You push your couch a distance of 3.8 m across the living room floor with a horizontal force of 180.0 N. The force of friction is 136.0 N. What is the work done by you, by the friction force, by gravity, and by the net force?
you 1
friction force 2
gravity 3
net force 4
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To find the work done by each force, we can use the formula:
Work = Force x Distance x cos(theta)
where:
- Work is measured in joules (J),
- Force is measured in newtons (N),
- Distance is measured in meters (m), and
- cos(theta) is the angle between the direction of the force and the direction of the displacement.
1. Work done by you:
The force you exert is horizontal, and since you are pushing the couch in the same direction, the angle between the force and the displacement is 0 degrees. Therefore, cos(theta) = 1. Plugging in the values into the formula:
Work = 180.0 N x 3.8 m x cos(0°) = 684 J
So, the work done by you is 684 joules.
2. Work done by the friction force:
The force of friction is acting in the opposite direction to the displacement. Therefore, the angle between the force and the displacement is 180 degrees. cos(180°) = -1. Plugging in the values:
Work = -136.0 N x 3.8 m x cos(180°) = -517.6 J
Note that the negative sign indicates that the work by friction is done against the displacement, resulting in energy loss. So, the work done by the friction force is -517.6 joules.
3. Work done by gravity:
Based on the given information, it seems that there is no vertical displacement, so the work done by gravity is zero. Gravity does not do any work in this case.
4. Work done by the net force:
The net force is the vector sum of all the forces acting on the couch. In this case, since we know the work done by you and the work done by friction, we can find the net force by subtracting the work done by friction from the work done by you:
Work (net) = Work (you) - Work (friction) = 684 J - (-517.6 J) = 1201.6 J
Therefore, the work done by the net force is 1201.6 joules.