A light body A and heavy body b have equal momentum then kinetic energy is equal to b or less than b or greater than b or zer0

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Physics

Haiden Mercado

3 April, 04:34

A light body A and heavy body b have equal momentum then kinetic energy is equal to b or less than b or greater than b or zer0

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Micah Richard · Answer 1

Momentum is P=mv

Let momentum of a be Pa and momentum of b be Pb. Since they are equal we let

Pa=Pb

And we can see that since a is less massive, its velocity is larger than b's.

That is va > vb.

Kinetic energy is E = (1/2) mv^2

Note that using the formula for momentum we can also say kinetic energy is E = (P/2) v

So kinetic energy of a is

Ea = (Pa/2) va

And kinetic energy of b is

Eb = (Pb/2) vb

But we know Pa=Pb so we can substitute this into one of the kinetic energy relations to get

Eb = (Pa/2) vb.

Now putting the two side by side (NOT setting them equal, just comparing them) we get

Ea = (Pa/2) va Eb = (Pa/2) vb

The first part of each equation is the same: Pa/2. The only difference between them is Ea is multiplied va and Eb is multiplied by vb. And because we know va > vb we can conclude that the kinetic energy of a is larger.