Can a unit of work be negative?

Answer 1

Yes. Work is the scalar product of vectors, force f and displacement r. Negative work is called exergy and positive work is called energy. Exergy means work is emmitted and energy means work is absorbed.

There are aspects of this question that will clarify physics and scientific education. Negative work is the result of a displacement vector in the direction of the force vector. w= f.r = - fvcos(x). An example of this is the dropping of a ball. The displacement is down, along the radius of the earth, -r and the force is down along the radius of the earth, gravity -f. this gives a negative work, which we call exergy, meaning energy out, w=-f.-r= - frcos(x).

Lifting the ball gives w= -f.r= frcos(x) an example of positive work, energy in.

The vectors f and r are vectors, mathematically complex numbers, and their squares are negative. Physics in use today uses J. Willard Gibbs vectors where the square of a vector is mathematically positive. This concept of vector is mathematically and physically wrong. This error permeates all of physics with errors. Minkowski's and Einstein's spacetime reflects this error in their "Interval" = x^2 + y^2 + z^2 + (ict)^2.

The Universe is quaternionic and consists of a real and three vectors p=ct + ix + jy + kz,

where i,j and k are vector units i^2=j^2=k^2= ijk= -1. This formulation preserves "associativity" and the property of groups for vector multiplication. The current Gibbs formulation of vectors in physics is mathematically and physically defective. Good physics depends on good mathematics, Quaternion vector!

Answer 2

No, a unit of work cannot be negative. Work is defined as the product of force and displacement in the direction of the force applied, and both force and displacement are scalar quantities. Therefore, work is always a positive value.

Answer 3

Yes - work can be done BY a system or ON a system. Depending on whether the work is going into the system or out of it the sign on the work can be negative or positive.