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A roller coaster car is elevated to a height of 30 m and released from rest to roll along a track. At a certain time T it is at a height of 2 m and has lost 25.000 J of energy to friction. The car has a mass of 800 kg. Answer the following questions. (a) How fast is the car going at time T? (b) How fast would the car be going at time T if the track were frictionless?

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MathPhys

Explanation:

Initial energy = final energy + work done by friction

PE = PE + KE + W

mgH = mgh + 1/2 mv² + W

(800)(9.8)(30) = (800)(9.8)(2) + 1/2 (800) v² + 25000

v = 22.1 m/s

Without friction:

PE = PE + KE

mgH = mgh + 1/2 mv²

(800)(9.8)(30) = (800)(9.8)(2) + 1/2 (800) v²

v = 23.4 m/s

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