Elastic Collisions: Momentum, Kinetic Energy, and Conservation of Energy, Slides of Physics

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Elastic Collisions

Momentum and Kinetic Energy 

An object in motion has a momentum based on itsmass and velocity.•

p

mv



The object also has kinetic energy.•

K

mv

2

p

2

m

Elastic Collision 

For conservative forces theenergy is conserved. 

After the collision of contactthe potential energy is zero. 

The total kinetic energy isconserved – equal beforeand after the collision. 

This an elastic collision.

f

i^

P

P

f

i^

K

K

Elastic

Double Conservation 

Elastic collisions conserveboth momentum and kineticenergy. 

Two equations govern allelastic collisions.

(^22) 2 1 2

(^21) 1 1 2

(^22) 2 1 2

(^21) 1 1 2

2 2 1 1 2 2 1 1

f

f

i

i

f

f

i

i

v m v m v m v m

v m v m v m v m

m

1 m

2

v^1

i v^2

i

before

m

1 m

2

v^1

f v 2 f

after

Related Velocities

(^

2 2 2 1 1 1

2 2 2 2 1 1 1 1 i

f

f

i

i

f

f

i

v v m v v m

v m v m v m v m



)

)(

(

)

)(

(

)

(

)

(

2 2 2 2 2 1 1 1 1 1

(^22)

(^22) 2

(^21)

(^21) 1

(^22) 2 1 2

(^22) 1 1 2

(^21) 1 1 2 (^21) 1 1 2

i f i f f i f i

i

f

f

i

i

f

f

i

v v v v m v v v v m

v v m v v m

v m v m v m v m























m

1

m

2

v^1

i^

v^2

i

momentum in a line kinetic energy conservation

solve for velocities

f

f

i

i

i

f

f

i

v

v

v

v

v

v

v

v

1

2

2

1

2

2

1

1

Equal Masses 

A 150 g ball moves at 1.4 m/s.•

The momentum is 0.21 kg m/s



It strikes an equal mass ball atrest.^ •

v^1

= 1.4 m/si

-^

v^2

= 0i

-^

Therefore,

v

1 f^

= 0

-^

and

v

2 f^

=

v

1 i

f

f

i

i

f

f

i

i

v

v

v

v

v

v

v

v

1

2

2

1

1

2

2

1











 m

1

m

2

v^1

i

m

1

m

2

v^2

f

momentum:kinetic energy:

Striking a Light Mass 

Let

m

1

m

, when a car 2

strikes a ball. 

The ball is at rest.^ •

v^2

= 0i



For a very heavy

m

1

, the

final velocity of

m

2

is twice

the initial velocity of

m

1

i

f

i

i

f

f

f

i

f

f

i

v

v

v

v

m

m

m

m

v

v

v

v

v m v m v m

1

2

1

1 2

1

2

1

1

1

2

1

1 1 2 2 1 1

momentum:kinetic energy:combined:

v^1

i

v^2

f

m

2