You are tasked with designing a roller coaster loop-the-loop with radius r. How

Question

You are tasked with designing a roller coaster loop-the-loop with radius r. How fast must the cart move at the top of the loop (when upside down), such that the normal force acting on the riders is equal to their weight?

(Practise to derive the answer by first drawing a free-body diagram and then applying Newton's 2nd Law.)

You are tasked with designing a roller coaster loop-the-loop with radius r. If the cart has just the required minimum speed (no normal force) at the top of the loop (when upside down), what is the carts speed at the bottom of the loop?

You are tasked with designing a roller coaster loop-the-loop with radius r. How fast must the cart move at the top of the loop (when upside down), such that the normal force acting on the riders is equal to their weight? (Practise to derive the answer by first drawing a free-body diagram and then applying Newton's 2nd Law.) You are tasked with designing a roller coaster loop-the-loop with radius r. If the cart has just the required minimum speed (no normal force) at the top of the loop (when upside down), what is the carts speed at the bottom of the loop?

Explanation / Answer

Part one

-mg = m(-a_c)

g = v^2/r

v=sqrt(gr)

Part two

mgy_0 + 1/2mv_0^2 = 1/2mv_f^2

g(2R) + 1/2(gR) = 1/2v_f^2

5gR = v_f^2

v_f = sqrt(5gR)

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