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Why do we multiply Force TIMES distance? It's the multiplication that confuses me

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- Thread starter cs23
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Why do we multiply Force TIMES distance? It's the multiplication that confuses me

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Drakkith

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russ_watters

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Since the amount of energy imparted to an object increases when both force and distance increase, they get multiplied together.

Ok, so why not add the 2 instead?

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russ_watters

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Well for starters, you can't add quantities together that have different units....

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sophiecentaur

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Because the energy needed is proportional both to the force and two the distance. The X sign is appropriate for that sort of calculation - same as multiplying speed times time to get distance or multiplying cost per item times number of items to get the total cost.Ok, so why not add the 2 instead?

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Why do we multiply Force TIMES distance? It's the multiplication that confuses me

In 1D:

F·dx=ma·dx=mdv/dt·dx=mdv·dx/dt=mvdv⇒∫F·dx=½mv²+constant. Similarly for the `impulse`,

F·dt=ma·dt=mdv/dt·dt=mdv⇒∫F·dt=mv+constant.

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