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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.

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Answer:

859.07 N

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

[tex]v^2-u^2=2as\\\Rightarrow a=\frac{v^2-u^2}{2s}\\\Rightarrow a=\frac{0^2-1.9^2}{2\times 0.165}\\\Rightarrow a=-10.93\ m/s^2[/tex]

Force

[tex]F=ma\\\Rightarrow F=870\times -10.93\\\Rightarrow F=859.07\ N[/tex]

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