Question

A car is equipped with a bumper designed to absorb collisions. The bumper is mounted to the car using pieces of flexible tubing. Upon collision with a rigid barrier (e.g. brick wall), the bumper is designed so that a constant horizontal force is developed. If the car is initially traveling at 1.5 m/s when it collides with a rigid brick wall, compute the magnitude of the distance needed to stop the car and cause the deformation of the bumper tubing. The car and passenger have a combined mass of 1500 Kg. Consider that k=2.3 x 105 N/m. Assume all the energy goes into the bumper.

Answer 1

given

car is initially traveling at 1.5 m/s = v

mass of 1500 Kg = m

k = 2.3 x 10⁵ N/m

the work done by force of the bumper is

W = -1/2 k d²

W = change in KE

change in KE = KE_final - KE_initial

KE_final - KE_initial = 0 - 1/2mv²

-1/2 k d² = 0 - 1/2mv²

-1/2 k d² = - 1/2mv²

k d² = mv²

d² = m v² / k

d = ( m v² / k )^1/2

= ( 1500 x 1.5² / 2.3 x 10⁵ )^1/2   

d = 0.1211 m

so the magnitude of the distance needed to stop the car and cause the deformation of the

bumper tubing is d = 0.1211 m