Question

A roller coaster car has a mass of 800 kg. It is launched horizontally from a giant spring (spring constant 35 kN/m), rolls 10m and then goes through a vertical loop-the-loop track of radius 7 m. On average, for every meter the car rolls on the track, thermal energy increases by 800 J. The designer, who wants to go home for the weekend, says that compressing the spring 3 m should give the car enough energy to safely go through the top of the loop. Is he right? (Hint: Check last week's suspiciously similar problem to get started with this one.)
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Answer 1

Solution If the car wants to complete the loop-the-loop the energy gained by the car from should not exhaust completely by the time it reaches the top of the loop Energy gained from the springka 0.5x35x103 x3 Total distane travelled by the car as it reaches the to of the loop 10 + tr -10+(3.14x7) 31.98m Average thermal energy dissipated- 31.98 x800 255.84 x102 J ompressing the spring by 3 m the car will have enough energy to go through the top of the loop.