Question

if momentum of the body is increased to 4 times. find the new kinetic energy.​

Answer 1

Explanation:

If we look at the definition of the momentum of an object and the definition of the momentum of the kinetic energy

p=mv

K=12mv2

Now the momentum as increased four times… but what has changed?

p′=4p

p′=4mv

Was it the mass or the velocity that was increased? In the case of mass increasing, we see the following

p′=(4m)v

K=12(4m)v2=4(12mv2)

BUT, if it was the velocity that increased, we see this occur

p′=m(4v)

K=12m(4v)2=16(12mv2)

In the first scenario, the kinetic energy increased four times whereas, in the second scenario, the kinetic energy increased SIXTEEN times! To take it even further, you should be able to play around with the values to have the kinetic energy increase by any number times between four and sixteen so…

K′=mK

where m∈[4,16]