Answer :
To solve this problem, we need to find the mass of an apple given its potential energy and height.
1. Understand the Formula for Potential Energy:
The potential energy (U) is given by the formula:
[tex]\[
U = m \times g \times h
\][/tex]
where:
- [tex]\( U \)[/tex] is the potential energy in joules,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on the surface of the earth),
- [tex]\( h \)[/tex] is the height in meters.
2. Identify Given Values:
- Potential energy ([tex]\( U \)[/tex]) = 6.00 joules
- Height ([tex]\( h \)[/tex]) = 3.00 meters
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.81 m/s² (a standard value)
3. Rearrange the Formula to Solve for Mass ([tex]\( m \)[/tex]):
We can rearrange the formula to solve for mass:
[tex]\[
m = \frac{U}{g \times h}
\][/tex]
4. Substitute the Known Values into the Formula:
[tex]\[
m = \frac{6.00}{9.81 \times 3.00}
\][/tex]
5. Calculate the Mass:
Upon calculation, the mass [tex]\( m \)[/tex] of the apple is approximately 0.204 kilograms.
Therefore, the mass of the apple is approximately 0.204 kg.
1. Understand the Formula for Potential Energy:
The potential energy (U) is given by the formula:
[tex]\[
U = m \times g \times h
\][/tex]
where:
- [tex]\( U \)[/tex] is the potential energy in joules,
- [tex]\( m \)[/tex] is the mass in kilograms,
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex] on the surface of the earth),
- [tex]\( h \)[/tex] is the height in meters.
2. Identify Given Values:
- Potential energy ([tex]\( U \)[/tex]) = 6.00 joules
- Height ([tex]\( h \)[/tex]) = 3.00 meters
- Acceleration due to gravity ([tex]\( g \)[/tex]) = 9.81 m/s² (a standard value)
3. Rearrange the Formula to Solve for Mass ([tex]\( m \)[/tex]):
We can rearrange the formula to solve for mass:
[tex]\[
m = \frac{U}{g \times h}
\][/tex]
4. Substitute the Known Values into the Formula:
[tex]\[
m = \frac{6.00}{9.81 \times 3.00}
\][/tex]
5. Calculate the Mass:
Upon calculation, the mass [tex]\( m \)[/tex] of the apple is approximately 0.204 kilograms.
Therefore, the mass of the apple is approximately 0.204 kg.
