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### AuthorTopic: Work and Energy  (Read 1063 times) Tweet Share

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#### /0

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##### Work and Energy
« on: February 22, 2009, 07:19:51 pm »
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Work and Energy just shits me. I created another topic because I think this topic warrants one.

$W = \vec{F} \cdot \vec{d}$

Let up be positive.

If an object falls from a height of 10m, gravity does $W=(10)(10)\cos{0^{\circ}} = 100J$ of work to the object. That means the object gains 100J of energy, right? But as a consequence, doesn't this mean that at a height of 10m, it doesn't actually have any energy?

Also, imagine lifting a book from the floor to a table 1m high at a constant rate. Gravity does $W = (10)(1)\cos{180^{\circ}} = -10 J$. Your hand does work against gravity equal to $W = (10)(1)\cos{0^{\circ}} = 10J$. But doesn't this mean that $\sum W = 0$? But how can this be, seeing as the book now has gained 'gravitational potential energy'?

And finally, in one of the questions, someone is towed up a slide with frictional force 300N. The total work done to bring them to the top of the slide is 22720J. The change in their GPE is 13720J. Does this mean that the object has an extra 9000J of energy if it was pushed up to the top instead of being lifted to the top? How can this be, if its start and end positions are the same?

#### mark_alec

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##### Re: Work and Energy
« Reply #1 on: February 22, 2009, 11:18:04 pm »
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1) At the top, the object has 100J gravitational potential energy. At the bottom, this has been converted to 100J kinetic energy.

2) By raising it a height, it gains gravitational potential energy. Your hand does this, by converting chemical potential energy (in food) to kinetic energy (muscles moving) to the gravitational potential energy.

3) No, more work is done because 9000J was lost due to friction. The GPE of the person is the same, regardless of the path they take.

#### Mao

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##### Re: Work and Energy
« Reply #2 on: February 22, 2009, 11:50:22 pm »
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Work is energy transfer from one object to another. When an object falls, Earth transfers some of the gravitational potential energy to the object as kinetic energy, hence doing work. When saying this, work is the change between the initial energy and final energy, an object doesn't necessarily have 'no energy' at one point, it all depends on what reference you use [as calculations are usually done relative to a zero point].
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#### /0

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##### Re: Work and Energy
« Reply #3 on: February 22, 2009, 11:52:37 pm »
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In response to mark_alec

For 2), why is it that if Net Work = 0, you can still transform energy from kinetic to G.P.E? Isn't it true that Work = Energy transformed?
And anyway, how do we come to the notion that Work = Energy transformed? Isn't the sole definition of Work: $Fd$? Or is Work = Energy transformed directly derived from this?

And in response to Mao,

So if my hand pushes with a constant force along a straight line to infinity, and I place an object in the way (a few meters from my incoming hand), are you saying you can define that object as having potential energy, even though it is, for the moment, perfectly still?

« Last Edit: February 23, 2009, 12:00:41 am by /0 »

#### Mao

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##### Re: Work and Energy
« Reply #4 on: February 23, 2009, 12:03:19 am »
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the object is made of matter, which may have chemical potential energy, gravitational potential energy, nuclear potential energy.... etc
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#### mark_alec

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##### Re: Work and Energy
« Reply #5 on: February 23, 2009, 12:43:32 am »
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For 2), why is it that if Net Work = 0, you can still transform energy from kinetic to G.P.E? Isn't it true that Work = Energy transformed?
And anyway, how do we come to the notion that Work = Energy transformed? Isn't the sole definition of Work: $Fd$? Or is Work = Energy transformed directly derived from this?
Net Work != 0. The net energy change of the system (being the object, you and the earth) is zero.

The real definition of work is $|W| = \int F.ds$