Problem — From kinetic energy to speed

From $E_k$ to speed. A $0{,}5\;\mathrm{kg}$ ball has kinetic energy $E_k = 100\;\mathrm{J}$. Calculate its speed.

Solution

Data: $m = 0{,}5\;\mathrm{kg}$, $E_k = 100\;\mathrm{J}$.

Invert the definition of kinetic energy $E_k = \tfrac{1}{2}mv^2$ to obtain $v$:

$v = \sqrt{\frac{2E_k}{m}} = \sqrt{\frac{2\cdot 100}{0{,}5}} = \sqrt{400} = 20\;\mathrm{m/s}$

$\ev{v = 20\;\mathrm{m/s}}$

Physical reading. The calculation is exact: $\sqrt{400} = 20$ with no approximation. Note the dependence $v \propto \sqrt{E_k}$: to double the speed you would need to quadruple the kinetic energy.

Collegamenti

Argomenti: Work and energy Concetti: Kinetic energy Competenze: Symbolic set-up