As shown in figure we have two objects , 1 and 2 . Each have a mass of 10 kg and height 1 meter. Suppose i lift object 1 to a height 1 meter. The energy required to lift object 1 is E= mgh ( m is mass, g is gravity , h is height ) E= 10×9.81×1 So E= 98.1 j. Now potential energy of this object is PE= mgh , = 10×9.81×1 so PE = 98.1 j. This shows that the energy required to lift the object upto any height is equal to the potential energy of that object at that height.
But , depending on height of the object and our consideration , there may be a difference between , the energy required to lift the object and the potential energy gain of that object. To understand this , now we talk about object 2. Object 2 has 10 kg mass and 1 meter height. Now suppose and consider that object 2 has two parts , A and B as shown in figure , mass of A is 5 kg and height 0.5 meter , mass of B is 5 kg and height is 0.5 meter. So together mass is 10 kg and height is 1 meter.
Now i lift object 2 upto 1 meter . As the mass of both objects ( 1 and 2 ) is same , the energy required to lift object 2 is also 98.1 j. Now we calculate the potential energy of object 2 considering the two parts A and B.
PE of B = mgh= 5×9.81×1= 49.05 j
PE of A ,
part A is on and above part B , the height of part B is 0.5 meter , so the total height for part A is 1+0.5 = 1.5 meter.
So PE of A= mgh= 5×9.81×1.5= 73.575 j.
So the total potential energy of object 2 = PE of A+PE of B = 122.625 j.
So from above calculations.
Energy required to lift object 1 = 98.1 j
Potential energy of object 1 = 98.1 j
Energy required to lift object 2 = 98.1 j
Potential energy of object 2 = 122.625 j
So in case of object 2 , the potential energy gain is more than the energy which was required to lift this object. It means that if any object is at any height , and if we assume and consider that object in parts , then it's potential energy is always more than the energy which was required to lift that object to that particular height.
So here we can see the violation of energy conservation.
Does it means that , by this way the law of conservation of energy is violated ?