Work and Power – Definition and Formula
Every day of your life you move through systems of power and that these powers make you perform your work. So, are work and power interrelated concepts? Are they interdependent on each other for their functioning? When you see two weightlifters, lifting the rings you will see both are performing the same work but their speed might differ. So what is that which makes them work at a different speed? All your questions will be answered by the end of this article. The faculties have compiled this important concept of physics in this article and try to make you understand them in a simple way.
In this particular article, we shall be learning about the following concepts -
Wok and power - an introduction
What is work?
What is power?
Difference between work and power
Fun facts
Frequently asked question
Let's get started!
What is Work?
Most often, you use the term ‘work’ to express doing some task. It can be either reading a book or sitting at your work-station to complete a job on the computer. However, the scientific term work done is not related to the stationary task. Science defines work as a task done when a force acts upon a body that produces displacement in it. In simple words, work is not complete until and unless force is applied, which moves an object. The standard unit of work is the Joule denoted as (J). You can define one Joule of work done as the amount of work done when 1 Newton of force brings about a displacement of 1 meter in the direction of the applied force.
You can measure the work you do as positive, negative, or zero.
Work done is positive when the direction of force acting on the object and displacement of the object both are in the same direction. For example: Kicking a ball Work done is negative when the direction of force acting on the object and displacement of the object are in the opposite direction. The angle between displacement and force is 1800. For example, work is done by gravity on a ball thrown in the upward direction.
Work done is zero, when the direction of the force acting on the object and displacement of the object are perpendicular to each other. The angle of displacement and force is 900. For example, work is done by gravity when a box is moving horizontally.
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Power
The scientific definition of power is the rate of doing work. Power is the energy you need to displace an object in a given time. You need the energy to stop a moving object, raise an object against gravity, or move an object having a certain velocity. In simple language, power is the proportion of work done in one unit of time. The standard unit of measurement of power in Watts and kilowatts is denoted as (W) and (kW) respectively. You can define one Watt as 1 Joule of work done per second. It means that when a body works at the rate of 1 Joule (J) per second, then its power becomes 1 watt, (W).
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Formula: Difference Between Power and Work
Now, let us look at the formulas that differentiate work from power.
Total Work Done (W) = Power (P) x Time (t)
Or
Work = Force x Displacement cos (Fd cos )
(Here, is the angle between force and displacement)
Power (P) = \[\frac{\text{Total Work Done (W)}}{\text{Time(t)}}\]
It would be easy for you to distinguish between work and power when you study the difference between work and power in tabular form.
Work and Power Difference in Tabular Form
Fun Facts on Work and Power
If you are kicking a ball, your work done is positive.
If you are sitting in the classroom, listening to lectures, the work done is said to be zero.
Industries, households, commercial establishments use 1 Kilowatt(kW) of power.
Force and displacement are both vector quantities, but their dot product gives work done, which is a scalar quantity.
FAQs on Work and Power
1. How can you tell the Difference Between Work and Power?
You can say that work is done when it satisfies two essential conditions. Firstly, force should act on the body. Secondly, the body should move in the direction of the force applied, or it should move in the opposite direction. In other words, the object must change its place. For example, a lady moves a bucket of water from the kitchen to the bathroom. Here, she applies force to the bucket and the place of the bucket changes position from the kitchen to the bathroom. Thus, work is equal to the product of force and distance of the bucket from the kitchen to the bathroom. Power is the energy the lady requires to move the bucket from one place to another in the given time.
2. Do you Think a Porter Does any Work When he Walks Horizontally Carrying a Suitcase from One Place to Another on his Head?
No, the porter does not do any work when he walks horizontally carrying a suitcase from one place to another on his head. The displacement is along the horizontal line and the force applied is perpendicular to the displacement. Don’t forget that work also depends on the angle between the force and displacement. The angle between the two, in this case, is 90 degrees.
cos 900 = 0
W = Fd cos
Thus, W=0.
However, if the porter pushes or pulls the suitcase from one place to another, work is said to be done. The angle between the displacement and force here is 00.
cos 00 = 1
Thus, W = Fd.
3. What exactly is work done in physics?
In physics, the meaning of work done is very well defined which sets it apart from the layman's understanding of the word. It is the force applied and a displacement involved in the process then the work is said to be done. It can be written as -
Work done = force * displacement in the direction of the force
For eg, hold a book in your book without moving. There is no work done as no force is applied neither the object got displaced. Now lift your hand which had the book. You will feel a force is applied to cause the displacement. Hence, the work is done.
4. Is it possible to do work when the force and displacement are not in the same direction?
If you tie a string around an object which is placed on the surface. Now, in order to make the object move, you will put some force by pulling the string. Notice that you are standing and applying the force which makes the object move straight on the surface. Despite the angular difference between the displacement and the force, the work is done.
Thus, you can find the force by finding the force on the imaginary right angle triangle of the displacement.
To understand the concept better you can watch the video lectures where teachers explain the concepts well by using diagrammatic representation.
5. What is the formula to find the work done when the force and displacement are not at the same angle?
We have already learned to find the work done by multiplying force and displacement. But another more powerful formula can be applied in any case when there is an angular difference. The formula is - F s cos θ, works for any angle which means even if the angular difference is zero the formula can be applied.
6. Under what condition the work done is zero?
Let us understand better with our example of weightlifter as discussed in the introduction part. So, when that weightlifter lifted the rings up to a certain height then the work is said to be done. However, even if she put all her efforts to hold the weight above her head, physics gets cruel as it doesn't consider any work done at that moment. The reason being, that the initial position of the rings was the same as its final position and there was no displacement at all. So, force when multiplied with displacement which is zero then the work done is also zero.
7. What is the difference between power and energy?
Let us understand this with an example - Suppose that a crane has to lift a container of a certain mass to a height of 8 meters. Now, for lifting the container the crane has to do a certain amount of work. So, the crane can raise the container at a certain speed, it could be slow or fast. So the speed at which the crane lifts the container is the power. It is the work done in the unit time. While the total work done by the crane in lifting the container to a height of 8 meters is the energy. Thus, energy is power multiplied by the total time consumed.
Watch the video lectures on the topic for a better understanding.
