4. A roller coaster ride contains a giant vertical loop: a circle of radius 8.50

Question

4. A roller coaster ride contains a giant vertical loop: a circle of radius 8.50 m.
a.) What is the minimum speed required at the top of the loop so that passengers will stay in contact with their seats and not fall out? Show your work.
b.) Suppose a 50.0-kg passenger rides the roller coaster car through the top of the loop at a speed of 13.00 m/s (roughly 30 miles/hour). At that moment, what is the magnitude of the normal force from her seat? What percentage of her weight is this? Show your work.

Explanation / Answer

a) At the top

T + mg = mv^2/r

for minimum speed , T = 0

v = sqrt(gr) = sqrt(9.8*8.5) = 9.13 m/s

b) T + 50*9.8 = 50*13^2 / 8.5

T = 504.11 N

W = mg = 50*9.8 = 490 N

% of weight = 504.11 / 490 *100 = 102.87 %

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