Momentum and its Conservation Chapter 9

Momentum Objects in motion are said to have a momentum.Objects in motion are said to have a momentum. Momentum depends on:Momentum depends on: VelocityVelocity MassMass

Momentum Momentum is a vector. MagnitudeMagnitude DirectionDirection

Momentum Momentum ( p unit:kgm/s ) A property a moving object has because of mass and velocity.

Momentum p=mv

Momentum of Systems Momentum of the ball changes!!!

Momentum of Systems Momentum of the pins change!!

Momentum of Systems Momentum of the ball and pins do not change!!

Impulse

Impulse Impulse Force applied on an object in a given amount of time

Impulse FΔt

Acceleration Δv Δt a=

Newton’s 2 nd Law F=ma Δv Δt F=m

Impulse / Momentum FΔt = m Δv Change in Momentum Impulse

ρ = m Δv ρ = m (v 1 -v 2 ) ρ = m v 1 -mv 2

Example A 100kg running back is moving at a speed of 12m/s is stopped by a linebacker in 0.5s. How much force did the linebacker apply to the running back?

Example Given: v 1 = 12 m/s v 2 = 0 m/s v 2 = 0 m/s m = 100kg m = 100kg Δt = 0.5s Find:F = ?

Equation: FΔt = m Δv F = m Δv F = m Δv Δt Δt F = m v 1 –v 2 F = m v 1 –v 2 Δt Δt F = (100kg)(12m/s – 0m/s) 0.5s 0.5s F = 2400N

Homework Practice Problems 2,3,4,13,14 & 15 Pages: 217 Due: 1/9/07

Conservation of Momentum The total momentum of a group of objects does not change unless outside forces act on the objects. The momentum before a collision is equal to the momentum after the collision.

Total Momentum Before = Total Momentum After

Example A 2000kg car going 25m/s rear ends an 500kg car going 15m/s on ice moving in the same direction. The two cars lock bumpers at collision. How fast does the wreckage move immediately after collision?

Example

Example Given: m 1 = 2000kg v 1 = 25m/s m 2 = 500kg v 2 =15m/s m 1,2 =2500kg Find: v 1,2 = ? Total Momentum Before = Total Momentum After

Example ρ before = ρ after ρ 1 + ρ 2 = ρ 1,2 m 1 v 1 + m 2 v 2 = m 1,2 v 1,2

Example (2000kg)(25m/s)+(500kg)(15m/s)= v 1,2 (2500kg ) m 1 v 1 +m 2 v 2 = v 12 m 12 V 12 = 23m/s

Homework Practice Problems 7-12 Page: 210 Due: 1/7/02

Explosion

Explosion ρ before = ρ after ρ before = ρ cannon + ρ ball ρ before = 0

Explosion 0 = ρ cannon + ρ ball ρ cannon = ρ ball mv cannon = mv ball

Explosion - Example A student, with a mass of 50kg, is standing in a boat, throws a 10kg medicine ball. The ball has a velocity of 10m/s. What is the speed of the student after the throw?

Explosion - Example Given: m s = 50kg m b = 10kg v b = 10m/s Find: v s = ?

Explosion - Example ρ before = ρ after ρ before = ρ student + ρ ball ρ before = 0 ρ student = ρ ball

Explosion - Example m s v s = v b m b v s = m b v b m s

Explosion - Example v s =(10kg)(10m/s) (50kg) v s = 2m/s

Homework Page: 217 Problems: 34, 35, 36 & 38 Due: 1/3/07

Homework Practice Problems Page: 214 Due: 1/7/02