Work & Energy: Understanding Negative Work & Potential Energy Gain

[Peter G.]

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

Thanks in advance

 

[azizlwl]

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.

 

[Peter G.]

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!?

 

[azizlwl]

ΔW=-ΔU by definition

Why negative sign? As in post#2.

 

[Peter G.]

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?

 

[azizlwl]

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 gravitational 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.