Gravitational potential energy is the energy moved procured by an item because of an adjustment of its position when it is available in a gravitational field. In straightforward terms, one might say that gravitational potential energy is an energy that is connected with gravitational power or to gravity.
Whenever an assortment of mass (m) is moved from endlessness to a point inside the gravitational impact of a source mass (M) without speeding up it, how much work done in uprooting it into the source field is put away as expected energy. This is known as gravitational likely energy. It is addressed with the image Ug.
Clarification: We realize that the possible energy of a body at a given position is characterized as the energy put away in the body at that position. In the event that the place of the body changes because of the utilization of outside powers the adjustment of potential energy is equivalent to how much work is done on the body by the powers.
Under the activity of gravitational power, the work done is autonomous of the way taken for an adjustment of position so the power is a moderate power. Also, all such powers have a few potentials in them.
The gravitation effect on a body at limitlessness is zero, consequently, potential energy is zero, which is known as a source of perspective point.
The condition for gravitational potential energy is:
⇒ GPE = m⋅g⋅h
Where,
Consider a source mass ‘M’ is set at a point along the x-pivot, at first, a test mass ‘m’ is at boundlessness. A limited quantity of work done in bringing it without speed increase through a tiny distance (dx) is given by
dw = Fdx
Here, F is an appealing power and the relocation is towards the negative x-hub heading so F and dx are in a similar course. Then, at that point,
dw = (GMm/x2)dx
Integrating on the two sides
\[w = \int_{\infty }^{r} \frac{GMm}{x^{2}}dx\]
\[w = -[\frac{GMm}{x}]_{\infty }^{r}\]
\[w = -[\frac{GMm}{r}] – (\frac{-GMm}{\infty })\]
\[w = \frac{-GMm}{r}\]
Since the work done is put away as its potential energy U, along these lines gravitational possible energy at a point which is a good ways off ‘r’ from the source mass is given by;
U = – GMm/r
On the off chance that a test mass moves from a point inside the gravitational field to the next point inside a similar gravitational field of source mass, then, at that point, the adjustment of likely energy of the test mass is given by;
ΔU = GMm (1/ri – 1/rf)
In the event that ri > rf, ΔU is negative.
Assuming that a body is taken from the outer layer of the earth to a point at a tallness ‘h’ over the outer layer of the earth, then, at that point, ri = R and rf = R + h then, at that point,
ΔU = GMm [1/R – 1/(R+h)]
ΔU = GMmh/R(R + h)
At the point when, h<<R, then, at that point, R + h = R and g = GM/R2.
On subbing this in the above condition we get,
ΔU = mgh
⇒ Note:
How much work is done in moving a unit test mass from limitlessness into the gravitational impact of source mass is known as gravitational potential.
Essentially, it is the gravitational potential energy moved by a unit test mass
⇒ V = U/m
⇒ V = – GM/r
⇒ Significant Points:
The formula(dimensional) of GPE(Gravitational Potential Energy) is M1 L2 T-2
Where,
(G.P.E) = Mass(M) . Acceleration due to gravity . Altitude . . . (1)
Gravitational potential energy is the energy put away in an item as the aftereffect of its upward position or tallness. The energy is put away as the aftereffect of the gravitational fascination of the Earth for the item.
Gravitational potential energy just relies upon the gravitational capability of the point and the mass of the article. Potential energy can rely upon numerous different factors like charge, flow, electric potential and numerous others.