1. A 200kg roller-coaster car is on a frictionless track initially moving at 3 m

Question

1. A 200kg roller-coaster car is on a frictionless track initially moving at 3 m/s at the top of the first hill. What is the speed of the roller coaster at each of the peaks of the rest of the hills (a,b) and when it reaches ground level (c)?

2.If the roller-coaster track was not frictionless and when the coaster reached point c it had a speed of 10 m/s, how much work must have been done by the frictional force?

Unable to post picture

Starting height 20m A 10m B 5m c is zero. Picture shows starting at 20 going down a hill back up the hill to A at 10m then down the hill to B at 5m then down the hill to c

Explanation / Answer

1. Applying energy conservation,

PEi + KEi = PEf + KEf

m g (20) + m (3^2 / 2) = m g h + m v^2 /2

v^2 = 40 g + 9 - 2 g h

vA^2 = (40 x 9.8) + 9 - (2 x 9.8 x 10)

vA = 14.3 m/s

vB^2 = (40 x 9.8) + 9 - (2 x 9.8 x 5)

vB = 17.4 m/s

vC^2 = (40 x 9.8) + 9 - 0

vC = 20.02 m/s

2. initial energy = (200 x 9.8 x 20) + (200 x 3^2 / 2)

= 40100 J

final energy = 0 + (200 x 10^2 / 2) = 10000 J

work done = final energy - initial energy

= - 30100 J

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