(8c8p4) In the figure, a frictionless roller coaster of mass 1000 kg tops the fi

Question

(8c8p4) In the figure, a frictionless roller coaster of mass 1000 kg tops the first hill at height, h = 26 m with speed 10.15 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

here,

mass of coaster, m = 1000 kg

height of first hill, h = 26 m
initial velocity of coaster in hill 1, v = 10.15 m/s

Work done = Change in Potential Energy of Coaster
w = mg* Net height

Part A:
as it's on it's original height , h therefore
Change in PE is Zero ( mg(h-h) )
Work done will be Zero.

Part B:
W = mg(h - h/2)
W = (1000)(9.8)(26-(26/2))
W = 127400 J

Part C:
W = mgh
W = (1000)(9.8)(26)
W = 254800 J

Part D:
PE = mg(h/2)
PE = (1000)(9.8)(26)/2
PE = 127400 J

Part E:
PE = mgh
PE = (1000)(9.8)(26)
PE = 3.39e5 J

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