My Math Forum Kinetic and potential energy of an object

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 April 20th, 2015, 11:43 AM #1 Senior Member     Joined: Feb 2014 From: Louisiana Posts: 156 Thanks: 6 Math Focus: algebra and the calculus Kinetic and potential energy of an object I have a question about the conservation of energy. Imagine that there is an object on a level plane with zero kinetic energy and zero gravitational potential energy. Now imagine moving this object at some constant velocity in the y-direction for a few meters. Since it was moved at a constant velocity, there was no chance in kinetic energy, and thus no work was done. However, at the new height, there is non-zero potential energy mgh. If no work was done, how did the object go from having 0 kinetic energy and 0 potential energy to having 0 kinetic energy and mgh potential energy? Where am I going wrong?
April 20th, 2015, 12:14 PM   #2
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 Originally Posted by Mr Davis 97 I have a question about the conservation of energy. Imagine that there is an object on a level plane with zero kinetic energy and zero gravitational potential energy. Now imagine moving this object at some constant velocity in the y-direction for a few meters. Since it was moved at a constant velocity, there was no chance in kinetic energy, and thus no work was done. However, at the new height, there is non-zero potential energy mgh. If no work was done, how did the object go from having 0 kinetic energy and 0 potential energy to having 0 kinetic energy and mgh potential energy? Where am I going wrong?
There is an impulse that started the object moving and another that stopped it. They put energy into the system and hence do work on the object. However the more telling part of the motion is that it moved upward at a constant speed. A force needs to be on the object in order for that to happen (otherwise v will decrease) and thus work is being done.

-Dan

April 20th, 2015, 01:13 PM   #3
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 Originally Posted by topsquark There is an impulse that started the object moving and another that stopped it. They put energy into the system and hence do work on the object. However the more telling part of the motion is that it moved upward at a constant speed. A force needs to be on the object in order for that to happen (otherwise v will decrease) and thus work is being done. -Dan
I still don't understand. You do positive work, gravity does work that is equal and opposite to the work done by you, so the net work done on the body is zero. Therefore, if there was no net work, no change of energy, then why is there mgh Joules of potential energy at the end?

April 20th, 2015, 05:39 PM   #4
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 Originally Posted by Mr Davis 97 I still don't understand. You do positive work, gravity does work that is equal and opposite to the work done by you, so the net work done on the body is zero. Therefore, if there was no net work, no change of energy, then why is there mgh Joules of potential energy at the end?
The net work done on the object is indeed 0 J. Call the force applied to the object during its motion F and call the distance it has moved vertically h. Then
$\displaystyle W_{net} = \Delta KE$

$\displaystyle W_{grav} + W_F = \Delta KE$

$\displaystyle -mgh + W_F = 0$

$\displaystyle W_F = mgh = \Delta PE$

Thus work has been done on the object and increases the object's PE, as required.

-Dan

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