Question

What happens to kinetic energy when momentum is doubled?

Answer 1

Step 1: Given:

Initial momentum = m

final momentum = 2m

Step 2: Formula

The kinetic energy is given by the equation $E=\frac{p^2}{2m}$
where $m$ is the mass and $p$ is the momentum.

Step 3: Calculation

1. The momentum is directly proportional to the velocity of the body.
2. The momentum of the body can be written as:$P=mv$ where $m$ is the mass and $v$ is the velocity of the body.
3. According to the question, when momentum is doubled

$$\begin{gathered} E=\frac{p^2}{2m} \\ E\text{'}=\frac{{\left(2p\right)}^2}{2m}E\text{'}isnewKEaftermomentumisdouble \\ E\text{'}=\frac{4p^2}{2m} \\ E\text{'}=4E \end{gathered}$$

Hence, If the momentum is doubled the kinetic energy is increased by 4 times.