Energy conservation

The total energy of a system is always constant. This means that energy can neither be created nor destroyed; it can simply be transformed from one form into the other. This is called the energy conservation principle. 

One simple example is the conservation of mechanical energy of a freely falling object. Imagine that an object of mass m is dropped from the top of a tower of height h. If we consider the bottom of the tower to be at zero level of potential energy, the object has a potential energy of mgh at the top of the tower. Here g is the acceleration due to gravity and its average value is 9.81 meters per second per second on the surface of the earth. The initial kinetic energy,  (1/2) m v^2,  of the object is zero because it is at rest  (v =0)  at that instant. Therefore, the total mechanical energy of the object is  mgh. Once it starts falling, its height from the bottom of the tower goes on decreasing and hence the potential energy of the object goes on decreasing. On the other hand, since the object is accelerating downwards, its velocity v goes on increasing, and hence its kinetic energy goes on increasing. At the bottom of the tower, the potential energy of the object is zero and the total energy of the object is its kinetic energy at this instant. By simple kinematics, we can show that the total energy is equal to  mgh at each point of the trajectory of the object. 

Test yourself

(1) A block of mass 5 kg is dropped from the top of a 10 meter tall tower. Calculate its potential energy at the top of the tower. Predict its velocity at the bottom of the tower using the formulas of kinematics. Then calculate the kinetic energy of the block at the bottom of the tower. Check whether the kinetic energy at the bottom of the tower is equal to the potential energy at the top of the tower.