An object of mass m1 has a kinetic energy K1 . Another object of mass m2 has a kinetic energy K2 . If the momentum of both objects is the same, what is the ratio of K1/K2?

A. m2/m1
B. m1/m2
The answer is A, but why is it not B?

1 Answer
Dec 12, 2017

I got #(v1)/(v2)# i.e. the ratio of the two velocities...

Explanation:

The momentum is the same so:
#p1=m1v1#
#p2=m2v2#
#m1v1=m2v2#
we know that:
#K1=1/2m1v1^2#
and
#K2=1/2m2v2^2#

Ratio:

#(K1)/(K2)=(cancel(1/2)m1v1^2)/(cancel(1/2)m2v2^2)=(m1v1v1)/(m2v2v2)=(cancel(p1)v1)/(cancel(p2)v2)=(v1)/(v2)#