# Centripetal Force Loop-the-loop (1 Viewer)

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#### JoshBuntu

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

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?

2. Relevant equations

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

3. 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!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

#### PhanthomJay

Homework Helper
Gold Member
1. The problem statement, all variables and given/known data

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?

2. Relevant equations

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

3. 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)
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.

#### JoshBuntu

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...

#### PhanthomJay

Homework Helper
Gold Member
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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