Physics

To find the tension in the rope, follow these steps:

1. Calculate the weight of the crate:

 

2. Calculate the normal force :

Let be the tension in the rope, which has a vertical component that affects the normal force. The vertical component of the tension can be calculated as follows:

 

The normal force can be expressed as:

 

3. Calculate the frictional force :

The frictional force is given by:

 

Substituting the expression for :

 

4. Write the equation of motion:

According to Newton's second law:

 

The net force in the horizontal direction is the horizontal component of the tension minus the frictional force: