To find the potential energy (PE) gained when Nan lifts the suitcase, we can use the formula:
\[ PE = mgh \]
where:
- \( m \) = mass in kilograms,
- \( g \) = acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) = height in meters.
Given:
- \( m = 14 , \text{kg} \)
- \( h = 40 , \text{cm} = 0.4 , \text{m} \)
- \( g \approx 9.81 , \text{m/s}^2 \)
Now, substitute the values into the formula:
\[ PE = 14 , \text{kg} \times 9.81 , \text{m/s}^2 \times 0.4 , \text{m} \]
Calculating this:
\[ PE = 14 \times 9.81 \times 0.4 \] \[ PE = 14 \times 3.924 \] \[ PE \approx 54.936 , \text{J} \]
Rounding this to two decimal places gives us approximately \( 54.94 , \text{J} \).
Thus, the closest response is:
54.88 J