Minimum Coefficient of Friction calculation using Centripetal force

[swag]

A() 61 kg child stands at the rim of a merrygo-round of radius 1.05 m, rotating with an
angular speed of 1.87 rad/s
The acceleration of gravity is 9.8 m/s^2

What is the child’s centripetal acceleration?
Answer in units of m/s

What minimum force between her feet and
the floor of the carousel is required to keep
her in the circular path?
Answer in units of N


What minimum coefficient of static friction is
required?

The Attempt at a Solution

1)
I found the centripetal acceleration since a = v^2/r and v = 1.9635 and r = 1.05.
The acceleration is 3.671745

2) I found the force which is F=ma
F = 61(3.671745) = 223.976445 N

3) I'm confused as to how I should solve for the minimum of coefficient of friction.

Help is appreciated!

 

[PeterO]

A() 61 kg child stands at the rim of a merrygo-round of radius 1.05 m, rotating with an
angular speed of 1.87 rad/s
The acceleration of gravity is 9.8 m/s^2

What is the child’s centripetal acceleration?
Answer in units of m/s

What minimum force between her feet and
the floor of the carousel is required to keep
her in the circular path?
Answer in units of N


What minimum coefficient of static friction is
required?

The Attempt at a Solution

1)
I found the centripetal acceleration since a = v^2/r and v = 1.9635 and r = 1.05.
The acceleration is 3.671745

2) I found the force which is F=ma
F = 61(3.671745) = 223.976445 N

3) I'm confused as to how I should solve for the minimum of coefficient of friction.

Help is appreciated!

Assumin it is the word "minimum"that is confusing you, remember that the usual formula F = μN refers to the maximum friction possible, so if the coefficient of friction was 2.3, only a fraction of the potential friction would be necessary.
If the friction force required matches the maximum friction available, then we have the minimum coefficient.

If it is the idea of friction that is confusing you, you better re-read the section of your text on friction

 

[swag]

But, I have to solve for the coefficient of static friction. The equation for static friction is f ≤ μN , the one you showed is for kinetic friction.

 

[PeterO]

But, I have to solve for the coefficient of static friction. The equation for static friction is f ≤ μN , the one you showed is for kinetic friction.

OK, replace the = in my response with ≤ and re-read.

EDIT: I don't distinguish between static and kinetic - since I am always aware which one I am using.

 

[asteriatic]

To find the minimum coefficient of friction, we can use the formula Ff = μN, where Ff is the force of friction, μ is the coefficient of friction, and N is the normal force. In this case, the normal force is equal to the force needed to keep the child in the circular path, which we found to be 223.976445 N in part 2. Therefore, the minimum coefficient of friction would be μ = Ff/N. Plugging in the values, we get μ = 223.976445/223.976445 = 1. This means that the coefficient of friction must be equal to or greater than 1 in order for the child to stay on the merry-go-round without slipping.