What is the relationship between mass and height in gravitational potential energy?

What is the relationship between mass and height in gravitational potential energy?

• A. Mass and height are inverse
• B. Higher mass decreases potential energy
• C. Both increase potential energy
• D. Height does not affect potential energy

Answer: (C)

The relationship between mass, height, and gravitational potential energy is directly proportional. Gravitational potential energy is calculated using the formula: \( PE = mgh \) where \( PE \) is the potential energy, \( m \) is the mass, \( g \) is the acceleration due to gravity (approximately \( 9.81 \, m/s^2 \) on Earth), and \( h \) is the height above a reference point. In this equation, both mass and height directly influence the potential energy. As the mass of an object increases, the potential energy increases as well, provided that the height remains constant. Similarly, if the height of the object increases while the mass stays constant, the potential energy also increases. Therefore, when both mass and height increase, the gravitational potential energy increases more significantly, leading to the conclusion that both factors contribute positively to increasing potential energy.

The relationship between mass, height, and gravitational potential energy is directly proportional. Gravitational potential energy is calculated using the formula:

( PE = mgh )

where ( PE ) is the potential energy, ( m ) is the mass, ( g ) is the acceleration due to gravity (approximately ( 9.81 , m/s^2 ) on Earth), and ( h ) is the height above a reference point.

In this equation, both mass and height directly influence the potential energy. As the mass of an object increases, the potential energy increases as well, provided that the height remains constant. Similarly, if the height of the object increases while the mass stays constant, the potential energy also increases. Therefore, when both mass and height increase, the gravitational potential energy increases more significantly, leading to the conclusion that both factors contribute positively to increasing potential energy.