$$ W = Fd\cos\theta $$
where:
- \(W\) is the work done (in joules, J)
- \(F\) is the force applied (in newtons, N)
- \(d\) is the displacement of the object (in meters, m)
- \(\theta\) is the angle between the force and the displacement
If the angle \(\theta\) between the force and the displacement is 0 degrees (i.e., the force is applied in the same direction as the displacement), then the work done is positive. If \(\theta\) is 180 degrees (i.e., the force is applied in the opposite direction of the displacement), the work done is negative.
Here's a simplified explanation:
- If you push an object and it moves in the direction you're pushing, you're doing positive work.
- If you push an object and it moves in the opposite direction you're pushing, you're doing negative work.
- If you push an object and it doesn't move, you're not doing any work.
Work is a scalar quantity, which means it has only magnitude (how much work is done) but no direction. It's important in physics because it allows you to calculate the energy transferred to or from an object when a force is applied.
