The Physics of NASCAR Collisions

There are two major types of collisions to consider when observing NASCAR races. The most common NASCAR collision is an elastic collision. An elastic collision is one in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision. In this type of collision, the cars do not stick together after colliding. The second type of collision is called an inelastic collision. An inelastic collision is one in which the total kinetic energy of the system is not the same before and after the collision. In this type of collision, the cars stick together after colliding. Momentum is conserved in each type of collision.

The general equations for elastic collisions are as follows:

Collisions in One Dimension

m1vf1 + m2vf2 = m1v01 + 0

1/2m1vf1² + 1/2m2vf2² = 1/2m1v01² + 0

Collisions in Two Dimensions

m1vf1x + m2vf2x = m1v01x + m2v02x

m1vf1y + m2vf2y = m1v01y + m2v02y

SAMPLE PROBLEM

The Home Depot racing car (3550lb) travels at a speed of 167mph during the Daytona 500. Its opponent, the Budweiser car (3432lb), is approaching at a speed of 164mph. Both of the cars are traveling due east on the second straight away. The Budweiser car loses control and hits the Home Depot car from an angle of 52 degrees and the Home Depot car skids off the track at speed of 157mph and an angle of 33 degrees. At what speed will the Budweiser car rebound if the collision is elastic? At what angle?

First, the x and y components of the cars must be found. In order to use the equations correctly, pounds must be converted to kilograms and mph must be converted to m/s.

3550lb(1/2.2kg) = 1613.6kg

3432lb(1/2.2kg) = 1560kg

167mph(1.609km/mi)(1000m/km)(hr/3600s) = 74.6m/s

164mph(1.609km/mi)(1000m/km)(hr/3600s) = 73.3m/s

157mph(1.609km/mi)(1000m/km)(hr/3600s) = 70.2m/s

x component

(1560kg)*vf1x + (1613.6kg)(70.2m/s)(cos 33) = (1560kg)(73.3m/s)(sin 52) + (1613.6kg)(74.6m/s)

vf1x = 74.0m/s

y component

(1560kg)*vf1y+ (1613.6kg)(-70.2m/s)(sin 33) = (1560kg)(-73.3m/s)(cos 52) + 0

vf1x = -5.58m/s

vf1 = [(74.0m/s)² + (-5.58m/s)²]^1/2

vf1 = 74.2m/s

Angle = arctan (5.58m/s / 74.0m/s) = 4.31 degrees

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