To calculate the potential energy of a stone with a mass of 500 grams raised to a height of 12 meters above the ground, assuming the acceleration due to gravity [tex]\( g = 10 \, \text{m/s}^2 \)[/tex], follow these steps:
1. Convert the mass to kilograms:
The mass is given in grams (500 grams). We need to convert this to kilograms because the standard unit of mass in the International System of Units (SI) is the kilogram.
[tex]\[
500 \, \text{g} = 500 / 1000 = 0.5 \, \text{kg}
\][/tex]
2. Identify the height:
The height to which the stone is raised is given as 12 meters.
3. Use the gravitational potential energy formula:
The formula to calculate gravitational potential energy ([tex]\( PE \)[/tex]) is:
[tex]\[
PE = mgh
\][/tex]
where [tex]\( m \)[/tex] is the mass (in kilograms), [tex]\( g \)[/tex] is the acceleration due to gravity (in meters per second squared), and [tex]\( h \)[/tex] is the height (in meters).
4. Substitute the values into the formula:
[tex]\[
m = 0.5 \, \text{kg}
\][/tex]
[tex]\[
g = 10 \, \text{m/s}^2
\][/tex]
[tex]\[
h = 12 \, \text{m}
\][/tex]
[tex]\[
PE = 0.5 \, \text{kg} \times 10 \, \text{m/s}^2 \times 12 \, \text{m}
\][/tex]
5. Calculate the potential energy:
[tex]\[
PE = 0.5 \times 10 \times 12 = 60 \, \text{J}
\][/tex]
Therefore, the potential energy of the stone raised to a height of 12 meters is [tex]\( 60 \, \text{J} \)[/tex].
