To calculate the gravitational potential energy of a 2 kg bottle of soda falling off of a kitchen table that is 0.76 meters tall, we can use the formula for gravitational potential energy:
[tex]\[ \text{Gravitational Potential Energy (GPE)} = mgh \][/tex]
Where:
- [tex]\( m \)[/tex] is the mass in kilograms (kg)
- [tex]\( g \)[/tex] is the acceleration due to gravity in meters per second squared (m/s²)
- [tex]\( h \)[/tex] is the height in meters (m)
Given:
- Mass [tex]\( m = 2 \)[/tex] kg
- Height [tex]\( h = 0.76 \)[/tex] m
- Gravity [tex]\( g = 9.8 \)[/tex] m/s²
Substitute the given values into the formula:
[tex]\[ \text{GPE} = (2 \, \text{kg}) \times (9.8 \, \text{m/s}^2) \times (0.76 \, \text{m}) \][/tex]
Now perform the multiplication step-by-step:
1. Multiply the height by gravity:
[tex]\[ h \times g = 0.76 \, \text{m} \times 9.8 \, \text{m/s}^2 = 7.448 \, \text{m}^2/\text{s}^2 \][/tex]
2. Multiply the result by the mass:
[tex]\[ GPE = 2 \, \text{kg} \times 7.448 \, \text{m}^2/\text{s}^2 = 14.896 \, \text{kg} \cdot \text{m}^2/\text{s}^2 = 14.896 \, \text{J} \][/tex]
Therefore, the gravitational potential energy of the 2 kg bottle of soda falling off of a 0.76 m tall kitchen table is 14.896 joules (J).
Among the given options:
A. [tex]\(\frac{1}{2}(0.76)(2)^2\)[/tex]
B. (2)(0.76)9.8
C. [tex]\(\frac{(2)(0.76)}{9.8}\)[/tex]
D. [tex]\(\frac{1}{2}(2)\left(0.76^2\right)\)[/tex]
Option B is the correct one because it accurately follows the formula for gravitational potential energy [tex]\( mgh \)[/tex]:
[tex]\[ \text{GPE} = (2) \times (0.76) \times 9.8 \][/tex]
So, the correct answer is:
B. (2) (0.76)9.8
