Question

If a 10 kg crate and a 5 kg crate have the same momentum of 50 kgm/s, which one has greater kinetic energy? Explain how you came to your answer

Answer 1

To answer this question, we need to find the speed of the crates:

$$v=\frac pM=50/10=5\text{ m/s},\\\space\\ u=\frac pm=50/5=10\text{ m/s}.$$

The kinetic energy is given by a half of product of mass and velocity squared. For the two crates:

$$K_1=\frac12 Mv^2=\frac12 10·5^2=125\text{ J},\\\space\\ K_2=\frac12 mu^2=\frac12 5·10^2=250\text{ J}.$$