Aspergerl-ch9.PDF Linear Momentum

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Prepared by Luke Asperger Lab: AP Review Sheets

Chapter 9 – Linear Momentum & Collisions

Background / Summary

This unit covers one of the most important concepts in mechanics, an objects momentum. In thisunit we will learn how to use conservation of momentum to analyze collisions.

Important EquationsKey Concepts

• momentum is

always conserved in

an isolated system!• an objects change

in momentum is

called its impulse

• In an elastic

collision, both

energy and

momentum are

conserved

• In an inelastic

collision,momentum is

conserved but

energy is not

• In a perfectly

inelastic collision,

momentum is

conserved and the

objects stick

together

Fdt = Δmv ∫ p = mv

m1v1+m2v2

= m1v1'+m2v2

'

m1v1+m

2v

2= v'(m

1+m

2)

1

2m1v1

2+

1

2m2v2

2=

1

2m1v1

'2+

1

2m2v2

'2



Sample Problem 1: Just Getting Started

Pitcher Zack Greinke of the Los Angeles Dodgers is pitchingto first baseman Carlos Quentin of the San Diego Padres.

With the Dodgers winning 2-1 in the sixth inning, Zack Greinke hits Quentin in the elbow with a 92 mph fastball on a

3-2 count. A major league baseball has a mass of 145 grams,and Carlos Quentin has a mass of 110 kilograms.

a. What type of collision is this? b. With what velocity is Quentin thrust back?

Assume the ball is not moving after the collision

Solutions

a) inelastic

b) 92mi

hr×1609m

mi×

hr

3600s= 41m /s

m1v1 +m2v2 = m1v1'+m2v2'

(.145)(92)+ (110)(0) = (.145)(0)+110v2

v2 = .12m /s



Sample Problem 2: A Little Trickier

Despite the fact that the pitch came with a full count in a one run game, Carlos Quentin charges

at 6 m/s toward the mound at Zack Greinke. Greinke, with a mass of 100 kg, lowers his shoulder towards Quentin at 1 m/s to receive the blow. The two players stick together as they fall to the

floor.a. What type of

collision is this? b. What is the

magnitude anddirection of the

players’ finalvelocity?

c. If the collision took place over .15

seconds, what

average force wasrequired for Quentinto fracture Zack

Greinke’scollarbone?

Solutions

a) perfectly inelastic

b)

c)

Ft = mΔv

F (.15) = (110)(6− 2.9)

F = 2.3 ×103 N

m1v1 + m2v2 = v'(m1 + m2 )

(110)(6)+ (100)(1) = v'(110+100)

v'= 2.9m / s



Sample Problem 3: No Way!

Later that night, Dodger’s center fielder Matt Kemp,

furious at Carlos Quentin, challenges Quentin to agame of pool. If the white ball is traveling at 6.0 m/s

and hits the eight ball, glancing off with an angle of 30º relative to its original path, determine the final

direction and velocity of each ball.

Solutions

It’s important to remember thatyou have to account for direction

when dealing with momentum.

This is an elastic collision, sokinetic energy is conserved.

Not that you do not accountfor direction when dealing

with energy.

Remember that when a moving ball hits a non moving ball of

the same mass in an elasticcollisions, their final paths

form 90º angles.

m1v1 +m2v2 = m1v1'+m2v2

'

m1 = m2

v1 + v2 = v1'cos30 + v2

'cos60

v1 + v2cos60 − v2

'= v1'cos30

1

2m1v1

2+

1

2m2v2

2=

1

2m1v1

'2+

1

2m2v2

'2

v1

2+ v2

2= (v1 + v2 − v2

' )2+ v2

'2

62+ 0 = (

6 +0 − v2 'cos60

cos30)2+ v2

'2

v2'= 3.0m /s

θ 2 = 60º

v1 + v2 = v1'cos30 + v2

'cos60

6 = v1'cos30 + 3cos60

v1'= 5.2m /s

θ 1 = 30º

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Aspergerl-ch9.PDF Linear Momentum