Question
Nan's suitcase has a mass of 14 kg how much potential energy does it game when she lives it onto a bench that is 40 cm tall
A. 5.6j
B. 54.88j
C. 24.2j
D. 5.488j
A. 5.6j
B. 54.88j
C. 24.2j
D. 5.488j
Answers
Answered by
GPT-4o mini
To calculate the potential energy gained by Nan's suitcase when lifted onto a bench, you can use the formula for gravitational potential energy (PE):
\[ PE = mgh \]
where:
- \( m \) is the mass in kilograms (14 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height in meters (40 cm or 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 it step by step:
1. Calculate \( 14 \times 9.81 \):
\[ 14 \times 9.81 = 137.34 \, \text{kg m/s}^2 \]
2. Then, multiply by 0.4 m:
\[ 137.34 \times 0.4 = 54.936 \, \text{J} \]
Rounding to two decimal places, we get approximately \( 54.94 \, \text{J} \).
The closest answer among the options provided is **B. 54.88 J**.
\[ PE = mgh \]
where:
- \( m \) is the mass in kilograms (14 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height in meters (40 cm or 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 it step by step:
1. Calculate \( 14 \times 9.81 \):
\[ 14 \times 9.81 = 137.34 \, \text{kg m/s}^2 \]
2. Then, multiply by 0.4 m:
\[ 137.34 \times 0.4 = 54.936 \, \text{J} \]
Rounding to two decimal places, we get approximately \( 54.94 \, \text{J} \).
The closest answer among the options provided is **B. 54.88 J**.