An object with a mass of #14# # kg# is on a plane with an incline of # - pi/3 #. If it takes #12# # N# to start pushing the object down the plane and #7 # # N# to keep pushing it, what are the coefficients of static and kinetic friction?
We have to assume that the motion is at constant velocity once the motion starts: the question doesn't say so, exactly, but it's the only way it makes sense.
There is a component of the weight force of the
The forces will be given by:
In this case, the negative sign just means the slope rises right-to-left rather than left-to-right. We can ignore the sign for our purposes.
To calculate the coefficient of static friction, we know that there is a force of
We have the expression for the static friction:
A frictional coefficient of 2 is a little unusual, but not impossible.
The argument for the coefficient of kinetic friction is the same, but the force that is required to maintain constant velocity versus the frictional force is