Grade 12 Physics, Coefficient of Friction

[JamesNam]

Homework Statement

Derivation of an equation for the coefficient of kinetic friction
*Since it's just a derivation, values won't be required, right?
*No mass was given

Homework Equations

Ff = μF_N
F_N = FgCosθ
F_net= F_app - Ff - FgSinθ <- Not sure about this.

The Attempt at a Solution

We had to draw a free body diagram so I"ll upload it

 

[tiny-tim]

Welcome to PF!

Good morning JamesNam! Welcome to PF!

Homework Statement

Derivation of an equation for the coefficient of kinetic friction
*Since it's just a derivation, values won't be required, right?
*No mass was given

Homework Equations

Ff = μF_N
F_N = FgCosθ

The Attempt at a Solution

We had to draw a free body diagram so I"ll upload it

I'm confused … what exactly is the question?

(and what's your answer?)

 

[JamesNam]

Thanks for the welcome! And we have to derive an equation for μ_k from the free body diagram that I have attatched.

 

[tiny-tim]

is it stationary or moving?

anyway, show us what you've tried ​

 

[Nickie]

.

I appreciate your attempt at a solution and your clear understanding of the necessary equations. However, I would like to clarify a few points.

Firstly, it is important to note that the coefficient of friction is a dimensionless quantity, meaning it does not have a unit. Therefore, it is not necessary to provide specific values for mass or other variables.

Secondly, your use of the free body diagram is a good start, but it is important to also consider the direction of the forces. In the equation Ff = μFN, the coefficient of friction is a proportionality constant that relates the force of friction (Ff) to the normal force (FN). This means that the direction of the force of friction is opposite to the direction of motion, or in the direction that opposes the relative motion between two surfaces.

Finally, the equation Fnet = Fapp - Ff - FgSinθ is a good representation of the net force acting on an object on an inclined plane. However, it is important to note that in this equation, Fapp represents the applied force (such as pushing or pulling), Ff represents the force of friction, and FgSinθ represents the component of the weight of the object that is parallel to the plane.

To derive an equation for the coefficient of kinetic friction, we can use the free body diagram and the equation Ff = μFN. By substituting FN = FgCosθ into this equation and rearranging, we get μ = Ff/FgCosθ. This equation represents the coefficient of kinetic friction, as it relates the force of friction to the weight of the object and the angle of the inclined plane.

I hope this helps clarify the derivation of the coefficient of kinetic friction. Keep up the good work in your studies of physics.