Question

If two objects have equal kinetic energies, do they necessarily have the same momentum? Defend your answer.

Answer 1

No, they do not necessarily have the same momentum.

Step-by-step explanation:

Lets take two objects with mass m1 and m2 ,their respective velocities as v1 and v2, and kinetic energies as K1 and K2.

Let momentum be g1 and g2.

g1=m1v1 g2=m2v2

When kinetic energies are equal

`K1=K2\\(1)/(2) m1v1^(2)=(1)/(2) m2v2^(2) \\\\m1v1^(2)=m2v2^(2) \\g1v1=g2v2`

when v1=v2 ; g1=g2 ; two objects can have the same momentum

but if v1≠ v2 ; g1≠g2 ; Therefore objects do not necessarily have the same momentum.