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Work and Energy

  1. Sep 13, 2012 #1
    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 :redface:

    Thanks in advance
  2. jcsd
  3. Sep 13, 2012 #2
    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.
  4. Sep 13, 2012 #3
    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!?
  5. Sep 13, 2012 #4
    ΔW=-ΔU by definition

    Why negative sign? As in post#2.
  6. Sep 13, 2012 #5
    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?
  7. Sep 13, 2012 #6
    Here an example from 3000 solved problem-Schaum's Series.

    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.

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