Question #e8598

2 Answers
Oct 1, 2017

41.4%

Explanation:

The relation between kinetic energy K and momentum p of an object is
p=2mK
where m is the mass of object

First let momentum is p1=p=2mK
and Kinetic Energy K1=K

Now Kinetic Energy of Body is increased by 100%.
Increase in Kinetic energy =K×100100=K

Now the total Kinetic Energy is K2=K+K=2K
Now Momentum p2=2mK2
p2=2m(2K)=2(2mK)=22mK
But 2mK=p1
p2=2p1=2p

Increase in Momentum = p2p1=2pp=(21)p
=0.414p

Percent increase in momentum =0.414pp×100%=41.4%

Oct 2, 2017

A 100% increase means that the Kinetic Energy is doubled. The final Kinetic Energy (Kf) will be twice the initial Kinetic Energy (Ki).

Kf=2Ki

Assuming that the mass of the object is unchanged, we can determine the momentum (p) in each case:

Pi=2mKi
Pf=2mKf=2m2Ki

The ratio between the final and initial momentum will give us the fractional increase in momentum.
PfPi=2m2Ki2mKi=21.414

The final momentum will be equal to 1.414 times the initial momentum. In terms of the initial problem statement, this is an increase of about 41.4%.

Notice that if you doubled the mass of the object to increase the Kinetic Energy by a factor of two, the momentum would also double. One assumption you must make with this problem statement is that the mass of the object is unchanged as the kinetic energy is increased. And that's probably the way this question was intended.