# What is the coefficient of friction between the plane and the block?

## Homework Statement

A 3 kg block slides down a 30 degree inclined plane with constant acceleration of 0.5 m/s2. The block starts from rest at the top. The length of the incline is 2 m. What is the coefficient of friction between the plane and the block?

Ff=uFn
Fn=Fg*cosA
Ff=Fg*sinA

## The Attempt at a Solution

Fn=(3)(9.8)*cos30
Fn=29.4*cos30
Fn=25.46N

Ff=(3)(9.8)*sin30
Ff=29.4*sin30
Ff=14.7N

Ff=uFn
14.7/25.46=u
u=0.58

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cepheid
Staff Emeritus
Gold Member

## Homework Statement

A 3 kg block slides down a 30 degree inclined plane with constant acceleration of 0.5 m/s2. The block starts from rest at the top. The length of the incline is 2 m. What is the coefficient of friction between the plane and the block?

## Homework Equations

Ff=uFn
Fn=Fg*cosA
Ff=Fg*sinA
This part in red is NOT TRUE in this situation! F|| = Fgsin(A) is the component of the weight that acts parallel to the plane, trying to pull the object down it. You would only equate that to the frictional force (in magnitude) IF the object were travelling at a constant velocity, suggesting that the net force was zero, suggesting that F|| = Ff (in magnitude).

In this case, the object is NOT travelling at a constant velocity. It is accelerating down the plane, suggesting the net force parallel to the plane is NOT zero. In fact, since the object is travelling down the plane, this suggests the net force is in the "down the plane" direction, requiring F|| > Ff.

what is the right formula to use in this situation?

cepheid
Staff Emeritus
Gold Member
what is the right formula to use in this situation?
Physics is not about memorizing formulae; it is about understanding and applying physical principles. Since you know the acceleration, you know the NET force in the || direction.* You also know that the net force has to be equal to the sum of the forces acting along that direction. There are are two such forces. One is F|| and the other is Ff.

*This knowledge comes as a result of Newton's second law, which is the principle that is applicable here.