How to determine the static frictional force?

[shizzledizzle]

Homework Statement

We have to do a lab on friction in which there was a pulley with a mass attached to it which is held by another mass on the table and an inclined plane with a mass on it. The question is "Based on your work above, show why μs = m/M". I don't understand how to do this. Also "what is the static frictional force on the wooden block equal to?"

Homework Equations

The mass on the table holding the mass dangling off the pulley is 'M' and the mass dangling off the pulley is 'm'

The Attempt at a Solution

Maybe the mass is giving off a force to the mass on the table? But how would I explain this? And the second question would it be that Fs = μN?

 

[Delphi51]

The question isn't clear! Could you draw a diagram?
The usual approach for this type of question is to draw the forces on each mass and then write that the sum of the forces = 0 for each one.

 

[kerimek]

To determine the static frictional force, you can use the formula Fs = μsN, where μs is the coefficient of static friction and N is the normal force. In this case, the normal force would be equal to the weight of the object on the inclined plane, which is equal to the mass times the acceleration due to gravity.

To show why μs = m/M, you can use the equation Fs = μsN and substitute in the values for the masses. Since the normal force (N) is equal to the weight of the object on the inclined plane, which is equal to the mass (m) times the acceleration due to gravity, and the static frictional force (Fs) is equal to the force required to keep the object from sliding down the inclined plane, we can set these two equations equal to each other:

Fs = μsN

Fs = μs(mg)

Since the mass on the table (M) is holding the mass on the pulley (m), the force required to keep the object from sliding down the inclined plane is equal to the weight of the hanging mass (m) times the ratio of the masses (m/M). Therefore, we can rewrite the equation as:

Fs = μs(m/M)Mg

Since the mass on the table (M) is cancelled out, we are left with:

Fs = μsmg

Now, we can equate this to the original equation we had for Fs:

μsmg = μsN

μs(mg) = μs(mg)

Therefore, we have shown that μs = m/M.

The static frictional force on the wooden block would be equal to μsN, where N is the normal force and μs is the coefficient of static friction. The normal force would be equal to the weight of the wooden block, which is equal to the mass times the acceleration due to gravity. This force is required to keep the wooden block from sliding down the inclined plane.