A driver loses control of his car and the car slams into a bumper protecting a b

Question

A driver loses control of his car and the car slams into a bumper protecting a bridge, compresses the bumper, and bounces back out. The driver steps on his brakes just as the car hits the bumper, so that the tires skid for the entire time of the collision. (The friction will be in a direction opposite to the velocity.) The police want to use the distance travelled, as measured by the skid marks on the road, to determine the initial speed of the car. The mass of the car is 675 kg, the spring constant of the bumper is 300000 N/m, and the frictional force of the tires on the road is 8500 N. If the skid marks show that the bumper compressed a maximum distance of 0.8 m, what was the initial velocity of the car? Give your answer in m/s to three digits. Do not include units in your answer. Your Answer:

Explanation / Answer

Ei + Wf = Ef 1/2 m vi^2 - f d = 1/2 kx^2 0.5*675*v^2- 8500*0.8=0.5*300000 *0.8^2 v=17.453 m/s

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