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Learn how work is defined in physics as the product of force and displacement, and how it depends on the angle between them. Find out the SI unit of work, examples of work and energy, and frequently asked questions.
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Sep 23, 2024 · Work is the measure of energy transfer when an object is moved by a force. Learn how to calculate work, its units, and its applications in physics.
- The Editors of Encyclopaedia Britannica
Work is the energy transferred by a force along a displacement. Learn how to calculate work, its units, its history and its applications in physics.
- Overview
- What does energy and work mean?
- How do we measure energy and work?
- How long do I have to push a heavy box around to burn off one chocolate bar?
- What if we aren't pushing straight on?
- What about lifting weights instead?
- What about simply holding a weight stationary?
Here we learn what work and energy mean in physics and how they are related.
Energy is a word which tends to be used a lot in everyday life. Though it is often used quite loosely, it does have a very specific physical meaning.
Energy is a measurement of the ability of something to do work. It is not a material substance. Energy can be stored and measured in many forms.
Although we often hear people talking about energy consumption, energy is never really destroyed. It is just transferred from one form to another, doing work in the process. Some forms of energy are less useful to us than others—for example, low level heat energy. It is better to talk about the consumption or extraction of energy resources, for example coal, oil, or wind, than consumption of energy itself.
•A speeding bullet has a measurable amount of energy associated with it; this is known as kinetic energy. The bullet gained this energy because work was done on it by a charge of gunpowder which lost some chemical potential energy in the process.
•A hot cup of coffee has a measurable amount of thermal energy which it acquired via work done by a microwave oven, which in turn took electrical energy from the electrical grid.
In practice, whenever work is done to move energy from one form to another, there is always some loss to other forms of energy such as heat and sound. For example, a traditional light bulb is only about 3% efficient at converting electrical energy to visible light, while a human being is about 25% efficient at converting chemical energy from food into work.
The standard unit used to measure energy and work done in physics is the joule, which has the symbol J. In mechanics, 1 joule is the energy transferred when a force of 1 Newton is applied to an object and moves it through a distance of 1 meter.
Another unit of energy you may have come across is the Calorie. The amount of energy in an item of food is often written in Calories on the back of the packet. A typical 60 gram chocolate bar for example contains about 280 Calories of energy. One Calorie is the amount of energy required to raise 1 kg of water by 1∘ Celsius.
[Wait, why are we using kilograms here instead of grams?]
This is equal to 4184 joules per Calorie, so one chocolate bar has 1.17 million joules or 1.17 MJ of stored energy. That's a lot of joules!
Suppose we're feeling guilty about eating a chocolate bar; we want to find how much exercise we need to do to offset those extra 280 Calories. Let's consider a simple form of exercise: pushing a heavy box around a room, see Figure 1 below.
Using a bathroom scale between ourselves and the box, we find that we can push with a force of 500 N. Meanwhile, we use a stopwatch and measuring tape to measure our speed. This comes out to be 0.25 meters per second.
So how much work do we need to do to the box to burn off the candy bar? The definition of work, W , is below:
W=F⋅Δx
The work we need to do to burn the energy in the candy bar is E=280cal⋅4184J/cal=1.17MJ .
Therefore, the distance, Δx , we need to move the box through is:
There is one thing we need to watch out for when doing these problems. The previous equation, W=F⋅Δx , doesn't take into account situations where the force we are applying is not in the same direction as the motion.
For instance, imagine we use a rope to pull on the box. In that case there will be an angle between the rope and the ground. To untangle this situation, we begin by drawing a triangle to separate out the horizontal and vertical components of the applied force.
The key point here is that it is only the component of the force, F|| , that lies parallel to the displacement that does work on an object. In the case of the box shown above, only the horizontal component of the applied force, Fcos(θ) , is doing work on the box since the box is being displaced horizontally. This means that a more general equation for the work done on the box by a force at an angle θ could be written as:
W=F||⋅Δx
W=(Fcosθ)⋅Δx
Which is more often written as,
In the previous example, we were doing work on a box which we were pushing around a floor. In doing so, we were working against a frictional force.
Another common form of exercise is lifting weights. In this case we are working against the force of gravity rather than friction. Using Newton's laws we can find the force, F , required to lift a weight with mass m straight up, placing it on a rack which is at a height h above us:
F=mg
The change in position—previously Δx —is simply the height, so the work, W , that we have done in lifting the weight is then
W=mgh
The exercise we have done in lifting the weight has resulted in energy being stored in the form of gravitational potential energy. It is called potential energy because it has the potential to be released at any moment with a crash as the weight falls back to the ground.
One frequent source of confusion people have with the concept of work comes about when thinking about holding a heavy weight stationary above our heads, against the force of gravity. We are not moving the weight through any distance, so no work is being done to the weight. We could also achieve this by placing the weight on a table; it is clear that the table is not doing any work to keep the weight in position. Yet, we know from our experience that we get tired when doing the same job. So what is going on here?
It turns out that what is actually happening here is that our bodies are doing work on our muscles to maintain the necessary tension to hold the weight up. The body does this by sending a cascade of nerve impulses to each muscle. Each impulse causes the muscle to momentarily contract and release. This all happens so fast that we might only notice a slight twitching at first. Eventually though, not enough chemical energy is available in the muscle and it can no longer keep up. We then begin to shake and eventually must rest for a while. So work is being done, it is just not being done on the weight.
Learn how work is defined in physics as the product of force and displacement in a given direction. See examples, diagrams, and equations for calculating work in one-dimensional and multi-dimensional motion.
Learn how work is a measure of energy transfer using force and displacement, and how to calculate it with a simple formula. Explore the history, types, and units of work in physics, and see examples and FAQs.
Work is the energy transferred by a force when it acts on something that moves. Learn how to calculate work for different forces and paths, and see examples of work in physics.
