A 15,000 kg fully loaded semi-truck descending a 2 km long 6° grade wishes to ma

Question

A 15,000 kg fully loaded semi-truck descending a 2 km long 6° grade wishes to maintain a constant speed of 20 m/s. (a) By how much does the truck’s potential energy change during the descent? (b) By how much does the truck’s kinetic energy change during the descent? (c) By how much does the truck’s thermal energy change? (e) The extreme heat can make the truck’s brakes fail. In some areas, ramps of loose gravel are constructed to stop runaway trucks. Suppose a gravel ramp slopes upward at 6° and the coefficient of rolling friction is 0.40 between the truck tires and the gravel. Use work and energy to find the length of a ramp that will stop the semi-truck.

Explanation / Answer

mass of the truck = 15000 kg

ramp length = 2 km

slope = 6 deg

height descended h = 2000Sin(6) = 209 m

change in pot. energy = mgh = 15000 *209 *9.8 = 30723000 J

b) KE = 0.5 mv2 , velocity is const.

          = 0.5 *15000 *202 = 3000000 J

          initial KE = 0 , assuming the truck start from rest.

=> change in KE   = 3000000 J

c) the difference on PE and KE is released as heat energy

change in thermal energy of the truck = 30723000 - 3000000

                                                              = 27723000 J

d) KE intial = 3000000 J

The truck rolls without slipping, frcitional force is always at the point of contact and no work is done by the frictional force.

KE = PE

h - height of the truck up the ramp

mgh = 3000000

h = 3000000 /15000*9.8 = 20.41 m

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