Work is a fundamental principle of particle dynamics and is the transfer of energy between a force and its displacement. In its simplest form, when the force is aligned with the direction of motion, the work is equal to the product of the force strength and the distance traveled. However, this is not the case for all forces, and work can be negative or zero in some cases. Work can change the potential energy of a mechanical system or can be used to transform thermal or electrical energy. It can also be a form of energy stored in a battery, or it can be transferred from a source to an object or vice versa.
The concept of work is often confusing because it is a scalar product, while both force and displacement are vectors. This is why it is sometimes referred to as the dot product in high school vector algebra class. The dot product is a value between two vectors that can only take on values of 0 or 1.
A force that does no work on an object is called conservative, while one that does work is known as a non-conservative force. The work done by a conservative force is equal to the change in the potential energy of the object, whereas the work of a non-conservative force is equal to the object’s kinetic energy.
Unlike other types of energies, work can be positive or negative, depending on the direction of the displacement with respect to the force. The work done by friction is a negative value, while the work of gravity is a positive value, because it is an upward force on an object that is displaced downwards.
The work done by a force F on a point that travels along a curve C is given by the line integral W =
In many cases, this is the same as the Newtonian equation of motion. For example, a baseball pitcher can do work on the ball by throwing it down and lifting it up. The amount of work done is equal to the force of the pitching arm multiplied by the displacement of the ball, which is up. Conversely, if the baseball is dropped by itself and it falls to the ground, the gravitational force will do no work on the ball because it is falling down at an angle perpendicular to the force of gravity. However, if the gravity pulls down on the ball and it moves up, then the force of gravity will do work on the ball. The sum of the total work that an object does during its entire trajectory is its cumulative energy. This can be measured in units such as the newton-metre, erg, the foot-pound, the watt-hour and the calorie. However, this type of measurement is not commonly used because it can be misleading and inaccurate.