Question

A student trying to calculate the coefficient of friction between a box and a surface. She measures that the 80kg box will slide if the student pushes with a force greater than 400n.

Answer 1

`\mu_s=0.51`

Step-by-step explanation:

Coefficient of friction

The static coefficient of friction is a measure of the force needed to start moving an object from rest along a rough surface.

It's calculated as:

`\displaystyle \mu_s=(F_r)/(N)`

Where Fr is the friction force and N is the normal force exerted by the surface over the object.

In the absence of any other vertical force, the normal is equal to the weight of the object:

`N = W = m.g`

The box has a mass of m=80 Kg, thus the normal force is:

`N = 80\ Kg * 9.8\ m/s^2`

N = 784 N

The student needs to push with a force of 400 N to make the box move. That is the force that barely outcomes the friction force. Thus:

`F_r=400\ N`

Calculating the coefficient:

`\displaystyle \mu_s=(400)/(784)`

`\mathbf{\mu_s=0.51}`