1. Work done by gravity on an object falling vertically:
* Formula: W = mgh
* Where:
* W = work done by gravity
* m = mass of the object
* g = acceleration due to gravity (approximately 9.8 m/s²)
* h = vertical distance the object falls
2. Work done by gravity on an object moving along a curved path:
* Formula: W = -ΔU
* Where:
* W = work done by gravity
* ΔU = change in gravitational potential energy
* ΔU = U_final - U_initial
* U_initial = mgh_initial (potential energy at the starting point)
* U_final = mgh_final (potential energy at the ending point)
3. Work done by gravity between two point masses:
* Formula: W = -GMm (1/r_final - 1/r_initial)
* Where:
* W = work done by gravity
* G = gravitational constant (6.674 x 10⁻¹¹ N⋅m²/kg²)
* M = mass of the larger object
* m = mass of the smaller object
* r_initial = initial distance between the masses
* r_final = final distance between the masses
Important Notes:
* The work done by gravity is negative when the object moves in the direction of the gravitational force (e.g., falling). It is positive when the object moves against the gravitational force (e.g., lifting).
* The formulas above assume that the gravitational force is constant. If the gravitational force is not constant (e.g., when dealing with large distances), more complex calculations are required.
It's essential to choose the correct formula based on the specific situation and the available information.
