# Apparent weightlessness problem?

**1. The problem statement, all variables and given/known data**

A roller coaster goes over the top of a semicircular track of radius R with a velocity Vtop, such that passengers momentarily feel weightless (zero ‘g’) at the top. The rollercoaster then accelerates to the bottom of another semicircular track of the same radius R. What effective ‘g’ do the passengers feel at the bottom? The difference in height between the top and bottom is 2R. (picture attached)

**2. Relevant equations**

[itex]F = G\frac{m1m2}{r^2}[/itex]

[itex]F = ma = \frac{mv^2}{r}[/itex]

[itex]E = U + K ????

[/itex]

**3. The attempt at a solution**

I am kinda confused as to how to solve this problem. I am also not entirely sure what they are asking or what my answer should look like or be in terms of. It looks like one of those problems that you solve using conservation of energy where I could make y1 = 2R v1 = Vtop, y2 = 0 and v2 =??, but since they didnt give any information on friction and this type of problem wouldnt give me any info about ‘g’ I am gonna guess I need to use the law of universal gravitation, but I don’t really know how to start.

My intuition would tell me that i should use the acceleration for circular motion formula (mv^2/r) with v as vtop and set it equal to -g. Maybe then i can solve that equality for vtop and at that point wouldnt it just be a conservation of energy problem to find the velocity in terms of g at the bottom? I am lost please help 🙁

http://ift.tt/1hduCsF

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