Question

1 p
20) The kinetic energy of a moving body of the linear momentum Pis
doubled then the final momentum of a body is
O 1) 2P
O 2)P/2
O 3) V2 P
O 4)P/V2​

Answer 1

Answer:

If the kinetic energy of a moving body is doubled, how does its linear momentum change?

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What a great question! For slow stuff, KE=(0.5)m(v^2), whereas momentum is mv.

So if you double the KE, you’ve doubled the m(v^2) [ the “0.5” is a constant].

Case1: Replace m with 2m — you’ve doubled the energy. Momentum is now 2mv. You have doubled the momentum, too.

Case2: You want v^2 to be doubled, so you multiply v by sqrt(2). The formula is yet (.05)m(v^2), but we’ve doubled the energy by increasing the speed. So the momentum is now (about) 1.414mv. (I’ve approximated the square root of 2 to be 1.414).

Therefore, you can see that doubling the energy does not restrict the increase in momentum to be one value. The momentum could be anywhere from 1.414 to 2 times the original momentum — depending on how the energy is changed! Was the mass doubled or was the speed increased by 1,414 (of course, there are cases between these two extremes; but those give the endpoints.)

Very good question. This leads to clear thinking.