To answer the question of how mass and height affect gravitational potential energy (GPE), we need to refer to the formula for GPE:
[tex]\[ \text{GPE} = mgh \][/tex]
Where:
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( g \)[/tex] is the acceleration due to gravity (which is approximately [tex]\( 9.81 m/s^2 \)[/tex]),
- [tex]\( h \)[/tex] is the height of the object above the reference point.
From the formula, it is evident that:
- Gravitational potential energy is directly proportional to both the mass [tex]\( m \)[/tex] of the object and the height [tex]\( h \)[/tex] above the reference point.
- The gravitational potential energy increases linearly with an increase in either mass or height.
Let's break down the contributions:
1. If you double the mass [tex]\( (2m) \)[/tex], the GPE will also double:
[tex]\[ \text{GPE} = (2m)gh \][/tex]
2. Similarly, if you double the height [tex]\( (2h) \)[/tex], the GPE will again double:
[tex]\[ \text{GPE} = mg(2h) \][/tex]
Hence, both mass and height have a multiplicative and equal effect on the gravitational potential energy. This means:
- The effect of mass on GPE is exactly the same as the effect of height.
Based on this analysis, the correct answer is:
C. Mass and height have the same effect on gravitational potential energy.
