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.

Explanation:

Step1: Recall the kinetic energy formula

The formula for kinetic energy is \(K = \frac{1}{2}mv^{2}\), where \(m\) is mass and \(v\) is velocity.

Step2: Analyze the given values

For the yellow ball, \(m_{y}=2\space kg\) and \(v_{y} = 3\space m/s\). For the red ball, \(m_{r}=3\space kg\) and \(v_{r}=3\space m/s\). Since \(v_{y}=v_{r}\), and \(m_{r}>m_{y}\).

Step3: Use the formula to compare

Substituting into \(K=\frac{1}{2}mv^{2}\), when \(v\) is the same, \(K\) is directly proportional to \(m\) (because \(\frac{1}{2}\) and \(v^{2}\) are constants). So the ball with larger mass has larger kinetic energy.

Answer:

The red ball has greater kinetic energy, because it has a greater mass.