Energy vs Momentum: Physics Examining the Difference

[aloshi]

Energy? or momentum?

a dorm ant crawled on 1kg affected by krfaften 10N, so it may be an acceleration of
10m / s ^ 2, then the following 1s have speeds 10m / s, and a movement of 5 m has taken place. continuing the body that are affected by the same power in 1 s to, it will then have the speed 20m / s and a total of a movement of 20 m, 15 m further. According to the work as it is defined as force * distance, has been eating more energy during the second second. but power over the other secondary was the same as in the first second. How can they actually require more energy to maintain the same effect during the second second??

why physics has chosen to define the work force multiplied by distance and not as a force multiplied by time (that is to say, momentum)?

 

[tiny-tim]

a dorm ant crawled on 1kg affected by krfaften 10N, so it may be an acceleration of
10m / s ^ 2, then the following 1s have speeds 10m / s, and a movement of 5 m has taken place. continuing the body that are affected by the same power in 1 s to, it will then have the speed 20m / s and a total of a movement of 20 m, 15 m further. According to the work as it is defined as force * distance, has been eating more energy during the second second. but power over the other secondary was the same as in the first second. How can they actually require more energy to maintain the same effect during the second second??

why physics has chosen to define the work force multiplied by distance and not as a force multiplied by time (that is to say, momentum)?

Hi aloshi!

Because work done = ∫F ds = ∫m dv/dt ds = (chain rule ) ∫m dv/ds ds/dt ds
= ∫mv dv/ds ds = ∫mv dv = 1/2 mv² + constant = kinetic energy + constant.

(and ∫F dt = ∫m dv/dt dt = ∫m dv = momentum + constant)

So the ant's speed (and momentum) is proportional to time, but its energy is proportional to distance.