Question #2d4b3

1 Answer
Jul 1, 2017

The kinetic energy will be halved.

Explanation:

Kinetic energy is given by:

E_k=1/2*m*v^2

It is proportional to the object's mass:

Epropm

If we double the mass, we double the energy:

E_1=1/2*1*v^2=1/2v^2

E_2=1/2*2*v^2=1v^2=color(blue)(2E_1)

Kinetic energy is also proportional to the square of the velocity:

Epropv^2

This means that if we halve the velocity, we quarter the energy:

E_1=1/2*m*1^2=1/2*m

E_2=1/2*m*(1/2)^2=1/2*m*(1/4)=1/8*m=color(blue)(1/4*E_1)

If we combine a doubled mass and halved velocity, our initial energy will be doubled and then quartered. This results in an overall halving of the energy:

E_2=E_1*2*1/4=1/2E_1