how to determine kinetic friction?

Dear Anil,

When an object rests on an inclined plane, a component of its weight is supported by the ramp as a force normal (perpendicular) to the ramp, and a component of its weight is acting parallel with the ramp in the downward direction. Use sin and cos to find the components of the weight that are acting normal and parallel to the ramp.

The component parallel to the ramp is the force that will cause acceleration down the ramp. But since we are told there is friction, we know that this force will be opposed by the kinetic friction sliding down the ramp. So, per Newton's Second Law, the sum of the forces acting on the box is equal to the mass times acceleration of the box.

So now we have a formula that relates the sum of the forces acting on the box with the acceleration. And we know the gravitational component of the force from above, so now all we need is the frictional component of the force acting on the box. See the link below for the formula for friction. And we already know the normal force from above. So now we can put everything together into one formula and solve for mu.

This can be solved without knowing the weight of the box because once you combine all parts of the formula into one you can see that the mass appears on both sides of the formula, so it can be removed by dividing both sides by the mass. The correct answer is given below just so you can check your work, but please go through the steps of forming the equations and showing your work.

Best Of luck

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Dear ANIL PANDEY,