A single car on a roller-coaster track starts from rest from the top hill A(25m)

Question

A single car on a roller-coaster track starts from rest from the top hill A(25m) above the base of the track. Hill B(20m). Hill C(20m). Hill D(20m). Use g = 10 m/sˆ2. Total mass of the car is 200 kg.

A) The top of hill B is shaped like a circular arc with r=10m. Calculate the normal force that is applied to the car as the car passes over the top of hill B. (Assume no work is done by non-conservative forces)

B) Calculate the work done on the car by the resistive forces as the car travels from the top hill A to the top hill B.

Explanation / Answer

velocity of car at hill b is V

by conservation of energy

mgh=1/2*m*v2

200*10*(25-20) = 1/2*200*v2

V = 10 m/s

hence normal force

F = mg-m*v2/R = 200*10-200*10/10 = 1800 newton

b) since work done by non conservative forces are zero

the work done on the car by the resistive forces as the car travels from the top hill A to the top hill B = 0 newton

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