How to find mu without the force of friction

[Chrismacs]

Homework Statement

Well I am trying to figure out how to find mu if you don't know the force of friction

Homework Equations

An example is a 2.25 kg block is accelerating at an acceleration of 5 m/s/s and is on a 40 degree
ramp. What is the force of friction and what is mu?

The Attempt at a Solution

When I first look at this problem I write what I know

a=5 m/s/s
m=2.25kg
theta=40

and the equations I know:
Fw=m*g
Fnetx(perp)=sin(theta)*w
Fnety(perp)=cos(theta)*w
Ff=mu*Fn
Fn=Fwperp

But you see I think I am doing this problem wrong here because wouldn't the force of the weight parallel be greater than the force of friction?

Please if you can answer ant of my questions will you please do so.

Thank you!

 

[picklepie159]

well, I would first find the resultant force, the force that's pulling the object down parallel the ramp.
Force resultant=sin(theta) mass x g

So if there was no friction, then the object would only have that force and would accelerate down more quickly than if there was
friction.

But since there's friction force acting in the opposite direction, then the object doesn't accelerate as quickly. So since Net force is what is currently acting on the object now, I would use
Net Force= Mass x Acceleration,
Net Force= 2.25 x 5

I would find the net force acting on the block. I would then subtract the resultant force from the Net force, and that would equal friction force.

With friction force, I would just then plug it into the equation. F(fric.)= Mu x (mg cos theta)

Note: This may not be correct, since I am also a newbie. However, I'm pretty sure it's right.