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?

one object is blue and one object is red.
one object has a greater volume than the other object.
one object has a greater density then the other object.
one object has a greater speed than the other object.

Answer 1

In this scenario, the key factor that allows one object to have greater kinetic energy than the other, despite both having equal masses, is their speeds.

The formula for kinetic energy (KE) is given by:

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

where \( m \) is the mass of an object and \( v \) is its speed.

Since both objects have equal mass, the kinetic energy of each object will vary with the square of its speed. Therefore, if one object (let's say the blue one) has a greater speed than the other object (the red one), it will indeed have a greater kinetic energy.

For example, if the blue object is moving at 4 m/s and the red object is moving at 2 m/s, their kinetic energies would be:

- Blue object: \( \text{KE} = \frac{1}{2} m (4^2) = 8m \)
- Red object: \( \text{KE} = \frac{1}{2} m (2^2) = 2m \)

In this case, the blue object has a greater kinetic energy than the red one, demonstrating how speed can lead to different kinetic energy values even for objects of equal mass.

So, the correct statement among the given options is: **one object has a greater speed than the other object.**