A 294 kg roller coaster car sits on a horizontal track. Ahead of it is a vertica

Question

A 294 kg roller coaster car sits on a horizontal track. Ahead of it is a vertical loop with radius of 5.17 m. The car is given an initial speed of 13.3 m/s and the car successfully traverses the loop. What is the maximum amount of energy taken away from the car by friction so that the car successfully travels through the loop? (Hint: think about the normal force that the track exerts on the car at the top of the loop, this should give you a minimum speed at the top of the loop.) Write your answer to three significant figures

Explanation / Answer

so at the top of the loop we have N+mg=mv^2/r so min N is N=0 so v^2=gr so v=sqrt(gr) then we can do energy Ei + W friction = Ef 1/2 294 * 13.3^2 + W friction = 1/2 *294*9.81*5.17 + 294* 2 * 5.17 solve for W friction, W friction =-15507 J so max that can be taken away is 1.55 E 4 J

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