Question
8. The potential energy of an apple is 6.00 joules. The apple is 3.00-meters high. What is the mass of the apple?
Answers
GPT-4o mini
To find the mass of the apple based on its potential energy, you can use the formula for gravitational potential energy:
\[
PE = mgh
\]
where:
- \( PE \) is the potential energy (in joules),
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) on Earth),
- \( h \) is the height above the ground (in meters).
Given:
- \( PE = 6.00 \, \text{joules} \)
- \( h = 3.00 \, \text{meters} \)
- \( g = 9.81 \, \text{m/s}^2 \)
We can rearrange the formula to solve for mass \( m \):
\[
m = \frac{PE}{gh}
\]
Now, substitute the known values into the equation:
\[
m = \frac{6.00 \, \text{joules}}{(9.81 \, \text{m/s}^2)(3.00 \, \text{m})}
\]
Calculating the denominator:
\[
gh = 9.81 \, \text{m/s}^2 \times 3.00 \, \text{m} = 29.43 \, \text{m}^2/\text{s}^2
\]
Now substitute this back into the equation:
\[
m = \frac{6.00}{29.43} \approx 0.203 \, \text{kg}
\]
Thus, the mass of the apple is approximately **0.203 kilograms**.
\[
PE = mgh
\]
where:
- \( PE \) is the potential energy (in joules),
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) on Earth),
- \( h \) is the height above the ground (in meters).
Given:
- \( PE = 6.00 \, \text{joules} \)
- \( h = 3.00 \, \text{meters} \)
- \( g = 9.81 \, \text{m/s}^2 \)
We can rearrange the formula to solve for mass \( m \):
\[
m = \frac{PE}{gh}
\]
Now, substitute the known values into the equation:
\[
m = \frac{6.00 \, \text{joules}}{(9.81 \, \text{m/s}^2)(3.00 \, \text{m})}
\]
Calculating the denominator:
\[
gh = 9.81 \, \text{m/s}^2 \times 3.00 \, \text{m} = 29.43 \, \text{m}^2/\text{s}^2
\]
Now substitute this back into the equation:
\[
m = \frac{6.00}{29.43} \approx 0.203 \, \text{kg}
\]
Thus, the mass of the apple is approximately **0.203 kilograms**.