a) Why are there no units attached to values of μ?
b)A force of 120 N is needed to push a box along a level road at a steady speed. If the force of gravity on the box is 250 N, what is the coefficient of kinetic friction between the box and the road?
a
because it is a ratio of friction force to normal force
b
see answer to a above
friction force / normal force = 120/250
a) The values of μ, often referred to as the coefficient of friction, do not have units because they are a ratio of two forces. The coefficient of friction is defined as the ratio of the force of friction between two surfaces to the normal force between them. Since both the force of friction and the normal force have units of Newtons (N), the units cancel out when you calculate the coefficient of friction. Therefore, the coefficient of friction is a unitless quantity.
b) To calculate the coefficient of kinetic friction (μ), we need to use the equation:
μ = (force of friction) / (normal force)
In this case, the force of gravity acting on the box (250 N) is equal to the normal force between the box and the road. This is because the box is on a level road, so the normal force is equal to the weight of the box.
So, the normal force (N) = 250 N.
Now, we know that the force of friction (F) is equal to the force needed to push the box at a steady speed (120 N).
Using the equation for the coefficient of kinetic friction:
μ = F / N
= 120 N / 250 N
Dividing these two values:
μ ≈ 0.48
Therefore, the coefficient of kinetic friction between the box and the road is approximately 0.48.