The magnitude of force acting on the bumper is 3760 N.
What is Work energy theorem?
It states that the Work done in moving a body is equal to the change in kinetic energy of the body
Kinetic energy = 1/2 mv²
Given is a car's bumper designed to withstand 4.32 km/h or 1.2 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.
The cushion collapses 0.180 m while bringing 940 kg car to rest from a initial speed of 1.2 m/s
Work done = Force x displacement
As the displacement of the bumper and force acted on it is in same direction, so the work done is
W = Fxcos0° = Fx
The body is coming to rest, so, final velocity is zero. Then, change in kinetic energy will be
ΔK.E = K.Ef - K.Ei
ΔK.E = m/2 (v² - u²)
According to work energy theorem, work done is
W = Fx = m/2 (v² - u²)
Substitute the value and calculate the force,
F = [940 x (0² - 1.2²)] / 2x0.180
F = 3760 N
Thus, the magnitude of force is 3760 N.
Learn more about work energy theorem.
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