In the figure, a frictionless roller coaster of mass 1000 kg tops the first hill

Question

In the figure, a frictionless roller coaster of mass 1000 kg tops the first hill at height, h = 50 m with speed 6.95 m/s. How much work does its weight do on it from that point to point A?

How much work does its weight do on it from that point to point B?

How much work does its weight do on it from that point to point C?

If the gravitational potential energy of the coaster-Earth system is taken to be zero at point C, what is its value when the coaster is at point B?

If the gravitational potential energy of the coaster-Earth system is taken to be zero at point C, what is its value when the coaster is at point A?

Explanation / Answer

a) We have no friction and no change in height. The net work done by the weight is 0 J.

b) work = mgh = 1000kg * 9.8m/s² * ½ * 50m = 245 kJ

c) Twice that to point B, or 490 kJ

d) 245 kJ

e) 360 kJ
Check: PE = mgh =1000kg * 9.8m/s² * 50m = 490 kJ

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