Understanding Conservative and Non Conservative Forces

Shuddhodan Sapre
20 Apr 0 0

While teaching my students, I found them to fumble in this topic, so I am writing this lesson to tell you all in simple terms what the topic is:
Consider two cases in both cases; a block moves from A to B point and back.
Let's say a block is pushed from point A on a rough surface with a velocity V and the block goes to point B. While this is happening, let's say only frictional force acts on the block towards A. We can see that the block is being slowed down by friction, or in other words, the force is reducing the kinetic energy of the block. Now when this block reaches B, it stops, and friction stops acting. Now you need to think about where did the kinetic energy of the block GO?
Now take case 2; let's say the block has a spring attached, and now it is pushed from A to B but on a smooth surface with no friction. So only the spring force acts and pulls the block backwards towards A. So the spring force is reducing the speed of the block like friction is reducing the kinetic energy. The block reaches B and stops. At this moment, where did the kinetic energy GO?
If you compare both the cases and think about the kinetic energy disappearing, we find something interesting happening. We know that when we rub our palms, heat is produced because of friction. Similarly, in the first case, heat is produced, which might be very small in amount but is produced, and it is transferred on the block and on the floor, which eventually cools. The energy is dissipated or lost in the surrounding, never to come back. So the KE is lost in the form of heat due to friction. Hence the block stops since it has no more energy and cannot return to point A unless someone pushes it again.
If you consider the spring and what happens to the block after reaching point B, we see the block is pulled by the spring back towards A. This happens when the block stops just for an Instant. Now, where did the spring get the energy to pull the block? Wolla! It's the same Kinetic Energy that the block had. So as the block. Slowed down, its kinetic energy started to get stored in the molecular bonds of the spring in the form of elastic energy. And this energy was again given back to the block as kinetic energy. So you might be thinking, when the block reaches A, does it get all of its KE back, and the answer is Yes.
Such force like friction which removes energy and doesn't give it back is a Non-conservative force; as the name suggests, it doesn't Conserve the initial energy, but a force like spring force keeps on exchanging energy unless someone stops the block. Hence this force is called Conservative Force since it is conserving or not losing any energy.
You can apply the same logic of moving the block and checking the behaviour of the forces.
Now you try on the following forces:
1) Electrostatic Force.
2) Viscous Force.
3) Gravitational Force.
Conservative Force: 1,3.
Non-Conservative Force: 2.

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