TYPES OF COLLISIONS

Elastic CollisionsInelastic Collisions

REMINDER: CONSERVATION OF MOMENTUM In a closed system, the total

momentum of all objects in the system will remain constant

In other words…the total momentum in the system right before an “event” will be equal to the total momentum right after the “event”

finalinitial pp

KINETIC ENERGY (K) The energy a body has because it is

moving

If a cheetah has a mass of 47.0 kg, andaccelerates from rest to a speed of 26.8 m/s in 6.00 s, what is her change in kinetic energy?

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2K m v

Inelastic: Objects impact and separate, but there has been damage done to each

Elastic: Objects bounce off each other undamaged

COLLISIONS

ConservedNOT conservedObjects impact and STICK

TOGETHER as one larger mass with the same, slower velocity

ConservedNOT conserved

ConservedConserved

MomentumKinetic Energy

TYPE

Perfectly Inelastic:

Elastic:1 1 2 2 1 1 2 2( ) ( )initial finalm v m v m v m v

ConservedNOT conserved

ConservedInelastic: NOT conserved

ConservedConserved

MomentumKinetic Energy

TYPE

1 1 2 2 1 1 2 2( ) ( )initial finalm v m v m v m v

Perfectly Inelastic:

1 1 2 2 1 2( ) ( )initial finalm v m v m m v

COLLISIONS

A freight train is being assembled in a switching yard. Boxcar #1 has a mass of 6.5 x 104 kg, and Boxcar #2 has a mass of 9.2 x 104 kg. If car 1 is moving with a velocity of +0.80 m·s-

1, and car 2 hits it from behind with a velocity of +1.2 m·s-1, with what velocity will the two cars move with together after coupling?

EXAMPLE PROBLEM:

EXAMPLE PROBLEM: SOLUTION

before afterp p

1 1 2 2 1 2( ) ( )·before afterm v m v m m v 4 1 4 1 4 4(6.5x10 )·(0.80 · ) (9.2x10 )·(1.2 · ) (6.5x10 9.2x10 )·

afterkg m s kg m s kg kg v

1 152000 · · 110400 · · (157000 )· afterkg m s kg m s kg v

-11162400 · ·

(157000 )1.0 m·safter

kg m sv

kg

PROBLEM 2:

Starting from rest, two ice skaters push off against each other on smooth, level ice. Skater 1 has a mass of 54 kg and moves away from her friend (mass = 88 kg) with a velocity of 2.5 m/s. Find the “recoil” velocity of the second skater.

PROBLEM 2: SOLUTION

1 1 2 2 1 1 2 2( ) ( )

before after

before after

p p

m v m v m v m v

120 (54 )(2.5 · ) (88 )·kg m s kg v

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1135 · ·

81.5 ·

8

kg m sv

km s

g