Question

The chandelier in my house has about 339 J of potential energy. if it is 3 meters off the ground, what is the mass of the chandelier?

Answer 1

To find the mass of the chandelier, we can use the formula for gravitational potential energy (PE):

\[
PE = mgh
\]

where:
- \( PE \) is the potential energy (in joules),
- \( m \) is the mass (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height (in meters).

We know that:
- \( PE = 339 \, \text{J} \)
- \( h = 3 \, \text{m} \)
- \( g = 9.81 \, \text{m/s}^2 \)

We can rearrange the equation to solve for \( m \):

\[
m = \frac{PE}{gh}
\]

Now we can substitute in the known values:

\[
m = \frac{339 \, \text{J}}{(9.81 \, \text{m/s}^2)(3 \, \text{m})}
\]

Calculating the denominator:

\[
9.81 \, \text{m/s}^2 \times 3 \, \text{m} = 29.43 \, \text{m}^2/\text{s}^2
\]

Now, substitute this result back into the equation for \( m \):

\[
m = \frac{339 \, \text{J}}{29.43 \, \text{m}^2/\text{s}^2} \approx 11.52 \, \text{kg}
\]

So, the mass of the chandelier is approximately **11.52 kg**.