Gravitational Potential Energy Conundrum?

📌 CONCEPT: Gravitational Potential Energy (GPE) is the energy an object possesses due to its position within a gravitational field, often denoted as U or V, and is a measure of the work required to move an object from a reference point to its current position.

📐 RULE / FORMULA: The formula to calculate the gravitational potential energy of two objects is U = -G × m1 × m2 / r, where U is the gravitational potential energy, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.

💡 WORKED EXAMPLE: To find the gravitational potential energy of a 10 kg object at a distance of 4 m from a 5 kg point mass, we can use the formula U = -G × m1 × m2 / r. Substituting the given values, we get U = - (6.67 x 10^-11 N m^2 kg^-2) × (10 kg) × (5 kg) / (4 m) = -8.31375 x 10^-11 J.

⚠️ COMMON MISTAKE: Students often forget to include the negative sign in the formula for gravitational potential energy, which can lead to incorrect calculations.