Question

Question #a9dae

Answer 1

This will cause a `0.05%` increase in momentum.

Explanation:

The kinetic energy of a body is given by:

`K.E. = 1/2 mv^2`

while the momentum is

`p=mv`

Both of these quantities is dependent on the mass ,`m`, of the object and the velocity `v`. We can safely assume that the mass of the body is not changing and therefore the change in the kinetic energy is due to the velocity changing. We can break the problem down to two timeframes, 1) before the change and 2) after then change - where the energy is `0.1%` more than when we start.

We know the relationship of kinetic energies before and after:

`K.E._2 = 1.001*K.E._1`

`=> 1/2 mv_2^2 = 1.001 1/2 mv_1^2`

then we can divide through by the mass to get rid of it in the relationship:

`=> 1/2 v_2^2 = 1.001 1/2 v_1^2`

What we are looking for is the same type of relationship for the momenta:

`p_2 = x*p_1`

`=> mv_2 = x*mv_1`

`=> v_2 = x*v_1`

where we have been asked to find the increase in momentum, `x`.

Let's go back to the equation for K.E. and solve for `v_2`:

`v_2 = sqrt(1.001) v_1`

Then we can use this in the equation we got from the momentum

`sqrt(1.001) v_1 = x*v_1`

So our factor of increase in momentum, `x` is

`x=sqrt(1.001) ~= 1.0005`

Which represents a `0.05%` increase in momentum.