Work done by a constant force
When a force causes displacement of a body, work is done. By work we mean mechanical work, as defined in physics. We will try to help you to understand this aspect of physics. Assuming that the force causing displacement does not change during the time of moving of an object, the formal definition of work is
(1)
Work done is equal to the scalar product of
force and displacement. The dot “
” between vectors representing
force and displacement denotes a scalar product. By definition, a scalar
product is equal to
(2)
where closing the vector between “| |” denotes the magnitude of this vector. The angle α is the angle between the directions of the vectors in the scalar product. See Fig.1 for definition of the scalar product of two vectors.
From the definition of the scalar product we see that the work done by force, Equations (1) or (2), is equal to the product of the displacement by the component of force which is parallel to the displacement.
A strange conclusion can be drawn from the equation defining work. If a person carrying a very heavy backpack is walking on a horizontal road there is no work done.
The equation defining work gives us helpful advice on how to minimize work when moving an object from place to place. Always apply the force parallel to the direction of theintended motion. If the force acts at some angle to the direction of motion, only the component of the force (Fcosα) is utilized, the other component is wasted.
In the next paragraph we will discuss the work done by force which is not constant while causing displacement. This will help you more deeply understand the concept of mechanical work. This next paragraph requires some knowledge of calculus, but at a very elementary level. The problems at the end of this chapter will help you understand the definition of mechanical work. As was often pointed out, this physics tutorial is constantly growing, so visit it after a few days and you will find new chapters and new problems.