If a duster is left on the top of the chalkboard, it is said to possess kinetic energy.

In the above diagram, we move by horizontally with a velocity to the right. But due to gravity the hand falls a distance as we move .

Therefore the time it takes to fall by a distance is given by =.

If = as →∞, then from the laws of motion

=12()22

Therefore for the whole journey from left to right our muscle has to give a beat up at an amount equal to the gravity force. So, the work supplied by the muscle for one trip would be

∫=∫012()22

A man is going to rub the chalk off a blackboard, he is going to choose a way to rub off the chalk in two ways

Starting from the upper left corner of the board and moving horizontally to the right and moving slightly down and then again moving to the right and then when it reaches the left corner and so on

The second way is given in the following: He starts at the top and rubs down and then up again and so on.

He is going to choose the way that is less tiring in his arms. i.e., less work done by his muscles!

Somehow from vague intuitive notion I am inclined to agree that it would be less tiring to rub off the chalk if he moves the duster beginning at the top and rubbing horizontally and gradually decreasing the height when one reach the corners till everything is off.

I tried to calculate the muscle work by considering the following ideas(please correct me if I'm wrong):

The nerves inside our muscle has to fire its signal continuously throughout the entire interval of the process of rubbing and its has to oppose the gravitational force keeping the hand up the air.

When the hand is at the highest point on the blackboard, the muscle has to work against gravity =, as the muscle continues to work against gravity throughout the interval from left to right (the horizontal path of the first case) I couldn't find the total work withstood by our muscle.