The roller - coaster car/ rider of mass M shown in the figure at right is releas

Question

The roller - coaster car/ rider of mass M shown in the figure at right is released from rest from a height h and then moves freely with negligible friction. The roller - coaster track includes a circular loop of radius R in a vertical plane. By working through different parts of this problem given below, you will first derive an expression for the minimum height h min from which the cart should be released if it is to barely complete the loop. Then you will derive an expression for the normal force exerted on the car/rider at the bottom of the loop (point B) for that starting height. Finally, you will compare magnitudes of this normal force and the weight of the car/rider and discuss implications of this comparison. Draw complete FBDs for the cart/rider combination when it is at the bottom (point B) and top (point T). Derive an example for the minimum speed Vtmin the cart/rider must have at the top if it is to barely complete a full loop. Derive an expression for the minimum height hmin the cart must start from if it to barely complete a complete loop. You must use energy methods. If the cart started at height hmin, derive an expression for the peed of the cart at the bottom of the loop, If the cart started at height hmin, derive an expression for the magnitude of the normal force N min experienced by the cart. By comparing toy answer to part(e) with the weight magnitude of the car/rider, discuss the weight felt by the rider at the bottom of the loop.

Explanation / Answer

sorry unable to upload the solution here so i am postinh the link of that solution

for a) , b) , c) the link is below

http://postimg.org/image/h2j37xby5/

for d) , e) , f) the link is below

http://postimg.org/image/n8vz7gaeh/

thank you.....

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