Question

A roller-coaster car has a mass of 500 kg when fully loaded with passengers. The car passes over a hill of radius 15 m, as shown. At the top of the hill, the car has a speed of 8.0 m/s. What is the force oof the track on the car at the top of the hill?

Answer 1

The centripetal acceleration is ac = v^2 / r = 64 / 15 m/s^2 = 4.27 m/s^2

So the net acceleration at the top of the hill is a = g - ac = 9.81 - 4.27 m/s^2 = 5.54 m/s^2

So the upward force of the track on the car is equal and opposite to the downward force of the car on the track:
f = m*a = 500kg * 5.54 m/s^2 = 2770N = 2.8 kN

Answer 2

2766.66N

Answer 3

F=mg-mv*v/r=m(g-v*v/r)=500(9.8-8*8/15)=2766.66N