How do I find the coefficient of friction when acceleration is involved?

Question

A force of 105 N is applied horizontally to a 20.0 kg box to move it across a horizontal floor. If the box has an acceleration of 3.00m/s^2, find the coefficient of friction.

I know F=ma is used somehow, but where do I use it? Help please!

Answer 1

F = M x A relates the net force to the acceleration and the mass. You have the mass and the acceleration so you can compute the net force.

The net force is the difference between the applied force and the drag due to friction:

F = P - D

You know F and P, so you can compute the drag force D.

The drag is equal to the normal force times the coefficient of friction.

D = N x Ck.

In this case, the normal force is just the weight - compute from the mass and the gravitational acceleration g (about 9.8 m/s^2).

Knowing the Drag force and the weight, you can compute the coefficient of friction.

Answer 2

you ought to decide on it into components. y direction: N - mgcos40 = 0 N = mgcos40 x direction: mgsin40 - friction = ma mgsin40 - (uk*N) = ma mgsin40 - (uk*mgcos40) = ma Now word that each and each unmarried variable has an m in it. this implies you will get a cancellation as quickly as you ingredient out the m's. m*[gsin40 - (ukgcos40)] = ma Divide the m's [gsin40 - (ukgcos40)] = a Simplifying extra yields: g(sin40 - uk*cos40) = a sin40 - uk*cos40 = a/g -uk*cos40 = a/g - sin40 remedy for uk (the coefficient of friction) employing the given acceleration, perspective, and of direction gravity.