Theoretical Question: Is W = PE?

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SUMMARY

The discussion centers on the relationship between work (W) and potential energy (PE) in physics. It establishes that while both W and PE can be expressed in terms of mass (m), acceleration (a), and distance (d), they are not equivalent under all conditions. Specifically, W is defined as W = Fd = mad, while PE is defined as PE = mgh. The conclusion drawn is that work can lead to changes in kinetic energy (KE) and potential energy, but W does not equal PE unless specific conditions are met, such as the force being perpendicular to the gravitational force.

PREREQUISITES
  • Understanding of basic physics concepts such as work, potential energy, and kinetic energy.
  • Familiarity with the equations W = Fd and PE = mgh.
  • Knowledge of vector components and angles in physics.
  • Basic grasp of units of measurement in physics, particularly energy and work.
NEXT STEPS
  • Study the relationship between work and kinetic energy using the work-energy theorem.
  • Explore the concept of torque and its relation to energy and work.
  • Investigate the conditions under which work done equals potential energy.
  • Learn about vector analysis in physics, particularly how angles affect work calculations.
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Students of physics, educators teaching mechanics, and anyone interested in understanding the principles of work and energy in physical systems.

Goldenwind
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This isn't a homework question, just something I was pondering one day.

W = Fd = mad
PE = mgh

m = m, obviously
g and a are both measurements of acceleration
h and d are both measurements of distance

If g = a, and h = d, is it fair to say that W = PE?

Therefore, W = a change in KE, so PE = Change in KE?
 
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Goldenwind said:
This isn't a homework question, just something I was pondering one day.

W = Fd = mad
PE = mgh

m = m, obviously
g and a are both measurements of acceleration
h and d are both measurements of distance

If g = a, and h = d, is it fair to say that W = PE?

Therefore, W = a change in KE, so PE = Change in KE?
Not quite. The work done on an object can result in a change in kinetic and/or potential energy. In order for W to be equal to KE, the accelerating force would have to be at right angles to the direction of the gravitational force.

The correct equations are:

PE = mgh
[tex]W = \vec F \cdot\vec d = m\vec a \cdot\vec d = mad\cos\theta[/tex]

ie. h would be 0 and [itex]\cos\theta[/itex] would be 1.

AM
 
Goldenwind said:
This isn't a homework question, just something I was pondering one day.

W = Fd = mad
PE = mgh

m = m, obviously
g and a are both measurements of acceleration
h and d are both measurements of distance

If g = a, and h = d, is it fair to say that W = PE?

Therefore, W = a change in KE, so PE = Change in KE?

All you can really show by this argument is that work and energy have the same units; this does not let us conclude anything at a deeper conceptual level by itself. You'll run into a more extreme case of this when you study torque: you'll learn that torque and energy have the same units but are not much related at all.
 

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