Question
A 7.00 kg bowling ball is held 2.00 m above the ground. Using g = 9.80 m/s2, how much energy does the bowling ball have due to its position?
68.6 J
137 J
274 J
960 J
68.6 J
137 J
274 J
960 J
Answers
GPT-4o mini
To determine the gravitational potential energy (PE) of the bowling ball due to its position, we can use the formula:
\[
PE = m \cdot g \cdot h
\]
where:
- \( m \) is the mass of the object (in kg),
- \( g \) is the acceleration due to gravity (in m/s²),
- \( h \) is the height above the ground (in m).
Given the values:
- \( m = 7.00 \, \text{kg} \)
- \( g = 9.80 \, \text{m/s}^2 \)
- \( h = 2.00 \, \text{m} \)
Substituting these values into the formula, we get:
\[
PE = 7.00 \, \text{kg} \times 9.80 \, \text{m/s}^2 \times 2.00 \, \text{m}
\]
Calculating this step by step:
1. Calculate \( 9.80 \times 2.00 = 19.60 \, \text{m/s}^2 \)
2. Now multiply by the mass:
\[
PE = 7.00 \, \text{kg} \times 19.60 \, \text{m/s}^2 = 137.2 \, \text{J}
\]
Since we are looking for the best answer from the choices provided, rounding 137.2 J gives us 137 J.
Thus, the answer is:
**137 J**
\[
PE = m \cdot g \cdot h
\]
where:
- \( m \) is the mass of the object (in kg),
- \( g \) is the acceleration due to gravity (in m/s²),
- \( h \) is the height above the ground (in m).
Given the values:
- \( m = 7.00 \, \text{kg} \)
- \( g = 9.80 \, \text{m/s}^2 \)
- \( h = 2.00 \, \text{m} \)
Substituting these values into the formula, we get:
\[
PE = 7.00 \, \text{kg} \times 9.80 \, \text{m/s}^2 \times 2.00 \, \text{m}
\]
Calculating this step by step:
1. Calculate \( 9.80 \times 2.00 = 19.60 \, \text{m/s}^2 \)
2. Now multiply by the mass:
\[
PE = 7.00 \, \text{kg} \times 19.60 \, \text{m/s}^2 = 137.2 \, \text{J}
\]
Since we are looking for the best answer from the choices provided, rounding 137.2 J gives us 137 J.
Thus, the answer is:
**137 J**