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sleet_krkn [62]
3 years ago
7

A roller coaster is going through a loop with a circular radius of 9.1 meters, how fast must the roller coaster be moving at the

top of the loop in order to stay on the track?
Physics
1 answer:
Verdich [7]3 years ago
8 0

Answer:

at least 20mph

Explanation:

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This type of a problem can be solved by considering energy transformations. Initially, the spring is compressed, thus having stored something called an elastic potential energy. This energy is proportional to the square of the spring displacement d from its normal (neutral position) and the spring constant k:

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So, this spring is storing almost 12 Joules of potential energy. This energy is ready to be transformed into the kinetic energy when the masses are released. There are two 0.2kg masses that will be moving away from each other, their total kinetic energy after the release equaling the elastic energy prior to the release (no losses, since there is no friction to be reckoned with).

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E_p =mv^2\implies v=\pm \sqrt{\frac{E_p}{m}}=\pm\sqrt{\frac{11.98J}{0.2kg}}=\pm 7.74\frac{m}{s}

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Answer: reaction force = -558N

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