A 12,000 N car starts from rest and rolls down a hill from a height of 10.0 m (s

Question

A 12,000 N car starts from rest and rolls down a hill from a height of 10.0 m (see figure). It then moves across a level surface and collides with a light spring-loaded guardrail.

A 12,000 N car starts from rest and rolls down a hill from a height of 10.0 m (see figure). It then moves across a level surface and collides with a light spring-loaded guardrail. Neglecting any losses due to friction, and ignoring the rotational kinetic energy of the wheels, find the maximum distance the spring is compressed. Assume a spring constant of 1.6 times 106 N/m. Calculate the maximum acceleration of the car after contact with the spring, assuming no frictional losses. If the spring is compressed by only 0.30 m, find the change in the mechanical energy due to friction.

Explanation / Answer

mgH = 1/2*K*x^2

12000*10 = 0.5*1.6*10^6*x^2

x = 0.387 m

initial velocity,

V W*H = 1/2*W/g*V^2

V = 14 m/s

acc = V.dV/ds

= 14*14/0.387

= 506.46 m/s2

change in m.e , mgh - 1/2*k*0.30^2

= 48000 J

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