How to prove that friction is limiting

[elemis]

I know that friction is limiting when F =$$\mu$$R

The problem I am is facing is as follows :

I am given an inclined plane with a mass in limiting equilibrium. A string is attached to it and has a tension in it acting PARALLEL to the surface of the plane.

I know the angle of inclination and it is a rough plane.

The first question will usually ask me to find the coefficient of friction or the normal force.

This I can do easily

The next question will be something like this :

The tension in the string is now reduced (they give a value for the new tension).

Determine if friction is still limiting.

How would I go about doing this ?

 

[gtoguy97]

To answer this question, you need to calculate the new normal force acting on the mass on the inclined plane. This will be the sum of the component of the new tension in the direction of the plane plus the component of gravity acting on the mass. You can then compare this new normal force to the friction force between the mass and the plane, which is equal to \mu R (where \mu is the coefficient of friction and R is the normal force). If the new normal force is greater than \mu R, then friction is not limiting. If the new normal force is less than \mu R, then friction is limiting.