Physics

To solve for the final velocity of the box when it reaches the bottom of the incline, we will use the work-energy principle. The total work done on the box is the sum of the work done by gravity and the work done by friction.

 

Forces acting on the box

1. Gravitational force component along the incline:

This is the force that causes the box to move down the incline.

 

2. Frictional force:

The normal force is:

The frictional force is:

This is the resistive force that opposes the motion.

 

Work done on the box

1. Work done by gravity:

The displacement along the incline is . The work done by the gravitational force is:

 

2. Work done by friction:

The work done by the frictional force is:

Since friction opposes the motion, this work is negative:

 

Net work done

The net work done on the box is the sum of the work done by gravity and the work done by friction:

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