Centripetal Force Loop-the-loop

AI Thread Summary
The discussion revolves around a physics problem involving a cyclist navigating a loop-the-loop. For part a, the calculated minimum speed to successfully pass over the top of the loop is questioned, with a suggestion that the initial answer of 98.1 m/s is incorrect. In part b, the apparent weight of the cyclist at the bottom of the loop is calculated as 972N, but this also requires reevaluation. The main confusion arises in part c regarding the normal force at the 3 o'clock position, where it is clarified that the normal force acts towards the center of the circle, and the cyclist's speed should be considered constant throughout the loop for accurate calculations. Understanding the normal force's role and using conservation of energy are emphasized as key concepts for solving the problem.
JoshBuntu
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Homework Statement



There is a loop-the-loop, thing, and a dude on a bicycle is going to ride around the loop. Total mass is 1 kg (I'm aware that isn't realistic at all...) and radius is 10 meters.

a) what is the minimum speed that the cyclist must have to make it over the top of the loop without falling off?
b) If this block has this minimum speed, then compute the apparent weight of the cyclist at the bottom of the loop.
c) what is the normal force on the cyclist at the 3 oclock position?

Homework Equations



a(centripetal)= (v^2)/r
F(gravity)=mg


The Attempt at a Solution



The answer I calculated to part a is 98.1 m/s. I assumed that Normal Force equals zero. For part b I got 972N . I assumed that F(normal) - F(gravity)=ma(centripetal)

I would really appreciate if someone could just double check those for me as I have no answer key.

I'm having significant problems with part c. I drew a free body diagram of the cyclist at the 3 oclock position. So normal force is acting to the left towards the center of the circle, with centripetal acceleration, and F(gravity) is acting downwards. If you're on a wall like that, then isn't normal force zero? But then I know that's not the case because the cycle is driving into the wall and normal force is pushing outward and...ok, so I don't really understand what the normal force is doing here. Could someone please explain the concept? I think if I understand the concept I could do the math, but I just don't understand it. Thanks!

 
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JoshBuntu said:

Homework Statement



There is a loop-the-loop, thing, and a dude on a bicycle is going to ride around the loop. Total mass is 1 kg (I'm aware that isn't realistic at all...) and radius is 10 meters.

a) what is the minimum speed that the cyclist must have to make it over the top of the loop without falling off?
b) If this block has this minimum speed, then compute the apparent weight of the cyclist at the bottom of the loop.
c) what is the normal force on the cyclist at the 3 oclock position?

Homework Equations



a(centripetal)= (v^2)/r
F(gravity)=mg


The Attempt at a Solution



The answer I calculated to part a is 98.1 m/s. I assumed that Normal Force equals zero.
that's the correct assumption, but your answer is incorrect. Please show your work
For part b I got 972N . I assumed that F(normal) - F(gravity)=ma(centripetal)
again right assumption, wrong answer. Are you using conservation of energy to find the speed ? of course, you need to correct part a first.
I'm having significant problems with part c. I drew a free body diagram of the cyclist at the 3 oclock position. So normal force is acting to the left towards the center of the circle, with centripetal acceleration, and F(gravity) is acting downwards. If you're on a wall like that, then isn't normal force zero? But then I know that's not the case because the cycle is driving into the wall and normal force is pushing outward and...ok, so I don't really understand what the normal force is doing here. Could someone please explain the concept? I think if I understand the concept I could do the math, but I just don't understand it. Thanks!
The normal force acts perpendicular to the object (cyclist) at a contact point, so that is the force acting to the left due to the centripetal acceleration at that point. You again should use conservation of energy to find the speed at that point.
 
Conservation of energy? Ohh uhhh...is there another way? We didn't learn energy yet so I'm assuming there's another way to do this...
 
Apparently, then, the speed of the cyclist is assumed constant throughout the loop, so after you calculate the min speed at the top, use that same value of speed everywhere, using Newton 2 to calculate the normal force at the bottom and 3 o'clock position.
 
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