Physics of a Rear-End Collision

time t

0.

mass 1

500.

velocity 1

70.

mass 2

1500.

velocity 2

30.

Two cars travel in the same direction on a slippery road. Initially they are 16 m apart. They have a rear-end collision at time

t

c

and travel together after that. Their masses are

m

1

(blue) and

m

2

(red), and their velocities are

v

1

and

v

2

. Using conservation of momentum, the velocity after the collision is calculated, as is the kinetic energy lost in the collision.

Details

The velocity of the cars after collision is

v

f

=(

m

1

v

1

+

m

2

v

2

)/(

m

1

+

m

2

)

. The kinetic energy lost is

ΔKE/

KE

i

=(

KE

f

-

KE

i

)/(

KE

1

+

KE

2

)

, where

KE

1

and

KE

2

are the kinetic energies of each car before the collision, and

KE

f

is the kinetic energy of both cars considered as a single body after the collision.

External Links

Velocity (ScienceWorld)

Conservation of Momentum (ScienceWorld)

Kinetic Energy (ScienceWorld)

Permanent Citation

Enrique Zeleny

"Physics of a Rear-End Collision"
http://demonstrations.wolfram.com/PhysicsOfARearEndCollision/
Wolfram Demonstrations Project
Published: September 16, 2010