Answer :
To determine the amount of energy a bowling ball has due to its position above the ground, we need to calculate its gravitational potential energy (GPE). Gravitational potential energy can be calculated using the formula:
[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, and
- [tex]\( h \)[/tex] is the height above the ground.
Given:
- [tex]\( m = 7.00 \, \text{kg} \)[/tex]
- [tex]\( g = 9.80 \, \text{m/s}^2 \)[/tex]
- [tex]\( h = 2.00 \, \text{m} \)[/tex]
Now, substitute these values into the formula:
[tex]\[ \text{GPE} = 7.00 \, \text{kg} \times 9.80 \, \text{m/s}^2 \times 2.00 \, \text{m} \][/tex]
First, do the multiplication for mass and gravity:
[tex]\[ 7.00 \times 9.80 = 68.6 \][/tex]
Then multiply this result by the height:
[tex]\[ 68.6 \times 2.00 = 137.2 \, \text{J} \][/tex]
So, the gravitational potential energy of the bowling ball is approximately [tex]\( 137.2 \, \text{J} \)[/tex].
Therefore, the closest answer choice is:
[tex]\[ \boxed{137 \, \text{J}} \][/tex]
[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, and
- [tex]\( h \)[/tex] is the height above the ground.
Given:
- [tex]\( m = 7.00 \, \text{kg} \)[/tex]
- [tex]\( g = 9.80 \, \text{m/s}^2 \)[/tex]
- [tex]\( h = 2.00 \, \text{m} \)[/tex]
Now, substitute these values into the formula:
[tex]\[ \text{GPE} = 7.00 \, \text{kg} \times 9.80 \, \text{m/s}^2 \times 2.00 \, \text{m} \][/tex]
First, do the multiplication for mass and gravity:
[tex]\[ 7.00 \times 9.80 = 68.6 \][/tex]
Then multiply this result by the height:
[tex]\[ 68.6 \times 2.00 = 137.2 \, \text{J} \][/tex]
So, the gravitational potential energy of the bowling ball is approximately [tex]\( 137.2 \, \text{J} \)[/tex].
Therefore, the closest answer choice is:
[tex]\[ \boxed{137 \, \text{J}} \][/tex]
