 # Potential energy and Law of Conservation of Energy

• Potential energy of a mass ‘m’ at height ‘h’ u = mgh.
• Potential energy of a stretched spring \tt u = \frac{1}{2} kx^{2}.
• Zero potential point is that where gravitational potential = 0.
• In a conservative force work done in round trip is zero.
• In a Non-conservative force work done in round trip is non zero.
• Relation between force and potential energy \tt F = - \frac{du}{dx}
• In stable equilibrium \tt F = 0 = \frac{du}{dx}
• In stable equilibrium potential energy is minimum.
• In stable equilibrium when a particle is slightly displaced it comes to initial position.
• In unstable equilibrium, when a particle is slightly displaced it moves further away.
• In unstable equilibrium potential energy is maximum.
• In neutral equilibrium when a particle is displaced it remains in that position.
• Potential energy is constant in Neutral equilibrium.
• In neutral equilibrium force is zero.
• In neutral equilibrium \tt \frac{d^{2}u}{dx^{2}} = 0
• For a particle moving in circular path centripetal force = \tt \frac{mv^{2}}{r} = \frac{K}{r}
• Kinetic energy of a particle in circular path = \tt \frac{K}{2r}
• Potential energy of a particle in circular path = \tt \frac{-K}{r}
• Total energy of a particle in circular path = \tt \frac{-K}{2r}
• One form of energy may be converted into other form called conservation of energy.
• In the principle of conservation of energy we include mass into energy.
• The principle of conservation of energy cannot be proved mathematically but is an empirical principle.
• Einstein’s mass energy equivalence E = Δmc2.
• The sum of kinetic energy and potential energy is constant.
• Wcon + Wnon con + Wext = KE2 − KE1

### View the Topic in this video From 13:46 To 58:46

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1. Potential energy = mgh.

2. Potential energy of the spring = \tt \frac{1}{2}kx^{2}

3. The electric potential energy of two point charges q1 and q2 separated by a distance r in vacuum is given by \tt U=\frac{1}{4\pi\varepsilon_{0}}\cdot\frac{q_{1}q_{2}}{r}

4. If spring is stretched from initial position x1 to final position x2 then work done = Increment in elastic potential energy
=\frac{1}{2}k\left(x_2^2-x_1^2\right)

5. For two particles of masses m1 and m2 separated by a distance r
Gravitational potential energy \tt U=-\frac{G\ m_{1}m_{2}}{r}

6. If a body of mass m is at height h relative to surface of earth then
Gravitational potential energy \tt U=\frac{mgh}{1+\frac{h}{R}}

7. If point mass m is pulled through a height h then work done W = mgh

8. Work done in pulling the hanging portion on the table.
\tt W=\frac{MgL}{2n^{2}}

9. Work done to raise the centre of mass of the chain on the table is given by
\tt W=\frac{MgL}{2n^{2}}

10. It is defined as the sum of kinetic energy K and potential energy U. i.e. E = K + U

11. Principle of conservation of mechanical energy: K + U = constant.