The Gravitron si ngle-car roller coaster consists of a single loop-the-loop. The

Question

The Gravitron si ngle-car roller coaster consists of a single loop-the-loop. The car is initially pushed, giving it just the right mechanical energy so the riders on the coaster will feel "weightless" when they pass through the top of the cireular arc. How heavy will they feel when they pass through the bottom of the are (that is, what is the normal force pressing up on them when they are at the bottom of the loop)? Express the answer as a multiple of mg (their actual weight) Assume any effects of friction or of air resistance are negligible.

Explanation / Answer

To feel weightlessness minimum speed at thr top of the loop,

v = sqrt(g*R)

let vi is the minimum speed of the car at the bottom of the loop,

vf^2 - vi^2 = 2*(-g)*h

v^2 - vi^2 = 2*(-g)*2*R

vi^2 = v^2 + 4*g*R

vi^2 = g*R + 4*g*R

vi^2 = 5*g*R

vi = sqrt(5*g*R)

Normal force acting on the car at the bottom of the circular track, Fn = m*g + m*vi^2/R

= m*g + m*(5*g*R)/R

= 6*m*g

Fn = 6 times of actual weight   <<<<<------Answer

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