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 0.165 m while bringing a 870 kg car to rest from an initial speed of 1.9 m/s.

Answer 1

859.07 N

Step-by-step explanation:

u = Initial velocity = 1.9 m/s

v = Final velocity

s = Displacement = 0.165 m

a = Acceleration

m = Mass = 890 kg

Equation of motion

`v^2-u^2=2as\\\Rightarrow a=(v^2-u^2)/(2s)\\\Rightarrow a=(0^2-1.9^2)/(2* 0.165)\\\Rightarrow a=-10.93\ m/s^2`

Force

`F=ma\\\Rightarrow F=870* -10.93\\\Rightarrow F=859.07\ N`

The magnitude of the average force on the bumper is 859.07 N