Question

A car's bumper is designed to withstand a 6.84 km/h (1.9-m/s) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses 0.285 m while bringing a 830 kg car to rest from an initial speed of 1.9 m/s.

Answer 1

F = 5.256 x
`10^(3) N`

Step-by-step explanation:

From the work energy theorem we know that:

The net work done on a particle equals the change in the particles kinetic energy:

W = F.d, ΔK =
`(1)/(2) mv^(2)_(f) - (1)/(2) mv^(2)_(i) , F.d = (1)/(2)mv^(2)_(f) -(1)/(2) mv^(2)_(i)`

where:

W = work done by the force

F = Force

d = Distance travelled

m = Mass of the car

vf, vi = final and initial velocity of the car

kf, ki = final and initial kinetic energy of the car

Given the parameters;

m = 830kg

vi = 1.9 m/s

vf = 0 km/h

d = 0.285 m

Inserting the information we have:

F.d =
`(1)/(2) mv^(2)_(f) - (1)/(2) mv^(2)_(i)`

F =
`((1)/(2) mv^(2)_(f) - (1)/(2) mv^(2)_(i) )/(d)`

F =
`( 0 - (1)/(2) X830 X 1.9^(2) )/(0.285)`

F = 5.256 x
`10^(3) N`