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- Homework Statement
- Loop Problem and Energy conservation

- Relevant Equations
- Fc=mv/2r , mg, E= 0.5mv^2, E= mgh

I have an assignment in physics and I can't understand the difference between the 2 questions. That's the question

A skier with mass m=70 kg stands on a ramp of height h. At the foot of the ramp, there is a loop with a radius of r=15 m. When entering the ramp, the speed is v1=0 m/s.

a) For test purposes, the skier is also held in the loop by a rail system so that he cannot fall off if his speed is too low. How high does the ramp have to be at least so that he can get through the loop in this case? Here I considered the loop as a hill that he needs to get through so I got that ramp should be 30m, since the radius is 30m.

b) Normal operation of the loop takes place without a safety rail system. In this case, how high does the ramp have to be so that the skier can get through the loop without falling off? Here I thought that the force of gravity must be equal to the centripetal force. So I got that h is 7.5, that means half of the r.

I can't understand what difference that makes if the person is held by a rail system or not. I tried to solve it in 2 ways considering the potential and kinetic energy, so I'm not sure that my answer is correct. It would be really helpful is someone could say that what I thought makes sense.

Thank you

A skier with mass m=70 kg stands on a ramp of height h. At the foot of the ramp, there is a loop with a radius of r=15 m. When entering the ramp, the speed is v1=0 m/s.

a) For test purposes, the skier is also held in the loop by a rail system so that he cannot fall off if his speed is too low. How high does the ramp have to be at least so that he can get through the loop in this case? Here I considered the loop as a hill that he needs to get through so I got that ramp should be 30m, since the radius is 30m.

b) Normal operation of the loop takes place without a safety rail system. In this case, how high does the ramp have to be so that the skier can get through the loop without falling off? Here I thought that the force of gravity must be equal to the centripetal force. So I got that h is 7.5, that means half of the r.

I can't understand what difference that makes if the person is held by a rail system or not. I tried to solve it in 2 ways considering the potential and kinetic energy, so I'm not sure that my answer is correct. It would be really helpful is someone could say that what I thought makes sense.

Thank you