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.

A.What is the minimum value of

h (in terms of R) such that the car moves around the loop without falling off at the top (point B)?

Express your answer in terms of R.

B.If the car starts at height

h= 4.30 R and the radius is R1 = 14.0 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.

C.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.

D. C ompute the tangential 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

If car starts with a total mechanical energy = GPE = mgh = mg(4.30)(14.0 ) = 60.2 mg

at point C the car has both GPE and KE:
It's GPE =14.0mg so
its KE =60.2mg - 14mg = 46.3mg = 1/2mV²
mV² = 92.4mg
V² = 92.4 x 9.81 = 906.444
V = 30.10 m/s ANS

Ac = V²/R =906.444/14 = 64.74 m/s² ANS

Atangential = g ANS

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