# Centripetal or CoEf ?

neonjr
Centripetal or CoEf ?

## Homework Statement

If the Coefficient of friction between the gym floor and your running shoes is 0.80, how fast could you run around a circle of radius 2.0m?

I don't know even where to start...

## The Attempt at a Solution

Oomair
you should draw a free body diagram and label the forces that are occurring

and apply F=ma, hence a = (v^2)/R

neonjr
you should draw a free body diagram and label the forces that are occurring

and apply F=ma, hence a = (v^2)/R

and how do i do that without having any mass to work with, any velocity to work with, any acceleration to work with.

Staff Emeritus
and how do i do that without having any mass to work with, any velocity to work with, any acceleration to work with.
These are the variables you are trying to solve for. You don't really need a mass as it will disappear in the end.

Oomair
centripetal acceleration is where a = (v^2)/R, so you know that F=ma, since the problem involves motion around a circle, then the sum of forces is F=m(V^2)/(R)

and you know that friction is a force...

Tentothe
Drawing a free-body diagram shows that there are three different types of forces acting on you in this situation: friction, normal, and gravitational. One of them is going to be unbalanced and cause the acceleration required to keep you running in a circle. Add up the forces acting on you to find the net force, which you should find is only this unbalanced force. Using Newton's second law, F_net = ma, where F_net is this unbalanced force and a is v^2/R, you can solve for the velocity. The mass does end up dropping out, the acceleration was substituted for in terms of velocity, and obviously you won't need the velocity because this is what you are trying to solve for.

Hint: Recall that the friction force is going to be $$\mu_{s}n$$, or the coefficient of friction multiplied by the normal force.

neonjr
still getting no where with this, I'm really not understanding without a complete equation. The statement "You don't really need a mass as it will disappear in the end." makes absolutely no sense to me.

And after drawing a FBD I am still not getting what I need to use here. I draw the circle figure out my distance, because i know the radius of the circle, so TTr^2. But to find out velocity in any situation, and GET an answer, not a theoretical answer like (xy2) you need more than one piece of info out of an equation. because V=d/t, all i have is distance, Gravity, and CoEf...I've talked to three people at home here and they are all lost.

Staff Emeritus
There is an upper limit on the centripedal force the shoes can exert. This upper limit maps directly to the maximum speed someone can run around the circle. A person can accelerate less than this upper limit, but this means the person is not running around the circle as fast as they can. What is this upper limit? (HINT: Use the coefficient of friction.)

neonjr
There is an upper limit on the centripedal force the shoes can exert. This upper limit maps directly to the maximum speed someone can run around the circle. A person can accelerate less than this upper limit, but this means the person is not running around the circle as fast as they can. What is this upper limit? (HINT: Use the coefficient of friction.)

i'm sorry to be abrupt, but perhaps i need to say this. but I'm not that bright. i have not got a clue what you are talking about. you need to explain this in terms a 5 year old could understand, and start from the beginning. please.

Staff Emeritus
Suppose the person has a mass m. What is the maximum horizontal force the person can exert with his shoes?

neonjr
Suppose the person has a mass m. What is the maximum horizontal force the person can exert with his shoes?

would this not be 9.8 N ?

Tentothe
Break this into dimensions first. What are your vertical forces and what are your horizontal forces?

Since the runner is not going to be moving in the vertical direction (not coming up off the ground or sinking through it), we know the acceleration in this direction is going to be 0. By Newton's second law, F=ma, where a is zero, the net force in the vertical direction must be therefore be zero. What does this say about the forces acting on the runner in the vertical direction? How can you use this information to analyze the horizontal direction?

In the horizontal direction, you do have an acceleration. It is what let's you run in a circle and is directed toward the center of the circle. Its magnitude is v^2/R. If you have an acceleration in the horizontal direction, you must therefore have a net force acting in the horizontal direction by Newton's second law.

Determine which forces you have in each dimension and set them equal to the mass times the acceleration in that dimension by Newton's second law. If the algebra is done correctly, the mass terms will drop out of the equation, allowing you to solve for the unknown you want: velocity.

You will be working with two equations here: one for each dimension.

Staff Emeritus