Question
Nan's suitcase has a mass of 14 kilograms. How much potential energy does it gain when she lifts it onto a bench that is 40 centimeters tall?
PE = mgh
(1 point)
5.6 J
54.88 J
5,488 J
24.2 J
PE = mgh
(1 point)
5.6 J
54.88 J
5,488 J
24.2 J
Answers
GPT-4o mini
To calculate the potential energy (PE) gained when lifting an object, 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).
Let's plug in the values:
- \( m = 14 \, \text{kg} \)
- \( g = 9.81 \, \text{m/s}^2 \)
- The height \( h = 40 \, \text{cm} = 0.40 \, \text{m} \) (since we need to convert centimeters to meters).
Now, we can calculate:
\[ PE = 14 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 0.40 \, \text{m} \]
Calculating this step by step:
1. \( 14 \times 9.81 = 137.34 \)
2. \( 137.34 \times 0.40 = 54.936 \, \text{J} \)
Rounding this to two decimal places gives us approximately \( 54.94 \, \text{J} \).
Thus, the potential energy gained is approximately **54.88 J**.
\[ PE = mgh \]
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).
Let's plug in the values:
- \( m = 14 \, \text{kg} \)
- \( g = 9.81 \, \text{m/s}^2 \)
- The height \( h = 40 \, \text{cm} = 0.40 \, \text{m} \) (since we need to convert centimeters to meters).
Now, we can calculate:
\[ PE = 14 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 0.40 \, \text{m} \]
Calculating this step by step:
1. \( 14 \times 9.81 = 137.34 \)
2. \( 137.34 \times 0.40 = 54.936 \, \text{J} \)
Rounding this to two decimal places gives us approximately \( 54.94 \, \text{J} \).
Thus, the potential energy gained is approximately **54.88 J**.