How to Calculate Work and Power: Key Concepts & Practice Problems
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 in Physics: Complete Guide
1. What is meant by 'work' in Physics, and how is it different from its everyday meaning?
In Physics, work is done only when a force applied to an object causes it to move or displace. If you push against a wall, you exert force but do no work because the wall doesn't move. For work to be done, two conditions must be met:
- A force must be applied to the object.
- The object must be displaced in the direction of the force (or a component of the force).
The formula to calculate work is W = F × d × cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and displacement vectors.
2. What is the fundamental difference between Work and Power?
Work and Power are related but distinct concepts. Work is the measure of energy transfer when an object is moved over a distance by a force. Power is the rate at which that work is done.
- Focus: Work measures the total task accomplished, while Power measures how fast the task is accomplished.
- Formula: Work (W) = Force × Displacement. Power (P) = Work / Time.
- SI Unit: The SI unit of work is the Joule (J), while the SI unit of power is the Watt (W), which is equivalent to one Joule per second (J/s).
For example, lifting a box to a shelf is 'work'. Lifting it in 2 seconds requires more 'power' than lifting it in 5 seconds, even though the work done is the same.
3. Under what conditions is the work done on an object considered zero, even if a force is applied?
Work done can be zero even when a significant force is acting on an object. This occurs under three specific conditions based on the formula W = Fd cos(θ):
- No Displacement (d = 0): If the object does not move, no work is done. For example, pushing a stationary wall.
- No Force (F = 0): If no net force is acting on the object, no work is done, even if it is moving with constant velocity.
- Force Perpendicular to Displacement (θ = 90°): If the applied force is at a right angle (90°) to the direction of motion, the work done is zero because cos(90°) = 0. A classic example is a porter carrying a suitcase on his head and walking horizontally; the lifting force is vertical, but the displacement is horizontal.
4. Can work done on an object be negative? Provide a real-world example.
Yes, work done can be negative. This occurs when the force applied to an object acts in the opposite direction of its displacement. In the formula W = Fd cos(θ), if the angle θ is 180°, then cos(180°) = -1, making the work negative.
A common real-world example is the work done by friction. When you slide a book across a table, the book moves forward, but the force of friction acts backward, opposing the motion. Therefore, the work done by the frictional force is negative, as it removes energy from the system.
5. What is the relationship between work and energy, as explained by the Work-Energy Theorem?
The Work-Energy Theorem provides a direct link between the net work done on an object and its energy. It states that the total or net work done by all forces acting on an object is equal to the change in its kinetic energy (ΔK.E.).
- Formula: W_net = K.E._final - K.E._initial = ΔK.E.
- Implication: If positive net work is done on an object, its kinetic energy and speed increase. If negative net work is done, its kinetic energy and speed decrease. If the net work is zero, its kinetic energy remains constant.
This theorem is a fundamental principle that connects the concepts of force and motion (dynamics) with energy.
