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.
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