Energy transformation in a roller coaster.

Classical Mechanics Level 1

A roller coaster is lifted to a height $H$ using an electric motor and is made to slide down until it reaches the lowest point of a circular hoop. It completes the motion around the hoop without any other form of external energy added to it during its motion. Ignoring energy losses due to friction and other factors what should the height H (in meters) be if the radius of the circular hoop is $2 \text{ m}$

2 sqrt(2) 4 2*pi

1 solution

Srinivasa Gopal
Dec 3, 2017

After the roller coaster is taken to height H it possesses only potential energy. This is converted to kinetic energy as the roller coaster slides down to the lowest point of the circular hoop. It needs to rise to a height of 4 meters after which it will fall down due to gravity from the highest point of the circular loop to the lowest point where it gains kinetic energy. So H should be equal to at least 4 meters.

I would argue that if the initial height is only 4 meters, the roller coaster will not make it around the loop (which is 4 meters off the ground*). It would lose all its velocity at the top and fall straight down. *UNLESS the wheels are locked to the track, and it can't fall. See: https://www.youtube.com/watch?v=XFJkFzRetSw&feature=emb_logo

Jeremy Sale - 7 months, 2 weeks ago

Under the assumptions that the normal force becomes zero when the roller coaster reaches the apex point the answer should be 5 meters. But I have calculated the height by using the law of conservation of energy which strangely does not involve the use of the centripetal force at all. Going by the video, I think the correct answer is 5 m.

Srinivasa Gopal - 7 months, 1 week ago

Energy transformation in a roller coaster.

1 solution

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