# What work is more, - 2J or - 5J?

I was studying a concept different from newtonian mechanics, but there was a concept which confused me. if work done by constant frictional force is considered in an experiment there are two values of it, one is -2J and another is - 5J, which one will be more? I think following integer rules is not correct here as - sign just shows that force is not in direction of displacement.

• Really confused by the downvotes here. I think it is valid to be confused by the use of a negative sign as an indication of "direction" rather than negative meaning "less" than positive May 24 at 3:55

Negative work is just positive work with the energy repositories switched. "A does 5J on B", "B does -5J on A", and "5J of system energy was moved from A to B" are all the same statement.

Friction is a force by means of which energy is transferred from a system's kinetic energy (excluding thermal internal energy) to the system's total thermal internal energy. "Forces doing work" is misleading shorthand for one mathematical object that holds energy doing work on another mathematical object that holds energy by means of a force.

When your introductory text tells you that friction (with something attached to the ground or very massive) does -5 Joules work on Alice, you should mentally replace it with "5 Joules is transferred from the kinetic energy associated with Alice's movement to the system's total thermal internal energy by means of the force of friction."

Similarly for another common misleading phrasing: "the force of gravity does -5J work on Alice" should be "5 Joules is transferred from the kinetic energy associated with Alice's movement to the potential energy associated with the configuration of the system's masses (aka the gravitational field) by means of the force of gravity."

• Thank you sir, I learnt many things new from your answer but I cannot understand which have done more work, one which caused 2J of energy to go into system's thermal energy or one that caused 10J of energy to go into system's thermal energy? May 23 at 20:23
• @rohan $-10 \lt -2$ no matter what you're counting, but the sign is a consequence of an arbitrary choice of direction and therefore so is the less-ness or more-ness. Just like "A does 5J on B" and "B does -5J on A" are the same statement, if $W_{AB_i}$ is an instance of work done by A on B and $W_{BA_i}$ is an instance of work done by B on A, $W_{AB_1} \lt W_{AB_2}$ and $W_{BA_1} \gt W_{BA_2}$ are the same statement. I much prefer to just state what actually happened than to worry about the words to use to describe an arbitrary choice of direction.
– g s
May 23 at 23:13

Negative work simply means the direction of the force on an object is away from the direction of the displacement of the object, i.e. the angle between the force and displacement vector is between 90 and 270 degrees. (In the case of negative work done by kinetic friction, it is 180 degrees.)

When a force does negative work on an object it takes energy away from the object. Kinetic friction is such a force. It takes kinetic energy from an object and dissipates it as heat at the sliding surfaces. The greater the negative friction work, the greater the energy taken from the object. Thus, -5J of kinetic friction work takes more kinetic energy away from an object than -2J of kinetic friction work.

Hope this helps.