U NIT II- M ECHANICAL E NERGY

W ORK When a force acts upon an object to cause a displacement of the object, it is said that work was done upon the object. If there is no applied force there will be no work done. In order for a force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement.

Work does not depend on the path taken. Equivalent amount of work done. The work done on the briefcase while walking up the stairs or going up the escalator is the same since they have the same applied force and displacement.

A RE THE FOLLOWING S TATEMENTS R EPRESENT W ORK BEING DONE ? A teacher applies a force to a wall and becomes exhausted. A book falls off a table and free falls to the ground. A rocket accelerates through space.

Work can be calculated mathematically or graphically. Mathematically: where F is the force, d is the displacement, and the angle ( theta ) is defined as the angle between the force and the displacement vector.

The SI unit for work is the Joule (J). One joule is the amount of work done when an applied force of one newton produces a displacement of one meter. 1 J = 1 Nm An alternative unit for work is the kWh: 1kWh = 3.6MJ [3.6 Million Joules]

A N E XAMPLE

N EGATIVE WORK In such instances, the force acts in the direction opposite the objects motion in order to slow it down. The force doesn't cause the displacement but rather hinders it. These situations involve what is commonly called negative work. Since the force vector is directly opposite the displacement vector, theta is 180 degrees. The cosine(180 degrees) is -1 and so a negative value results for the amount of work done upon the object.