 # Work and Power

## Difference Between Work and Power

Though the term work and power are interconnected, there is a vast difference between work and power. You cannot complete work without the help of power. You need the energy to complete a task, whereas people define energy as power. Since both work and power are a scalar quantity, students are often confused. How will you explain the difference between work and power when people use the two terms interchangeably?  First, let us study the definition of work and power.

### 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.

### 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 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).

### 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) = Total Work Done (W) / 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

 Criteria Work Power Definition The definition of work is the power you apply to displace an object over a distance in a given time. Power is the energy you need to complete a given task. Formula Total Work Done (W)  = Power (P) x Time (t)       orWork = Displacement x Force Power (P) =Total Work Done (W) / Time (t) Measurement Unit (SI unit) The standard unit of work is the Joule denoted as (J).  Furthermore, you can measure work in electron volt (eV), kWh, GWh, and MWh The standard unit of measurement of power in Watts and kilowatts denoted as (W).  Furthermore, you can measure power in kW, MW, and GW. Example A person is said to do work if he/she is pushing or pulling a box. A lamp needs the energy to light the bulb.

### Fun Facts on Work and Power

1. If you are kicking a ball, your work done is positive.

2. If you are sitting in the classroom, listen to lectures, the work done is said to be zero.

3. Industries, households, commercial establishments use 1 Kilowatt(kW) of power.

4. Force and displacement are both vector quantities, but their dot product gives work done, which is a scalar quantity.

Q1. How can you tell the Difference Between Work and Power?

A1. 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.

Q2. Do you Think a Porter Does any Work When he Walks Horizontally Carrying a Suitcase from One Place to Another on his Head?

A2. 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.