To calculate the potential energy (PE) gained by Nan's suitcase when she lifts it onto a bench, we can use the formula:
\[ PE = mgh \]
where:
- \( m \) = mass in kilograms (14 kg)
- \( g \) = acceleration due to gravity (approximately 9.81 m/s²)
- \( h \) = height in meters (40 cm = 0.4 m)
Now, substituting the values into the formula:
\[ PE = 14 , \text{kg} \times 9.81 , \text{m/s}^2 \times 0.4 , \text{m} \]
Calculating this step by step:
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Calculate \( 9.81 , \text{m/s}^2 \times 0.4 , \text{m} \): \[ 9.81 \times 0.4 = 3.924 , \text{m}^2/\text{s}^2 \]
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Now multiply by the mass: \[ PE = 14 , \text{kg} \times 3.924 , \text{m}^2/\text{s}^2 = 54.936 , \text{J} \]
Rounding to two decimal places, the potential energy gained by the suitcase is approximately:
\[ PE \approx 54.94 , \text{J} \]
Among the options provided, the closest is:
54.88 J