The gravitational potential energy (GPE) of an object can be calculated using the formula:
\[ \text{GPE} = m \cdot g \cdot h \]
Where:
- \( m \) is the mass of the object (in kilograms),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height above the reference point (in meters).
For the given object:
- Mass \( m = 3.4 , \text{kg} \)
- Height \( h = 2.3 , \text{m} \)
- Acceleration due to gravity \( g \approx 9.81 , \text{m/s}^2 \)
Now, substituting the values into the formula:
\[ \text{GPE} = 3.4 , \text{kg} \cdot 9.81 , \text{m/s}^2 \cdot 2.3 , \text{m} \]
Calculating this step-by-step:
- Calculate \( 3.4 \times 9.81 \):
\[ 3.4 \times 9.81 \approx 33.434 \]
- Now multiply by the height \( 2.3 \):
\[ 33.434 \times 2.3 \approx 76.9 , \text{J} \]
Therefore, the gravitational potential energy of the object sitting on the shelf is approximately \( 76.9 , \text{J} \).
Among the options given, the closest value is:
76.6 J
1 answer