A 41kg box is being pushed a distance of 7.0m across the floor by a force P whose magnitude is 158N. The force P is parallel to the displacement of the box. The coefficient of Kinetic friction is 0.25. Determine the work done on the box by each of the four forces that act on the box. The applied force, fictional force, normal force and gravity .Be sure to include the proper plus or minus sign for the work done by each force.


Work done = distance*forceP

Four forces: P, friction, gravity, normal force from floor upward.
On the normal force...notice the displacement in that direction is zero.

To determine the work done on the box by each of the four forces (applied force P, friction, gravity, and normal force), we need to calculate the work done using the formula:

Work = Force * Distance * cos(theta)

Here, theta is the angle between the direction of force and the direction of displacement. Since the force P is parallel to the displacement, the angle theta is 0 degrees, and cos(0) = 1.

1. Work done by the applied force P:
The magnitude of force P is given as 158 N, and the distance moved by the box is 7.0 m. Therefore, the work done by force P is:

Work P = P * Distance * cos(0)
= 158 N * 7.0 m * 1
= 1,106 N·m or 1,106 J (Joules)

The work done by the applied force P is positive because the force and displacement are in the same direction.

2. Work done by friction:
The work done by friction can be calculated using the formula:

Work Friction = Frictional Force * Distance * cos(theta)

The frictional force can be determined using the formula:

Frictional Force = coefficient of kinetic friction * Normal Force

Given that the coefficient of kinetic friction is 0.25, we need to find the normal force acting on the box. The normal force is equal in magnitude and opposite in direction to the force of gravity.

3. Work done by gravity:
The work done by gravity can be calculated using the formula:

Work Gravity = Weight * Distance * cos(theta)

The weight is equal to the force of gravity acting on the box, which can be calculated using the formula:

Weight = mass * acceleration due to gravity

Given that the mass of the box is 41 kg, and the acceleration due to gravity is approximately 9.8 m/s², the weight can be determined as:

Weight = 41 kg * 9.8 m/s²
= 401.8 N

Now, we can calculate the work done by gravity:

Work Gravity = Weight * Distance * cos(180°)
= (-401.8 N) * 7.0 m * cos(180°)
= -2,812.6 N·m or -2,812.6 J

The work done by gravity is negative because the force of gravity and the displacement are in opposite directions.

4. Work done by the normal force:
The normal force does no work since the displacement in that direction is zero. Therefore, the work done by the normal force is zero.

In summary, the work done on the box by each force is as follows:

- Work done by the applied force P: +1,106 J
- Work done by friction: -1,106 J
- Work done by gravity: -2,812.6 J
- Work done by the normal force: 0 J