Answer :
To determine how much gravitational potential energy is added to a wheel of mass [tex]\(38 \, \text{kg}\)[/tex] when it is lifted to a height of [tex]\(0.8 \, \text{m}\)[/tex], we use the formula for gravitational potential energy (GPE):
[tex]\[ \text{GPE} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (in meters per second squared),
- [tex]\( h \)[/tex] is the height to which the object is lifted (in meters).
Given:
- [tex]\( m = 38 \, \text{kg} \)[/tex]
- [tex]\( h = 0.8 \, \text{m} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
Plugging in these values into the formula:
[tex]\[ \text{GPE} = 38 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.8 \, \text{m} \][/tex]
Calculating this product:
[tex]\[ \text{GPE} = 38 \times 9.8 \times 0.8 \][/tex]
The result is:
[tex]\[ \text{GPE} = 297.92 \, \text{J} \][/tex]
So, the gravitational potential energy added to the wheel is [tex]\(297.92 \, \text{J}\)[/tex]. Therefore, the correct answer is:
A. [tex]\(297.9 \, \text{J}\)[/tex]
[tex]\[ \text{GPE} = m \cdot g \cdot h \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (in meters per second squared),
- [tex]\( h \)[/tex] is the height to which the object is lifted (in meters).
Given:
- [tex]\( m = 38 \, \text{kg} \)[/tex]
- [tex]\( h = 0.8 \, \text{m} \)[/tex]
- [tex]\( g = 9.8 \, \text{m/s}^2 \)[/tex]
Plugging in these values into the formula:
[tex]\[ \text{GPE} = 38 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.8 \, \text{m} \][/tex]
Calculating this product:
[tex]\[ \text{GPE} = 38 \times 9.8 \times 0.8 \][/tex]
The result is:
[tex]\[ \text{GPE} = 297.92 \, \text{J} \][/tex]
So, the gravitational potential energy added to the wheel is [tex]\(297.92 \, \text{J}\)[/tex]. Therefore, the correct answer is:
A. [tex]\(297.9 \, \text{J}\)[/tex]
