A 200 kg wooden crate is dragged at a constant speed by a rope through a distance of 4 m along a wooden floor . The coefficient of sliding friction is .2 . If the work done is 1568 j , and the rope is horizontal, calculate the tension in the rope

To solve this problem, we need to use the work-energy theorem.

The work done on an object is equal to the change in its kinetic energy. In this case, the work done on the wooden crate is equal to the change in its kinetic energy:

Work = Change in Kinetic Energy

Since the crate is being dragged at a constant speed, its kinetic energy does not change. Therefore, the work done on the crate is zero.

Now let's calculate the work done on the crate using the formula:

Work = Force * Distance

The force we are interested in is the tension in the rope. The distance is given as 4 m. The work done is given as 1568 J.

1568 J = Tension * 4 m

To find the tension in the rope, we can rearrange the equation:

Tension = Work / Distance

Tension = 1568 J / 4 m = 392 N

Therefore, the tension in the rope is 392 Newtons.