An automobile of mass 900 kg is moving at a speed of 125 ms

An automobile of mass 900 kg is moving at a speed of 12.5 m/s when it encounters a hill. At the bottom of the hill the car speed increases to 14.6 m/s. If the elevation of the hill is 15.3 m, how much work did the brakes do while going down the hill? Select one: a. -1.09x105 J b. -9.59x104 J c. 2.05x105 J d. 1.33x105 J

Solution

mass of automobile m = 900 kg

Speed at top u = 12.5 m/s

Speed at bottom v = 14.6 m/s

Elevation of the hill h = 15.3 m

Decrease in potential energy U = mgh

                                          = 900x9.8x15.3

                                          = 134946 J

Increase in kinetic energy K =(1/2)m[v ²- u ²]

                                         = 0.5x900x[14.6 ² -12.5 ²]

                                         = 25609.5 J

work did the brakes do while going down the hill W = -(U - K )

                                                                          = -(134946 J - 25609.5 J )

                                                                          = -1.09 x10 ⁵ J