# Meaning of point of application

Work is done when an applied force displaces the point of application in the same direction as the force. I don't understand this definition. The point of application is defined as the point at which the force is applied to a body. So doesn't this point remain unchanged if the force is applied to the same point. Could point of application mean the point at which the force is applied in space?

• An ice skater applies a force $F$ to a wall. Per Newton’s third law the wall exerts an equal and opposite force $F$ to the skater. As a result the skater accelerates away from the wall acquiring kinetic energy. Has the wall done work on the skater? Commented Aug 3 at 0:56

Work is defined as $$dW=\vec{F}\cdot\vec{dr}$$ or $$W=\int_{r_1}^{r_2}\vec{F}\cdot\vec{dr}$$ Now ig you are getting confused that point at which force is being applied is not changing, but let's take perspective of a person at origin. For him he will solve the above integral, to find the work done.

But the person who sitting on the particles POV, he will see that he is at rest while person at origin is going away with pseudo force, and he will calculate zero work done since according to him he is at rest.

Remember that work done is frame dependant.

For many classroom problems, the point of application is a distraction. It is ignored.

Two people grab the same handle on a a long rectangular mass and pull equally hard in opposite directions. If you apply equal and opposite forces to an object, the object is unaccelerated. This result is the same as if no forces were applied.

Sometimes it does matter. Suppose they grab handles on opposite ends of the mass. The object will rotate to line up with the direction they are pulling. The object as a whole is still unaccelerated. But the effect isn't the same as the first case. See Toppling of a cylinder on a block for more on this.

Perhaps an example would be helpful.

An ice skater applies a force $$F$$ to a wall. Per Newton’s third law the wall exerts an equal and opposite force $$F$$ to the skater. As a result the skater accelerates away from the wall acquiring kinetic energy. Has the wall done work on the skater? The answer is no.

Although the wall applied a force to the skater and the skater acquired kinetic energy, the wall did no work on the skater. That’s because there was no displacement of the skater’s hands at the point of application of the force while the force was exerted by the wall.

The kinetic energy acquired by the skater is the result of conversion of chemical potential energy of the muscles in the skater’s arms to kinetic energy of the skater’s body as a whole. A mechanical analogy is a mass attached to a spring initially pressed against a wall compressing the spring. The mass is released acquiring kinetic energy from the elastic potential energy stored in the spring. The wall does no work.

Hope this helps.