Question

You are told 3 things...1. That there are two objects with equal masses. 2. Both objects are in motion. 3. One object has a greater kinetic energy than the other. How is this possible?

Answer 1

The situation described can be explained by the relationship between kinetic energy and velocity. Kinetic energy (\( KE \)) is given by the formula:

\[
KE = \frac{1}{2} mv^2
\]

where \( m \) is the mass and \( v \) is the velocity of the object.

Given that both objects have equal masses and are in motion, it is possible for one object to have greater kinetic energy than the other if they are moving at different velocities. Specifically, if one object is moving faster than the other, it will have a greater kinetic energy despite having the same mass.

For example, if we have two objects each with a mass of \( m \):

- Object A: mass \( m \), velocity \( v_1 \) (let's say \( v_1 = 2 \, \text{m/s} \))
- Object B: mass \( m \), velocity \( v_2 \) (let's say \( v_2 = 3 \, \text{m/s} \))

Calculating the kinetic energies:

\[
KE_A = \frac{1}{2} mv_1^2 = \frac{1}{2} m (2)^2 = 2m
\]

\[
KE_B = \frac{1}{2} mv_2^2 = \frac{1}{2} m (3)^2 = \frac{9}{2}m
\]

In this case, object B has greater kinetic energy than object A because it is moving at a higher velocity, even though both objects have the same mass. This demonstrates how an object can have greater kinetic energy than another with the same mass by having a higher velocity.