total momentum and the total kinetic energy remain constant

• After the collision, the two objects move independently

• For 2 objects colliding elastically…Σp before = Σp after

m1v1i + m2v2i = m1v1f + m2v2f

and

ΣKEbefore = ΣKEafter

½ m1v1i2 + ½ m2v2i

2 = ½ m1v1f2 + ½ m2v2f

2

In Real life…

• Only particle collisions are truly elastic, however, many collisions are close enough to be approximated as elastic (ie…billiard balls)

• Macroscopic collisions are somewhere along a continuum of between being elastic and perfectly inelastic

Practice #1

• A 0.015 kg marble moving to the right at 0.225 m/s makes an elastic head-on collision with a 0.030 kg marble moving to the left at 0.180 m/s. After the collision, the smaller marble moves to the left at 0.315 m/s. What is the velocity of the 0.030 kg marble after the collision?

Practice #2

• A 1850 kg luxury sedan stopped at a traffic light is struck from the rear by a compact car with a mass of 975 kg. The two cars become entangled as a result of the collision. If the compact car was moving at a velocity of 22.0 m/s to the north before the collision, what is the velocity of the entangled mass after the collision?

Practice #3

• 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?