If the mass of an object is tripled, how does the gravitational potential energy

If the mass of an object is tripled, how does the gravitational potential energy change for a constant height?

If the mass of an object is tripled, how does the gravitational potential energy change for a constant height?

Step 1: Understand what gravitational potential energy (GPE) is. It is the energy an object has due to its position in a gravitational field, usually calculated using the formula GPE = mass × gravity × height.
Step 2: Identify the variables in the formula. Here, mass is the weight of the object, gravity is the acceleration due to gravity (which is constant near the Earth's surface), and height is how high the object is above the ground.
Step 3: Note that if the mass of the object is tripled, we can represent the new mass as 3 × original mass.
Step 4: Substitute the new mass into the GPE formula. The new GPE will be GPE = (3 × original mass) × gravity × height.
Step 5: Compare the new GPE with the original GPE. The original GPE is GPE = original mass × gravity × height. The new GPE is three times the original GPE.
Step 6: Conclude that if the mass is tripled, the gravitational potential energy also triples, as it is directly proportional to mass.

Gravitational Potential Energy – Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field, calculated as GPE = mass × gravitational acceleration × height.
Direct Proportionality – The relationship between mass and gravitational potential energy is direct; if mass increases, GPE increases proportionally, assuming height and gravitational acceleration remain constant.