Kinetic and Potential Energy (Physics) PDF

## 6.2.1 Kinetic Energy The energy possessed by a body due to its motion is called kinetic energy. A moving bullet is able to do work by overcoming forces when it strikes something e.g. wood. Similarly kinetic energy is felt during a collision. A football is kicked by a boy - it moves because...

## 6.2.1 Kinetic Energy The energy possessed by a body due to its motion is called kinetic energy. A moving bullet is able to do work by overcoming forces when it strikes something e.g. wood. Similarly kinetic energy is felt during a collision. A football is kicked by a boy - it moves because it possesses kinetic energy. Now think: a tennis ball and a football moving with the same speed. Which possesses greater ability to do work? Of course, it is the football with larger mass, which is difficult to stop. Similarly, now two footballs are approaching you with different speeds, which can do more work? Again, it is easy to answer as the football with greater speed is difficult to stop. Therefore the object's mass and its speed contribute to its kinetic energy. Like all energies, kinetic energy is also a scalar quantity. Consider a constant force 'F' is acting on an object of mass 'm' and as a result the object moves on a frictionless surface. The kinetic energy of an object will be equal to work done. The work done on the force-displacement graph can be calculated by finding the area of the figure under the force-displacement graph as shown in figure 6.2. **Change in kinetic energy (Ex) = Work done = F.d** **Work done = area under force displacement graph** Therefore the area under the force displacement graph is the area of a rectangle, thus: **Change in kinetic energy (E₁) = Area of rectangle = width x length = (F)(d)** Or **Ex = (ma)(vavt)** Where: **Vave = (V; + Vf)/2** As the speed is increasing its velocity from Vi = 0 to Vf = v, therefore the average speed Vave is: **Vave = (0+V)/2 = V/2** And acceleration can also be written as: **a = (Vf-Vi)/t = V/t** Substituting equation 2 and equation 3 into equation 1, we get: **Ex = m(V/t)Vt = (1/2)mv²** ## 6.2.2 Potential Energy The energy possessed by a body by virtue of its position (in a force field or in configuration) is called potential energy. Consider the work you do on a book when you lift it from the floor and place it on the top shelf. The work you did on your book is now stored in the book by virtue of its position. ## Work and Energy By doing work against the force of gravity, you have given your book a special form of potential energy called gravitational potential energy (figure 6.4). If you release the book from the top shelf, it will accelerate, gaining kinetic energy, thus gravitational potential energy is released and has the ability to do useful work. Gravitational potential energy is only one of several forms of potential energies. For example, doing work on an elastic spring by stretching it stores elastic potential energy in the elastic spring (slingshot, shock absorber, winding spring in toys and watches are all examples of elastic potential energy). Chemical potential energy is stored in the food you eat. A battery contains both chemical and electro-chemical potential energy during working of the battery. Similarly, in a capacitor, which consists of two conductive plates with opposite charges, the electrostatic potential energy is stored in the electric field between the plates. **Mathematically, Gravitational potential energy is the product of mass 'm', the acceleration due to gravity 'g', and the change of height 'h'.** **Ep,grav = mgh** Like all energies potential energy is also a scalar quantity. For example, if we lift a stone of mass 5Kg from the ground to 20m high, the work is done against the force of gravity - this work appears as 980J of potential energy. Consider an object of mass 'm' being lifted vertically by a force 'F' to 'h' as shown in figure 6.6. The work done by the force F is given by the equation: **W = Ep,gray = FS** (1) Since the force in this case is equal to its weight: **F = W = mg** (2) Here the distance moved is the height 'h'. **S = h** (3) Substituting equation 2 and 3 into equation 1, we get: **Ep,gray = mg ×h = mgh** (6.3)