A car in an amusement park ride rolls without friction around the track shown in

Question

A car in an amusement park ride rolls without friction around the track shown in the figure (Figure 1) . It starts from rest at point A at a height h above the bottom of the loop. Treat the car as a particle.

If the car starts at height h= 5.00 R and the radius is R = 25.0m , compute the speed of the passengers when the car is at point C, which is at the end of a horizontal diameter.

If the car starts at height h= 5.00 R and the radius is R = 25.0m , compute the radial acceleration of the passengers when the car is at point C, which is at the end of a horizontal diameter.

If the car starts at height h=  5.00 R and the radius is R = 25.0m , compute the tangential acceleration of the passengers when the car is at point C, which is at the end of a horizontal diameter.

Explanation / Answer

If car starts with a total mechanical energy = GPE = mgh = mg(5)(25.0) = 125mg

at point C the car has both GPE and KE:

It's GPE = 25mg so

its KE = 125mg - 25mg = 100mg = 1/2mV2

mV2 = 200mg

V2 = 200 x 9.81 = 1962

a) Required Speed = V = 44.29447 m/s

b) Required Radial Acceleration is Ac = V2/R = 1962/25 = 78.48 m/s2

C) Tangential Acceleration = At = g = 9.81 m/s2

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