To determine the gravitational potential energy (GPE) added to the wheel when it is lifted, we can use the formula for gravitational potential energy:
[tex]\[ \text{GPE} = m \times g \times h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity,
- [tex]\( h \)[/tex] is the height the object is lifted.
Given:
- [tex]\( m = 38 \, \text{kg} \)[/tex]
- [tex]\( h = 0.8 \, \text{m} \)[/tex]
- [tex]\( g = 9.81 \, \text{m/s}^2 \)[/tex]
We substitute these values into the formula:
[tex]\[ \text{GPE} = 38 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 0.8 \, \text{m} \][/tex]
When we perform this calculation, we get:
[tex]\[ \text{GPE} \approx 298.224 \, \text{J} \][/tex]
Therefore, the gravitational potential energy added to the wheel is approximately [tex]\( 298.224 \, \text{J} \)[/tex].
Looking at the provided answer choices:
A. 30.4 J
B. [tex]$11,321 J$[/tex]
C. 3.1 J
D. 297.9 J
The closest value to our calculated gravitational potential energy is:
D. 297.9 J
