Work, Energy and Power

The Concept of Potential Energy

In earlier classes, we defined the potential energy of an object as the energy by virtue of its height. However, here we shall see that this energy can also be a result of an objects configuration or its relative position inside a field. The concept of potential energy is basic to many branches of physics, let’s learn more!

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Potential Energy

Potential energy is basically that form of energy that’s stored in an object due to its position in comparison to a certain zero position. For example, a rock on the top of a hill has a stored energy in it. This energy is relative to its peak position that takes its form when thrown from that height. Similarly, huge ball in the demolition machine has energy stored in it when held at an elevation.

potential energy

In a nutshell, every object situated at some height, with a possibility to come back on the ground has energy stored in it. This energy is called so because it has the potential to be converted into some other form of energy. This form of energy can be converted into Kinetic energy, Mechanical energy heat and light energy etc.

Some of the other examples of this form of energy around us

  • Electricity produced from water turbines in dams is the result of energy stored in the water of reservoirs.
  • The stretched bow is also a good example of potential energy. This energy helps the arrow to move forward with greater velocity.

potential energy

Kinds of Potential Energy

The potential energy is a function of some field. Whenever there is a field of a force of some kind, any object that interacts with the force gains energy. This energy comes as a result of the interaction of the object with the force or the field. We call this the potential energy.

For example, around a mass, we have the gravitational field. Any mass in that field will experience a force and thus will have an energy associated with it. This is the gravitational potential energy. Similarly, we see the following kinds of potential energy.

Elastic Potential Energy

As the name signifies, every object that behaves like an elastic or spring is a source of elastic potential energy. The best examples are rubber bands, springs etc. These elastic objects follow the Hooke’s Law. The stretching and compressing of elastic items lead to storage of energy in the form of Elastic Potential energy.

Compression of a spring requires force, the more the compression the greater is the force. This implies that amount of force is directly relative to the amount of compression or stretch(x). The constant of proportionality here can be termed as spring constant (k). Therefore, F = k×x.

Thus the force at equilibrium position is zero because at this position the spring is neither stretched nor compressed. The following equation is used when the spring is not in an equilibrium position: F=1/2 k×x. The energy because of the work that this elastic force does is given by W = 1/2 (kx2); where the letters have their usual meaning.

Gravitational Potential Energy

We know that Earth has a gravitational force that pulls objects towards the surface. This constant attraction between Earth and the object leads to Gravitation Potential energy. This form of energy depends on the mass and height of the object. Gravitational potential energy is directly related to both mass and height.

The greater the mass the greater will be the gravitational potential energy. Similar is the case with height, an object at a higher elevation will have greater gravitational energy stored in it.

An Instance of the Gravitational Potential Energy

Suppose an object of mass M is lying at point A on the surface of the earth.  g here is the acceleration due to gravity on Earth’s surface and the force of attraction towards the center of the Earth is M*g, which equals the weight of the object. Now, If we have to move the object to B, from point A then the force that equals M*g has to be applied in the upward direction.

The amount of work done by the object at height h shall be M*g*h.This is also the gravitational potential energy stored in the object at height h. Therefore, V= M×g×h (g here is constant, 9.8N/kg). It is essential to know that the gravitational potential energy solely depends on the displacement of the object from an initial height to the final height.

Now, if the object moves upwards to height (h) then the gravitational force (F)  acting on the object is negative of P.E. So here when an object moves away from the surface we get, F = -d/dh (V) = -mg

The negative sign here denotes that as the object is moving upwards, the gravitational force is pulling it downwards. The kinematic relation here comes into play and is denoted by the change in speed when the object falls back to the ground. Here the speed of this falling object increases. Hence, v2 = 2 gh or (1/2) mv2 = mgh

Energy as a Negative Constraint

This denotes that the potential energy of the object of mass m at a height h converts into kinetic energy as soon as it falls on the ground. As the force acting on an object situated at a height is against the gravitational force from earth, the potential energy in that object behaves as a negative constraint.

But this energy by virtue of heigh becomes a positive constraint as soon as the object reverts to the ground. Potential energy  (V) further, for a force F (x)  is:

∫ F(x) dx = – ∫VdV = Vi – Vf  [ here F(x)= – dV/dx ]. Vi is the initial value of the potential or the value of the potential at the initial position and Vis its value at the final position. The distance between the two points is irrelevant here as gravity depends only on the initial and final positions of the object.

The potential energy stored in an object has dimensions ML2T-2  and the unit here is Joule or J. This is similar to Kinetic energy or work and the change in Potential energy with respect to the conservative force acting on it is the negative of the total work done by that force. Therefore, Δ V = -F(x)Δx

Chemical Potential Energy

The attractive force between two atoms forms a chemical bond. This bond between atoms and molecules results in storage of energy in the form of Chemical potential energy.The potential energy during chemical bonds and reactions converted into heat and light. The normal batteries and cells are the best examples of Chemical Potential energy.

Solved Example For You

Q: A body is falling from a height h. After it has fallen a height h/2, it will possess

  1. only potential energy
  2. only kinetic energy
  3. half potential and half kinetic energy
  4. more kinetic and less potential energy

Solution: (c) At height h the K.E of the object is 0 while P.E is mgh. At height h/2 the P.E becomes mgh/2 while the other half of P.E is converted into K.E due to the virtue of its motion. So mgh – mgh/2 = mgh/2. Hence, the body has half its energy in the form of potential energy and the other half is in the form of kinetic energy

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