Answered

A wheel of mass [tex]38 \, \text{kg}[/tex] is lifted to a height of [tex]0.8 \, \text{m}[/tex]. How much gravitational potential energy is added to the wheel? The acceleration due to gravity is [tex]g = 9.8 \, \text{m/s}^2[/tex].

A. [tex]297.9 \, \text{J}[/tex]
B. [tex]30.4 \, \text{J}[/tex]
C. [tex]3.1 \, \text{J}[/tex]
D. [tex]11,321 \, \text{J}[/tex]



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]