A body weighing 8.5 newtons rests on a rough horizontal plane. A horizontal force is acting on it, causing it to be on the point of moving. Given that the force of the friction was 3.4 newtons, find the coefficient of static friction.
We have a body that weighs 8.5 newtons. This is the weight, not the mass. And this means that the force acting downwards on the plane itself is 8.5 newtons. Then, according to Newton’s third law of motion, there is an equal and opposite force acting on the body by the plane. We could call that 𝑅. But of course, since the body is at rest, we know that 𝑅 must be equal to 8.5 newtons itself.
We then have a horizontal force acting on the body. And since the plane itself is rough, we also have a force acting in the opposite direction. This is the frictional force. And we know that frictional force is equal to 𝜇𝑅, where 𝜇 is the coefficient of friction and 𝑅 is the reaction force. Since the body is at the point of moving, it’s in limiting equilibrium. So, the net forces horizontally are equal to zero. Or 𝐹 is equal to 𝜇𝑅.
Now, of course, the forward force and the backward force due to friction must be equal. So, 𝐹 is equal to 3.4. We don’t know 𝜇. That’s what we’re trying to calculate. But we do know the reaction force to be equal to 8.5. So, we have an equation in 𝜇 that we can solve. To solve, we simply divide through by 8.5. That’s 𝜇 equals 3.4 over 8.5, which is equal to 0.4. And so, the coefficient of static friction in this question is 0.4.
Now, a good way to check is to make sure that the coefficient of friction is between zero and one. And our answer is. So, it’s a good indication we’ve probably done most of our working correctly.