A car in an amusement park ride rolls without friction around a track (Figure 1)

Question

A car in an amusement park ride rolls without friction around a track (Figure 1). The car 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 = 4.90 R and the radius is R_1 = 17.0 m, compute the speed of the passengers when the car is at point C, which is at the end of a horizontal diameter. Express your answer with the appropriate units. Compute the radial acceleration of the passengers when the car is at point C. which is at the end of a horizontal diameter. Express your answer with the appropriate units.

Explanation / Answer

The first sentence contains an oxymoron.
Rolling can NOT take place in the absence of friction!!
Every physics student should be made aware of this fact...when enough are...
then wording of questions like this would change in honor of the understanding
of this fact.

If car starts with a total mechanical energy = GPE = mgh = mg(4.9)(17.0) = 83.3mg

at point C the car has both GPE and KE:
It's GPE = 17mg so
its KE = 83.3mg - 17mg = 66.3mg = 1/2mV²
mV² = 132.6mg
V² = 132.6 x 9.81 = 1299.48
V = 36.04 m/s ANS

Ac = V²/R = 1299.48 /17 = 76.44 m/s² ANS

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