# Work

Intuitively, work is the change in an object’s state of motion that results from the application of a force; no work is performed unless the object is displaced in the same direction as the applied force. Sideway displacements do not contribute, so no work can be done by a force that is perpendicular to the displacement. When force is at an angle, only the component of force in the direction of motion must be considered. To move an object twice the distance, with the same amount of force, twice the work must be done. Likewise, if it requires twice the effort to move an object the same distance, the work performed will still be two times as much. It is therefore understandable to define work as the product of the force (F) times the distance (d).

$W=F.d \qquad \qquad(1)$

When force is at an angle, only the component of force in the direction of motion must be considered.

In SI units, force is given in newtons (N) and distance in meters (m). The work is therefore given in newton-meters (N.m) or joules (J).

Question: Which of the following represents the performance of work?

a. An apple falls off an apple tree

b. A horse pulls a carriage

c. A balloon ruptures and air rushes out

e. A boy pushes against a wall until exhausted

Answer: In each of the first three instances, a force has caused a movement in the direction of the force. In case a, the force of gravity causes the apple to fall. In case b, the horse applies a force in the direction of motion. In case c, the higher pressure in the balloon forces air out of the balloon. Instances d and e, however, do not constitute work. The force that the woman applies to the basket is upward and perpendicular to the direction of her motion. Similarly, when the boy pushes on a wall, there is no displacement and he performs no work. This might be quite confusing, as in both instances the person can become very tired. In fact, the body does continuous work to pump the blood to various organs of the body, to expand and contract various muscles in hands and feet, and force air in and out of our lungs; all of these actions serve to maintain the normal body functions. Although no mechanical work was performed in cases d and e, both the woman and boy use up a lot of chemical energy via metabolism.

Question: A boy is moving a heavy box along a hallway. If the boy wants to move the box with the smallest amount of effort (putting in the least amount of work), which approach should he choose?

a. Pull the box with a rope parallel to the floor.

b. Push the box parallel to the floor.

c. Pull the box with a rope at an angle.

d. All of the above require the same amount of effort.

Answer: The answer is d. Although the boy might be a bit more comfortable in one situation over another, the work done is exactly the same in all cases. Work is needed because of friction between the two surfaces; the amount of work is equal to the magnitude of the friction force multiplied by the distance traveled. The component of force perpendicular to the ground is not doing any work. The smart thing to do is probably to put the box on a wheeled cart or a dolly to reduce the friction.

Question: You inflate a balloon by blowing into it. Do you perform work? By how much?

Answer: Yes, you do work because you are applying a force (moving your diaphragm to push the air out) through a distance (expanding the balloon outward). The amount of work is equal to the stored elastic potential energy; that is, the amount of energy needed to stretch (deform) the balloon.

Having defined work in terms of forces and displacements, we can now turn to defining mechanical energy as the energy acquired by an object upon which work is performed. Alternatively, it can be said that an object which possesses mechanical energy is capable of doing work. Mechanical energy can be described as either kinetic energy or potential energy.

## References

(1) Toossi Reza, "Energy and the Environment:Sources, technologies, and impacts", Verve Publishers, 2005