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Energy read
- 1. Energy Ability to dowork is energy. If work is done on the body, energy of the body increases. If work is done by the body, energy of the body reduces. A cyclist pedals the cycle and does work on cycle, so energy of cycle and cyclist increases. If Breaks are applied to a vehicle in motion, work is done by vehicle against the force of friction. So, energy of the vehicle decreases. Thus when work is done, there is exchange of energy. Work is a process. Body cannot possess 'work', it can possess energy. Unit of energy is also joule. There are many types of energy, out of which we will study kinetic energy and potential energy. Kinetic Energy Suppose a person tries to hit you with a bullet, held in his hand. Another person tries to fire a bullet from his gun. In which case you would be hurt more ? It is obvious that you are more hurt by bullet fired from gun, as its speed is more, and so it hurts more. Why is it, so ? It is clear that the bullet having more speed has more energy. Thus, energy associated with motion is called kinetic energy. Ability of a body to do work due to its motion is called kinetic energy. There are two ways to measure kinetic energy of a body moving with velocity v. (1) A body moving with velocity v, becomes stationary after some time, if force is applied opposite to its motion. We can calculate work done during this time and calculate kinetic energy. (2) Work required to be done to make a stationary body, move with velocity v, gives the value of kinetic energy acquired by it. In this context, work done by a vehicle moving with some velocity v, when brakes are applied, during the time in which its velocity reduces to zero, can be calculated. It is clear that if magnitude of v is more, work done will be more. So, higher the speed, more will be the kinetic energy. So, now let us obtain an expression for kinetic energy. Suppose a body of mass m is lying stationary on a frictionless horizontal surface. When a force F acts on it, in time t, it undergoes a displacement s, and acquires velocity v. If work done during the process s W, w = F X s
- 2. But F =m a :. W = ma x s Also V2 - U2 = 2as and taking initial velocity u = 0, we get V2 = 2 a s Therefore as = 1/2 V2 So work done from above equation is, W =1/2 mV2 This equation shows that energy to be given to a stationary body of mass m, so that it can move with velocity v, is 2nv 2 , which results into its kinetic energy. Thus, kinetic energy (K) of a body of mass m moving with velocity v can be given by K= 1/2 mV2 In this context when force F acts on a body moving with initial velocity u if the body acquires velocity v during displacement s then work done W = F X s W = mas = m (1/2 V2 - 1/2 U2 ) ( V2 - U2 = 2 as) W = ½ mV2 - ½ mU2 Thus, when work is done, there is change in kinetic energy of a body. Gravitational Force Path of Moon
- 3. Now consider thecase of uniform circular motion. Since its speed is constant (v = u). Thus, hange in its kinetic energy is zero. So, work is also zero. Also centripetal force is perpendicular to displacement. So, work is zero. Example 1 - A ball of mass 200g is moving with speed 27 km/h. Calculate its kinetic energy. Solution:- m = 200 g = 0.2 kg, v = 27 km/h =27x1000/3600 m/s = 7.5 m/s Kinetic Energy K = ? K= ½ mV2 =1/2 * 0.2* (7.5)2 = 5.625 J Example 2. Kinetic energy of a car, having mass 1000 kg, is 1,12,500 J. Driver applies brakes when an obstacle is sighted, and car comes to halt after travelling 100m distance. (Without meeting with an accident) Calculate frictional force. Solution Here work = F s Initial kinetic energy K0 = 1,12,5001, mass m = 1000 kg, Final kinetic energy K = 0 Distance s = 100 m Work W = F s and W = K - Ka .. Fs=K-K0 =0-Ka .. F(lOO) = 0 - 1,12,500 .. F = -1125N Work W = change in K.E = K - K0 Here force and displacement are in opposite directions, so force is negative.
- 4. Potential Energy Ability ofa body to do work due to its position or configuration is known as potential energy of the body. The concept of potential energy is very important for the force fields like gravitational field, electric field and magnetic field. Here we will discuss the potential energy of a substance kept in the gravitational field (gravitational potential energy) only. Generally potential energy is always mentioned along with reference point. This means that potential energy is relative. It is impossible to find the absolute value of potential energy. Also changes in potential energy are more important rather than its absolute value. Generally at reference point potential energy is taken to be zero. Potential Energy of an object can be negative also. In which condition Think!!! Activity : Take an object of 5 kg mass and another object of 10 kg mass. First take the object of 5 kg mass to 1m, 2m and 3m height. In which case you have to do more work ? Now try to take both the objects to 5m height. For which object you have to do more work ? Where does the energy spent in doing this work go ? You must have understood, from the activitygiven above, that when a body is taken to a height we have to do work against the gravitational force and to do this work we have to spend energy which is stored in the object in form of potential energy. Value of the potential energy depends on gravitational force acting on a body (gravitational force acting on a body with larger mass is more) and height. Now let us put this fact in the form of a formula. Suppose as shown in the figure, potential energy at reference level is zero. Now on applying a force, having magnitude equal to the gravitational force acting on it, in the opposite direction, it is moved with constant velocity to a height h. Work done in this case is W = force x displacement As magnitude of applied force is equal to magnitude of gravitational force. Force = mg
- 5. Work = mgh Energy spent in doing this work is stored in the body in form of potential energy, so potential energy at height h from the reference level can be given by the following formula. U = mgh Also this gravitational potential energy depends on the height from the reference level.