Finding Static Friction

A box resting on a surface experiences a normal force of magnitude \(\text{30}\) \(\text{N}\) and the coefficient of static friction tween the surface and the box, \(\mu_s\), is \(\text{0.34}\). What is the maximum static frictional force?

Step 1: Maximum static friction

We know that the relationship between the maximum static friction, \(f_s^{max}\), the coefficient of static friction, \(\mu_s\) and the normal, \(N\), to be:\[f_s^{max} = \mu_sN\]

We have been given that \(\mu_s = \text{0.34}\) and \(N=\text{30}\text{ N}\). This is all of the information required to do the calculation.

Step 2: Calculate the result

\begin{align*} f_s^{max} &= \mu_sN \\ &= (\text{0,34})(\text{30}) \\ & = \text{10,2} \end{align*}

The maximum magnitude of static friction is \(\text{10.2}\) \(\text{N}\).

The forwards of your school's rugby team are trying to push their scrum machine. The normal force exerted on the scrum machine is \(\text{10 000}\) \(\text{N}\). The machine isn't moving at all. If the coefficient of static friction is \(\text{0.78}\) what is the minimum force they need to exert to get the scrum machine to start moving?

Step 1: Minimum or maximum

The question asks what the minimum force required to get the scrum machine moving will be. We don't know a relationship for this but we do know how to calculate the maximum force of static friction. The forwards need to exert a force greater than this so the minimum amount they can exert is in fact equal to the maximum force of static friction.

Step 2: Maximum static friction

We know that the relationship between the maximum static friction, \(f_s^{max}\), the coefficient of static friction, \(\mu_s\) and the normal, \(N\), to be:\[f_s^{max} = \mu_sN\]

We have been given that \(\mu_s = \text{0.78}\) and \(N=\text{10 000}\text{ N}\). This is all of the information required to do the calculation.

Step 3: Calculate the result

\begin{align*} f_s^{max} &= \mu_sN \\ &= (\text{0,78})(\text{10 000}) \\ & = \text{7 800}\text{ N} \end{align*}

The maximum magnitude of static friction is \(\text{7 800}\) \(\text{N}\).