Question

An object whose momentum is 200 kg-m/s has a kinetic energy of 1000J. What is its mass?

Answer 1

An object whose momentum is $200\,\mathrm{kg}\cdot \mathrm{m/s}$ has a kinetic energy of 1000J. What is its mass?

Solution

A kinetic energy of the object is defined by

$$K = \frac{m v^2}{2}.$$

where $m$ – mass of the object and $v$ – its velocity.

A momentum of the object is defined by

$$P = m v.$$

We have a set of equations

$$\left\{ \begin{array}{l} K = \frac{m v^2}{2} \\ P = m v \end{array} \right. \rightarrow \left\{ \begin{array}{l} K = \frac{m v^2}{2} \\ v = \frac{P}{m} \end{array} \right. \rightarrow K = \frac{m}{2} \left(\frac{P}{m}\right)^2 = \frac{P^2}{2m},$$ $$m = \frac{P^2}{2K} = \frac{200^2}{2 \cdot 1000} = 20\,\mathrm{kg}.$$

Answer: $20\,\mathrm{kg}$