Determining the coefficient of friction? (example inside)

[Nonchalant]

Homework Statement

A physics student is performing an experiment to determine the coefficient of friction between a physics textbook and a 2.5 m wooden ramp. He places the textbook, which has a mass of 1.2 kg, on the inclined ramp and gradually increases the angle of the incline. At an angle of 30 degrees, the textbook starts to slip. It slides down the ramp in 4.0 s. Determine the coefficient of friction.

Homework Equations

The Attempt at a Solution

Well i was working on it with my friend in class, and he came up with

friction = tan 30 degrees = 0.58

but then, I don't think that's all to it right? Any help please?

 

[G01]

The coefficient of static friction is indeed:

$$\mu_s=\tan\theta$$ where $$\theta$$ is the angle at which the block starts to slip.

You can work on deriving this yourself by starting with the following information:

At the angle where the block just starts to slip the component of gravity along the hill (x direction) much equal the force of static friction:

$$F_{gx}=F_{static f}$$

Can you fill in for the forces above and solve for the coefficient? If you can, you should end up with the expression given by your friend.