Kinetic energy of body is increased by 300 % momentum of body is increased by?

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Answer 1 · 2018-08-03T23:33:02

Momentum increased to double, an increase of 100%.

Assume the increase is because of increase in speed (instead of increase in mass -- a bit hard to imagine how that would happen).

If initial KE was #KE_i# and KE was increased by 300% it is now

#KE_i + 3*KE_i = 4*KE_i#.

The formula for KE is

#KE = 1/2*m*v^2#

Since we assume the only parameter that changed was the velocity, the final velocity is 4 X the initial velocity. Therefore the final velocity is

#v_f = sqrt(4*v_i^2) = 2*v_i#

Since momentum is m*v,

the original momentum was #m*v_i#.

Since the final velocity is #2*v_i#,

final momentum is #m*2*v_i#

Momentum increased to double, an increase of 100%.

I hope this helps,
Steve