 # Unit of Work

The SI unit of work is Joule,  symbolized as J. The unit is named in honor of James Prescott Joule, a physicist who studied work in the mid-1800s.

For example,

The image above shows the amount of work required to lift a unit weight through a unit distance against gravitation.

In physics,  work is said to be done by a force acting on the body provided that the body is displaced actually in any position except in a direction perpendicular to that of force. In the case of work, the standard metric unit is Joule (denoted by J). One Joule is equal to one Newton of force F making a displacement of one meter. Hence, Joule is the unit of work.

### How to Measure Work Done?

In everyday life, we consider work to be a synonym of effort, labour, toil, or energy spent. However, the term work is entirely different from all these terminologies.

The work done is measured in Joules denoted by J. The amount of work done is calculated by multiplying the force by the amount of displacement of an object.

Work done in different ways are described below by example

Consider a box, when a force F is applied to displace a box from one position X to Y by a distance S, then work done will be W = F . S

Where work is a scalar quantity with no direction.

Work Done by a Constant Force

When a constant force F acting on the object produces a displacement S in that body, then work done by the force is the dot product of the force and displacement given by,

 W = F . S …(1)

If Ө is an angle between F and  S, then from eq(1),

 W = F S CosӨ

If Ө = 0°, then,

 W = FS

Which means the two vectors F and S are in the same direction.

If  Ө = 90°, then,

 W = 0

No work will be done as the force applied is in a direction perpendicular to the distance. It states that the body under the action of multiple  forces is equal to the work done by the resultant force. Hence the body is at equilibrium.

### Measuring Work for Gases

W = P ΔV

Here, W is the work done in expanding the volume of the gas in a piston.

Work has a magnitude and it does not have a direction. Hence it is a scalar quantity.

### What is Work Done Measured in?

Work done (W) by a force (F) is measured in newtons (N) distance (S) moved along the line of action of the force is measured in meters (m) is measured in Joule (J).

### Unit of Work

In SI the base unit is: Kg m² s⁻²

Here, Kg m² s⁻² is the MKS unit.

The MKS stands for meter-kilogram-second

The CGS (centimeter-gram-second) unit for work is dyne-cm or erg.

### State the SI Unit of Work and Define it

Work done is defined as the 1 Newton of force required to move an object by the displacement of 1 meter.

Here, 1 Joule is equal to Newton-meter (N-m).

Other units are Foot-pound, erg.

Dimensional formula for work is [M L² T⁻²]

Hence the unit of work is the same as that of energy.

### SI unit of Force and Work

A body like spring has potential energy stored in itself and when it is stretched from its mean position, it starts vibrating to and fro. The more the force is applied, the more is the displacement and more will be the restoring force acting within in the spring.

Therefore, the restoring force F is measured in Newton (N).

The dimensional formula is given by [MLT⁻²].

The work done by the spring to come back in its mean position is measured in Newton-meter or Joule and its dimensional formula is given by [ML²T⁻²].

## Conversion of the Units of Work

 S.no. Unit Conversion 1. British thermal unit (BTU) 1055.06 Joule 2. 1 erg 10⁻⁷ Joule 3. 1 horsepower-hour 2684519.5377 Joule 4. 1 foot-pound 1.36 Joule 5. 1 Kilo-watt hour 3.6 million Joule 6. 1 Newton-meter 1 Joule

### Do you know?

A weight lifter does work in lifting the weight off the ground (force by the muscles to work against gravitational pull),  however, no work is done in holding the weight up.

Q1: What are the Types of Work?

Ans: There are two types of work, namely, positive work and negative work.

Positive work

The work is described by the equation, W = FSCosӨ.

When Ө is acute i.e. Ө< 90° then work is said to be positive.

Examples

• When a lawn roller is pulled by applying force along with the handle. The work done by the applied force F is positive.

• Work done by the stretching force in spring is positive.

Negative work

It happens when Ө is obtuse i.e. Ө> 90°.

The angle between the force F and displacement S is 180°. Therefore, the work done by gravity on moving a body upwards is negative.

Examples

• Rocket propulsion

• Work done in pulling the load.

• Pulling the water from the well.

• Flying an airplane.

Q2: Write Some Real-Life Examples of Work.

Ans: There are certain real-life examples to describe the work.

• Sitting in front of the laptop and typing something on it is the work.

• When the road is busy, the force applied by a vehicle to slow down the speed is work.

• The work done against the gravitational pull to escape an object from the earth.

• The work done by the earth to rotate about its polar axis and around the Sun.

• The work done by the pendulum to move to and fro when pulled from its rest position.