To understand how mass and height affect the gravitational potential energy (GPE) of an object, we need to delve into the formula for calculating GPE:
[tex]\[ \text{GPE} = mgh \][/tex]
where:
- [tex]\( m \)[/tex] is the mass of the object (measured in kilograms),
- [tex]\( g \)[/tex] is the acceleration due to gravity (approximately [tex]\( 9.81 \, m/s^2 \)[/tex] on Earth),
- [tex]\( h \)[/tex] is the height above the reference point (measured in meters).
Let's break down how each variable influences the gravitational potential energy:
1. Mass ([tex]\( m \)[/tex]):
- The mass of the object directly influences the GPE.
- If the mass doubles, the GPE will double.
- This means GPE is directly proportional to mass.
2. Height ([tex]\( h \)[/tex]):
- The height at which the object is located also directly influences the GPE.
- If the height doubles, the GPE will double.
- This means GPE is also directly proportional to height.
Both mass and height appear in the formula for GPE in the same way: as linear factors. Therefore, any change in mass ([tex]\( m \)[/tex]) or height ([tex]\( h \)[/tex]) results in a proportional change in the gravitational potential energy.
Given this direct proportionality, mass and height have equal influence on gravitational potential energy. Neither has a greater or lesser impact than the other when it comes to altering the GPE.
Therefore, the correct answer is:
A. Mass and height have the same effect on gravitational potential energy.
