To calculate the potential energy (PE) gained by Nan's suitcase, you can use the formula:
\[ PE = mgh \]
Where:
- \( m \) 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).
Given:
- Mass \( m = 14 , \text{kg} \)
- Height \( h = 40 , \text{cm} = 0.40 , \text{m} \)
- Acceleration due to gravity \( g = 9.81 , \text{m/s}^2 \)
Substituting the values into the formula:
\[ PE = 14 , \text{kg} \times 9.81 , \text{m/s}^2 \times 0.40 , \text{m} \]
Calculating:
\[ PE = 14 \times 9.81 \times 0.40 \] \[ PE = 14 \times 3.924 \] \[ PE \approx 54.936 , \text{J} \]
Rounding to two decimal places, the potential energy gained is approximately \( 54.94 , \text{J} \).
So, the closest response from the options provided is 54.88 J.