Understanding Gravitational Potential Energy

What is the basic formula for gravitational potential energy on the surface of the Earth?

• PE = Gm1m2/r

• PE = mg/r^2

• PE = 1/2 mv^2

• PE = mgh

Why does the formula PE = mgh not hold true for large distances?

• Because height cannot be measured accurately

• Because mass changes with distance

• Because the Earth's radius is too small

• Because gravity is not constant over large distances

What law is used to refine the gravitational potential energy formula for large distances?

• Newton's First Law

• Kepler's Laws

• Newton's Law of Universal Gravitation

• Einstein's Theory of Relativity

What mathematical method is used to calculate the work done by gravity over large distances?

• Differentiation

• Integration

• Algebraic manipulation

• Matrix operations

What does the integration of force with respect to radius help determine?

• The time taken to fall

• The mass of an object

• The speed of an object

• The potential energy

What is the nature of gravitational potential energy as an object moves infinitely far from Earth?

• It becomes infinite

• It approaches zero

• It becomes positive

• It remains constant

What does it mean when an object has negative potential energy relative to Earth?

• The object is gaining energy

• The object is losing energy

• The object is moving away from Earth

• The object is trapped in a gravity well

What is the significance of the slope of the gravitational potential energy curve?

• It represents the speed of the object

• It represents the time taken to fall

• It represents the force by gravity

• It represents the mass of the object

What future topic is hinted at in the conclusion regarding gravitational potential energy?

• The energy of black holes

• The energy of chemical bonds

• The energy of satellites in orbit

• The energy of nuclear reactions

What happens to gravitational potential energy when an object is dropped into a hole to the center of the Earth?

• It becomes zero

• It becomes infinite

• It decreases

• It increases