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.(part a)If the car starts at height h= 5.00 R and the radius is R = 17.0m , compute the speed of the passengers when the car is at point C, which is at the end of a horizontal diameter.(part b)If the car starts at height h= 5.00 R and the radius is R = 17.0m , compute the radial acceleration of the passengers when the car is at point C, which is at the end of a horizontal diameter.(Part c) If the car starts at height h= 5.00 R and the radius is R = 17.0m , 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

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(3)(23.0) = 69mg at point C the car has both GPE and KE: It's GPE = 23mg so its KE = 69mg - 23mg = 46mg = 1/2mV² mV² = 92mg V² = 92 x 9.81 = 902.52 V = 30.0 m/s ANS Ac = V²/R = 902.52/23 = 39.2 m/s² ANS Atangential = g ANS

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