# Work and Energy

For some reason I am getting stuck with problems that seem to be very simple.

I get quite confused with the matter that, when fields do negative work, an object gains energy.

So, for example. When we raise a book to a shelf, we are doing positive work equal to mgh and gravity is doing negative work equal to -mgh. Yet, the book gains potential energy. How?

Similarly, when we move a positive charge towards a negative plate through a distance s, we perform work equal to qEs, the field does -qEs and the charge gains potential energy. How?

Sorry if I am failing to spot anything really simple! I might have had a bit too much of studying today Related Introductory Physics Homework Help News on Phys.org
Potential energy represents stored work. If a conservative
force does positive work (as does gravity on a falling object), then potential energy must
decrease—and that means ΔU must be negative.

Hi. Thanks for your answer! The only thing that still bothers me is the negative work. How can there be a gain in potential energy if there is positive and negative work of equal magnitudes acting on a object!?

ΔW=-ΔU by definition

Why negative sign? As in post#2.

But then doesn't that imply the gain in PE is a result of the external force doing work and the negative work done by the field?

Here an example from 3000 solved problem-Schaum's Series.

7.40
How much work is done in moving a body of mass 1.0kg from an elevation of 2 m. to an elevation of 20m,
a) by the gravitional field of the earth?
b) by the external agent lifting the body?

a) W=-ΔU=-176.4J
The work is negative because the force oppose the motion.

b)W'=ΔK+ΔU
If the body is unaccelerated(ΔK=0), then W'=176.4J, the negative of the gravitational work.