Physics > Work Energy and Power > 6.0 Potential energy $\left( {\Delta U} \right)$
Work Energy and Power
1.0 Introduction
2.0 Work done by a constant force
3.0 Spring Force
4.0 Conservative & Non-conservative forces
5.0 Kinetic Energy $(K)$
6.0 Potential energy $\left( {\Delta U} \right)$
6.1 Potential energy $\left( {\Delta U} \right)$ is negative of the work done by conservative forces.
6.2 Types of potential energy
6.3 Law of conservation of mechanical energy
7.0 Work energy theorem
8.0 Power
9.0 Types of equilibrium
10.0 Work done by a distributed mass
6.3 Law of conservation of mechanical energy
6.2 Types of potential energy
6.3 Law of conservation of mechanical energy
The total mechanical energy of a system remain constant if only conservative forces are acting on a system of particles and work done by all the other forces is zero. This is called law of conservation of mechanical energy.
Mechanical energy is the energy associated with the motion and position of the particle. It is defined as the sum of kinetic energy and potential energy of the particle at any instant.
Example: Let us assume a ball starts rolling down a frictionless incline wedge.
- At the highest point potential energy $(PE)$ is maximum and the kinetic energy $(KE)$ is zero.
- As we know that only conservative force (i.e. gravitational force) acts on the system.
- So, the law of conservation of mechanical energy holds good.
- Therefore, when the ball reaches the bottom of incline wedge, the potential energy is converted into kinetic energy.
- Since the bottom of the incline wedge is chosen as a reference, so the potential energy $(PE)$ at the bottom of the wedge is zero.
- At the lowest point potential energy $(PE)$ is zero and the kinetic energy $(KE)$ is maximum.
Examples
- Swinging pendulum
At position 1, the potential energy is maximum and the kinetic energy is zero as the velocity at this position is zero.
At position 2, the potential energy is minimum and the kinetic energy is $\frac{1}{2}m{v^2}$. Since the total mechanical energy is conserved. Therefore, the potential energy is converted into kinetic energy.
At position 3, the potential energy is maximum and the kinetic energy is zero as the velocity at this position is zero. Since the total mechanical energy is conserved. Therefore, the kinetic energy is converted into potential energy.
- Rollercoaster
The rollercoaster is an amusement ride. The car is not self-powered. They are pulled upto the maximum height (i.e. at position $A$).
(a). At position $A$, the potential energy $(PE)$ is maximum.
(b). As the car race down along the track, the accumulated potential energy $(PE)$ is converted into kinetic energy $(KE)$.
(c). We assume that the friction (non-conservative force) does not act between car and track. Therefore, the law of conservation of mechanical energy holds good.
(d). When the car reaches the bottom, the potential energy becomes minimum and the kinetic energy $(KE)$ becomes maximum.
