Question #2f990

Jul 22, 2016

Kinetic energy increases by 21%

Explanation:

$\vec{p} = m \vec{v}$

Assuming this increase occurs in the same direction we will just work with magnitudes. I've also assumed this is classical mechanics and that the mass remains constant.

$p = m v$

The object starts with ${p}_{1} = m {v}_{1}$ and ends with ${p}_{2} = m {v}_{2} = 1.1 {p}_{1}$.

$\frac{{p}_{2}}{{p}_{1}} = \frac{\cancel{m} {v}_{2}}{\cancel{m} {v}_{1}} = \frac{{v}_{2}}{{v}_{1}}$

$\therefore {v}_{2} = {v}_{1} \frac{{p}_{2}}{{p}_{1}} = 1.1 {v}_{1}$

Kinetic energy given by

$K E = \frac{1}{2} m {v}^{2}$

$\frac{K {E}_{2}}{K {E}_{1}} = \frac{\cancel{\frac{1}{2} m} {\left({v}_{2}\right)}^{2}}{\cancel{\frac{1}{2} m} {\left({v}_{1}\right)}^{2}}$

$K {E}_{2} = {\left(1.1 {v}_{1}\right)}^{2} / {\left({v}_{1}\right)}^{2} K {E}_{1}$

$K {E}_{2} = 1.21 K {E}_{1}$