A roller coaster car loaded with people has mass M=320 kg. It goes over the top
ID: 1590353 • Letter: A
Question
A roller coaster car loaded with people has mass M=320 kg. It goes over the top of a "hill on the track" (the track goes up, curves vertically, then comes back down again) with a speed v of 21.4 m/s. The car is riding on top of the track, but has wheels both above and below the track for safety. The radius of curvature R of the hill is 15.8 m.
(a)
What is the force that the track must exert on the car? (positive is up) ____N ( ± 20 N)
(b)
What must be the force that the car exerts on a 61 kg passenger? _____ N ( ± 20 N)
Explanation / Answer
a) Let N is the force that the track must exert on the car.
Net force on car, Fnet = M*g + N
M*a = M*g + N
==> N = Mg - M*a
= M*g - M*v^2/R
= 320*9.8 - 320*21.4^2/15.8
= -6139 N
b) let N be the force that the car exerts on a 61 kg passenger
Net force on passenger, Fnet = m*g + N
m*a = m*g + N
==> N = mg - m*a
= m*g - m*v^2/R
= 61*9.8 - 61*21.4^2/15.8
= -1170 N
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