Chapter 5: Work, Power, and Energy
5.1 Work: The Scientific Definition
Authors: Paul Peter Urone, Roger Hinrichs
Adapted by: Rob Pryce, Alix Blacklin
Learning Objectives
By the end of this section, you will be able to:
- Explain how an object must be displaced for a force on it to do work.
- Explain how relative directions of force and displacement determine whether the work done is positive, negative, or zero.
What It Means to Do Work
The scientific definition of work differs in some ways from its everyday meaning. Certain things we think of as hard work, such as writing an exam or carrying a heavy load on level ground, are not work as defined by a biomechanist. The scientific definition of work reveals its relationship to energy—whenever work is done, energy is transferred.
For work, in the scientific sense, to be done, a force must be exerted and there must be displacement in the direction of the force.
Formally, the work done on a system by a constant force is defined to be the product of force times distance. More specifically, it is the product of the component of the force in the direction of motion times distance through which the force acts. For one-way motion in one dimension, this is expressed in equation form as
where [latex]W[/latex] is work and [latex]\mathbf{d}[/latex] is the displacement of the system.
Similar to other equations involving force, if the force is not acting in exactly the same direction of motion (collinear), then we can determine the component of the force that acts in direction of motion (as [latex]Fx = \mathbf{F}*\text{cos}\theta, where [latex]\theta[/latex] is the angle between the force vector [latex]\mathbf{F}[/latex] and the displacement vector [latex]\mathbf{d}[/latex], as in the figure below).
So, we combine the above formulas and write work as:
To find the work done on a system that undergoes motion that is not one-way or that is in two or three dimensions, we divide the motion into one-way one-dimensional segments and add up the work done over each segment.
What is work?
The work done on a system by a constant force is the product of the component of the force in the direction of motion times the distance through which the force acts. For one-way motion in one dimension, this is expressed in equation form as
where [latex]W[/latex] is work, [latex]F[/latex] is the magnitude of the force on the system, [latex]d[/latex] is the magnitude of the displacement of the system, and [latex]\theta[/latex] is the angle between the force vector [latex]\mathbf{F}[/latex] and the displacement vector [latex]\mathbf{d}[/latex].
To examine what the definition of work means, let us consider the other situations shown in the figure above. The person holding the briefcase in Figure 7.2 (b) above does no work, for example. Here [latex]d=0[/latex], so [latex]W=0[/latex]. Why is it you get tired just holding a load? The answer is that your muscles are doing work against one another, but they are doing no work on the system of int