A truck with mass m has a brake failure while going down an icy mountain road of constant downward slope angle ? (Fig. P7.58). Initially the truck is moving downhill at speed v0. After careening downhill a distance L with negligible friction, the truck driver steers the runaway vehicle onto a runaway truck ramp of constant upward slope angle ?. The truck ramp has a soft sand surface for which the coefficient of rolling friction is µr. What is the distance that the truck moves up the ramp before coming to a halt? Solve by energy methods.

Solution 66P Step 1: In the left hand side where the mass is sliding without friction, The height is, h = l sin . Step 2: The potential energy was, P.E = mgh = mgl sin . The kinetic energy is, K.E = 1/2 mV = 1/2 m V 02 . The total mechanical energy hence was, E = mgl sin + 1/2 m V 02 .