Analyzing Kinetic Energy

Question

A yellow ball with a mass of 2 kg is rolling across the floor at 3 m/s. A red ball with a mass of 3 kg is rolling across the same floor at 3 m/s. Which ball has greater kinetic energy, and why?

The yellow ball has greater kinetic energy, because it is rolling at a higher position above the ground.
The red ball has greater kinetic energy, because it has a greater mass.
The yellow ball has greater kinetic energy, because it is rolling at a greater speed.
The red ball has greater kinetic energy, because it is releasing more thermal energy.

Answer 1

To determine which ball has greater kinetic energy, we can use the kinetic energy formula:

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

where \( KE \) is the kinetic energy, \( m \) is the mass of the object, and \( v \) is its velocity.

For the yellow ball:

• Mass \( m = 2 \) kg
• Velocity \( v = 3 \) m/s

Calculating the kinetic energy: \[ KE_{yellow} = \frac{1}{2} \cdot 2 \cdot (3^2) \] \[ KE_{yellow} = 1 \cdot 9 = 9 ) Joules

For the red ball:

• Mass \( m = 3 \) kg
• Velocity \( v = 3 \) m/s

Calculating the kinetic energy: [ KE_{red} = \frac{1}{2} \cdot 3 \cdot (3^2) \] [ KE_{red} = 1.5 \cdot 9 = 13.5 ) Joules

Now, comparing the two kinetic energies:

• Kinetic energy of the yellow ball = 9 Joules
• Kinetic energy of the red ball = 13.5 Joules

Since 13.5 Joules (red ball) is greater than 9 Joules (yellow ball), the red ball has greater kinetic energy, because it has a greater mass.