Two watermelons fall off a kitchen counter. The masses and speeds of the fruits are in the table. How do the kinetic and/or the potential energies of the fruits compare?

Answer 1

To compare the kinetic and potential energies of the two watermelons, we'll need to understand the formulas for both types of energy:

1. Kinetic Energy (KE) is given by the formula: \[ KE = \frac{1}{2} mv^2 \] where \( m \) is the mass of the object and \( v \) is its speed.

2. Potential Energy (PE) is given by the formula: \[ PE = mgh \] where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity (approximately \( 9.81 , m/s^2 \)), and \( h \) is the height above the ground.

To compare the energies, you would perform the following steps:

Step 1: Calculate Kinetic Energy

For each watermelon, using the given mass and speed from the table, calculate the kinetic energy using the KE formula.

Step 2: Calculate Potential Energy

For each watermelon, if the height from the counter to the ground is known or can be assumed, calculate the potential energy using the PE formula.

Step 3: Comparison

• Compare the calculated kinetic energies. The watermelon with the greater speed and/or mass will have higher kinetic energy.
• Compare the calculated potential energies. The one at a greater height will have a higher potential energy.

If you provide the specific masses, speeds, and height of the counter, I can help you with the calculations and comparisons.