If the mass of an object is halved and the distance from the center of the Earth
Practice Questions
Q1
If the mass of an object is halved and the distance from the center of the Earth is doubled, what happens to the gravitational potential energy?
It remains the same.
It doubles.
It halves.
It quadruples.
Questions & Step-by-Step Solutions
If the mass of an object is halved and the distance from the center of the Earth is doubled, what happens to the gravitational potential energy?
Step 1: Understand that gravitational potential energy (GPE) depends on two things: mass and distance from the center of the Earth.
Step 2: Remember the formula for gravitational potential energy: GPE = (mass * gravitational constant * height).
Step 3: If the mass is halved, it means we multiply the mass by 0.5.
Step 4: If the distance from the center of the Earth is doubled, it means we multiply the height by 2.
Step 5: When we calculate the new GPE, we have: New GPE = (0.5 * mass * gravitational constant * (2 * height)).
Step 6: Simplifying this gives us: New GPE = (0.5 * mass * gravitational constant * height * 2) = mass * gravitational constant * height.
Step 7: This shows that the new GPE is equal to the original GPE, meaning it does not change.
Gravitational Potential Energy – Gravitational potential energy (U) is given by the formula U = -G(m1*m2)/r, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Proportional Relationships – Understanding how changes in mass and distance affect gravitational potential energy, specifically that it is directly proportional to mass and inversely proportional to distance.
