Work Done in Piling Blocks Problem and Solution

Each identical block when placed on the earth, has some potential energy. Potential energy is the energy possessed by the body by virtue of its position. As the block has distributed mass, we shall consider a point where its mass is concentrated and the point of a body which represents its motion is called center of mass. For regular bodies center of mass is at its geometrical centre. So if the block is having a side a , its center of mass will be at a/2 .

We would like to keep one block over the other block, like constructing a flat wall. We need to do some work in lifting the blocks one over the other. After doing this work, the blocks are arranged like a wall. Any way the work done by us in piling the blocks can not disappear. As per the law of conservation of energy, this work done shall be converted into potential energy stored in the system.

So, if we measure the potential energy of the system after piling the blocks together, that itself will we work done.

Initial potential energy of the system is potential energy of one block multiplied by number of blocks as all blocks are identical.

We can identify the new center of mass of the system as the half of the total height of the new system. Hence it will have a different potential energy as shown.

Work done is the difference in the final potential energy and the initial potential energy of the system.

It is show in detail in the following video.