# Nature of Work done by Forces

I am confused about the possible nature of work that a conservative and non conservative force can do.

1. Do Non conservative forces like friction only do negative or zero work and not positive?
2. Can conservative force also do negative work, I know Gravitational Force is conservative force and it can do negative work, but I read somewhere that net work done by conservative forces is positive. Can someone please clarify?

## 2 Answers

Work done $W$ is the dot product of a force $\vec F$ and the displacement of the force $\vec s$.

$W=\vec F \cdot \vec s$

The work done is positive if the force and the displacement are in the same direction and negative if they are in opposite directions.

You watch a lorry accelerating.
A box on the back of a lorry also accelerates and the kinetic energy of the box increases.
The only horizontal force on the box is friction and so it is the frictional force which is doing positive work on the box.

Ignoring air resistance, if you throw the box vertically upwards, the gravitational force on the box is downwards so the work done on the box by the gravitational force is negative and the kinetic energy of the box decreases.

Wait a little until the box starts falling and the the work done by the gravitational is then positive as the kinetic energy of the box is increasing.

When the box arrives at the place it started from just after it left your hand, the net work done by the gravitational force is zero and it has the same kinetic energy as at the start.

• Is the net work done by conservative forces always greater than or equal to 0? – drake01 Mar 17 '18 at 10:57
• @drake01 If you lift a box you can think of the gravitational force on the box doing negative work. – Farcher Mar 17 '18 at 11:55

Yes force of friction can do positive work Work done by conservative forces may be positive.negative or zero

• How can friction do positive work if it's always opposing the direction of motion? – mathematician Aug 29 '17 at 4:36
• No friction opposes relative motion. It may be in the direction of motion as on a body pllaced on a moving car .friction acting on your shoes while rou walk – Rajendra Pd Aug 29 '17 at 4:56
• Yes, as an example a block placed upon another block moves when a Force is applied on the lower due to force of friction, here work is positive. – drake01 Aug 29 '17 at 9:37
• When you're walking and your foot is in contact with the ground it is not moving. No work is being done on your foot. "when a Force is applied on the lower due to force of friction" Which block is moving? If the block isn't changing position no work is done on it. See physics.stackexchange.com/questions/206229/… – mathematician Aug 30 '17 at 19:18