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# Work done watch

1. I am confused on this topic.

W = Fs

but does F represent frictional force or the resultant force ? I have seen differing statements

thx
2. The work done by each individual force is the force multiplied by the distance it acts over so the formula can work for individual forces or the resultant force I think, hope that helps

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3. (Original post by sabre2th1)
I am confused on this topic.

W = Fs

but does F represent frictional force or the resultant force ? I have seen differing statements

thx
I will try to clarify by example.

Suppose you are pushing a box of mass on a horizontal rough surface. There are four forces at work:
1. "Push", usually denoted by just ;
2. Friction, which I often write as (uncommon?);
3. Weight, written as ;
4. Surface normal reaction force, which I write as .

"Push" is a force applied by you. Given a distance over which you pushed the box, then gives you the work done by you, because you applied that force (assuming that the pushing is completely horizontal).

Friction is a force applied due to an interaction of the box and the rough surface. tells you how much energy is wasted in friction. This energy is not converted into kinetic energy: ie not used to move the box.

Weight is a "vertical" force. The object is moved horizontally; it moved a distance of 0 vertically. Work done by weigh is . Similarly, 0 for R.

In the case of this box, the resultant force is the force applied into moving the box. Applying the force formula on the resultant force gives you the "moving" energy inside the box: the increase in the kinetic energy of the box.

Note: whenever you use the equation , you define what is.
4. (Original post by sabre2th1)
I am confused on this topic.

W = Fs

but does F represent frictional force or the resultant force ? I have seen differing statements

thx
F represents the force (or forces) that work is being done against. These examples might help to clear it up:

1. If you lift a box of mass m by a height h, you do work against the gravitational force (the box's weight) and so W = F x s = mg x h.

2. If you push a box up a smooth inclined plane, you do work against the gravitational force and so W = F x s = mg x h (where h is the vertical height raised, not the distance moved along the plane).

3. If you push a box up a rough inclined plane, you do work against the gravitational force and against the frictional force. In this case, the total work done is the sum of the work done against each individual force:

work done against gravity, W1 = F x s = mg x h.
work done against friction, W2 = F x s, where F is the magnitude of the frictional force and s is the distance moved along the plane (since this is the distance you have travelled against the frictional force).
Total work done against resistive forces W = W1 + W2.

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Updated: January 6, 2013
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