Can Work Done Be Negative and Is Potential Energy Ever Negative?

[vivekfan]

Homework Statement

Is work done by something always negative and work done on something always positive, or do you determine that by the cos theta portion of the work equation. Also, can potential energy be negative

Homework Equations

W=Fdcos theta
PE=mgd

The Attempt at a Solution

I've been generalizing, and sometimes it makes me come out with the wrong sign, so that's why I need clarification.

 

[dancingfish]

I've learned that a negative or a positve merely show direction, and as long as you're consistent throughout the problem, the magnitude of the answer is what matters. For example, the acceleration of gravity is commonly known as -9.8m/s2. However, if you want down to be positive it can be as long as you make up negative. I hope that made sense.

 

[Doc Al]

Is work done by something always negative and work done on something always positive, or do you determine that by the cos theta portion of the work equation.

The work done by a force on an object can be positive or negative depending upon the direction of the force with respect to the displacement. If the force and displacement are in the same direction (more generally, if the cosine of the angle between them is positive), then the work done is positive; if they are in opposite directions (if the cosine is negative), the work done is negative.

Also, can potential energy be negative

Sure.