To determine the gravitational potential energy added to a wheel with a given mass when it is lifted to a certain height, we use the formula for gravitational potential energy (GPE):
[tex]\[ \text{GPE} = mgh \][/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 to which the object is lifted.
Given in the problem:
[tex]\[ m = 38 \, \text{kg} \][/tex]
[tex]\[ g = 9.8 \, \text{m/s}^2 \][/tex]
[tex]\[ h = 0.8 \, \text{m} \][/tex]
Substitute these values into the formula:
[tex]\[ \text{GPE} = 38 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.8 \, \text{m} \][/tex]
This calculation yields:
[tex]\[ \text{GPE} = 297.92 \, \text{J} \][/tex]
Therefore, the gravitational potential energy added to the wheel is approximately [tex]\( 297.9 \, \text{J} \)[/tex].
Looking at the provided multiple-choice options:
A. [tex]\( 30.4 \, \text{J} \)[/tex]
B. [tex]\( 11,321 \, \text{J} \)[/tex]
C. [tex]\( 3.1 \, \text{J} \)[/tex]
D. [tex]\( 297.9 \, \text{J} \)[/tex]
The closest and correct answer is:
D. [tex]\( 297.9 \, \text{J} \)[/tex]
