A car in an amusement park ride rolls without friction around the loop track. It

Question

A car in an amusement park ride rolls without friction around the loop track. It starts from rest at point A, height h above the bottom of the loop. A few grandmas, who ditched Sunday school for some better thrills, embark on the joyride.

a. What is the minimum value of h (in terms of R) such that the car moves around the loop without ralling off at the top (point B)?

b. We now assume h=3.5R, R=30m

      i. What is the reaction force of the track at point B?

      ii. Compute the speed, radial acceleration and tangential acceleration the screaming grandma's experience when the car is at point C. This point is located at the end of a horizontal diameter. Show these acceleration compomnents in a diagram, approximately to scale.

     iii. How many g's are the grandmas experiencing at the bottom of the loop?

Please show all steps and diagrams

Explanation / Answer

According to law of conservation of Energy

       mgh = mg R + 1/2mv2

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