Question

A 4kg box sits on 3o degree incline. Calculate the normal force, the frictional force, andthe coefficient of friction needed to keep the box from slidding.

Answer 1

Normal = 33.95N

Friction = 19.6 N

Coefficient of friction = 0.58

Step-by-step explanation:

We can represent the situation as follows:

First, we need to calculate the normal force. Since the box is not moving perpendicular to the incline, the normal force and the weight in that direction has to be equal, then

Fn = mgcos30

Fn = (4kg)(9.8 m/s²)cos30

Fn = 33.95 N

In the same way, the box won't slide when the force of friction is equal to the parallel component of the weight, so

Ff = mgsin30

Ff = (4kg)(9.8 m/s²)sin(30)

Ff = 19.6 N

Additionally, the friction force is equal to

Ff = μFn

Where μ is the coefficient of friction, so solving for μ and replacing the values, we get:

μ = Ff/Fn

μ = 19.6/33.95

μ = 0.58

Therefore, the answers are:

Normal = 33.95N

Friction = 19.6 N

Coefficient of friction = 0.58