Water falls from the top of a hill to the ground. Why?
This is because the top of the hill is a point of higher gravitational potential than the surface of the Earth i.e.Vhill > Vground
The motion of particles can be analyzed more easily using scalars like U ( r )or V(r) than vector quantities like or . In modern theories of physics, the concept of potential plays a vital role.
Consider four masses m1, m2, m3, and m4 arranged on the circumference of a circle as shown in figure below
a) The gravitational potential energy of the system of 4 masses shown in figure.
b) The gravitational potential at the point O due to all the 4 masses.
The gravitational potential energy U( r ) can be calculated by finding the sum of gravitational potential energy of each pair of particles.
If all the masses are equal, then m1 = m2 = m3 = m4 = M
The gravitational potential V(r) at a point O is equal to the sum of the gravitational potentials due to individual mass. Since potential is a scalar, the net potential at point O is the algebraic sum of potentials due to each mass.