Question

Nan's suitcase has a mass of 14 kg how much potential energy does it gain when she lifts it onto a bench that is 40 cm tall

Answer 1

To calculate the potential energy gained when lifting an object, you can use the formula for gravitational potential energy (GPE):

\[
\text{GPE} = m \cdot g \cdot h
\]

Where:
- \( m \) is the mass of the object (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height (in meters).

In this case, the mass \( m \) of Nan's suitcase is 14 kg, the height \( h \) is 40 cm (which we convert to meters: \( 40 \, \text{cm} = 0.4 \, \text{m} \)), and \( g \) is \( 9.81 \, \text{m/s}^2 \).

Now, substitute the values into the formula:

\[
\text{GPE} = 14 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 \cdot 0.4 \, \text{m}
\]

Calculating this gives:

\[
\text{GPE} = 14 \cdot 9.81 \cdot 0.4
\]
\[
\text{GPE} = 14 \cdot 3.924
\]
\[
\text{GPE} \approx 54.936 \, \text{J}
\]

Therefore, the potential energy gained by Nan's suitcase when she lifts it onto the bench is approximately **54.94 joules**.