Derivation of Gravitational Potential Energy
When a particle is transported over an infinitely short distance, dr. The work done on the second particle by the gravitational force is represented by -Fdr.
dW = -Fdr……(1)
where F is the Gravitational force acting on the particles and is given by,
F = G m1 m2 / r2
where G is the Gravitational constant, m1, and m2 are the masses of the two particles in contact respectively.
On substituting F in equation (1), we get,
dW = -(G m1 m2) dr / r2……(2)
The negative sign in the equation comes from the fact that the displacement is in the opposite direction as the force. The change in gravitational potential energy of the two-particle system during this short movement is equal to the negative work done on the second particle by definition. When a particle is transported over an infinitely short distance, dr.
The work done on the second particle by the gravitational force is denoted by – Fdr.
dU = -dW
= (G m1 m2) dr / r2……(3)
As the second particle goes from B to C, the change in gravitational potential energy of the two-particle system is a function of distance r, and is represented by,
Gravitational Potential Energy
The energy possessed by objects due to changes in their position in a gravitational field is called Gravitational Potential Energy. It is the energy of the object due to the gravitational forces. The work done per unit mass to bring the body from infinity to a location inside the gravitational field of any object is known as gravitational potential and the energy change here is called Gravitational Potential Energy. Let’s learn about Gravitational Potential Energy in detail in this article.
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