Work Units: 19 Important Factors Related To It

What is the Units of Work?

Unit of work or work units are the amount of work done by the object when a force acts on the object through a distance.

Joule (J) = Unit of Work in the International System of Units (SI).

Work Formula

“The work (W) of any object is equal to the product of applied force (F) and the displacement(s) of the object.”

$W = F \\ast s$

SI Unit of Work

The units of work depends on three key ingredients – force, displacement, and cause.

For a force to declare work done, there requisite a displacement of the object.

Every new quantity introduced in physics has a system of measurement called “SI Units.”

For example, in the case of force, the SI unit is Newton (abbreviated N), and for displacement, it is Meters (abbreviated m).

The units-of-measure or SI unit for force and displacement determines the unit-of-measure or SI unit for work.

1 Joule Formula

$1 Newton \\ast 1 meter = 1 Joule$
$1 N \\ast 1 m = 1 J$
One newton of force causing a displacement of one meter is equivalent to one joule of Work, known as the 1 Joule Formula. Therefore, the SI unit of Work is Joule(J).

What Unit is Work measured in?

Dimensionally Newton-Meter (N-m) is sometimes used as the measuring unit for work, but this can also be used as the unit of torque. However, this usage is generally not encouraged by SI authority.

Therefore, the work is measured in the Joule.

Different Units of Work

Non-standard or different units of work is given below:

$foots \\ast pounds$

$kg \\ast (m/s^2) \\ast m$ or

$kg \\ast (m^2/s^2)$

SI Base and Derived Units

The SI units classified into two groups, i.e., base units and derived units.

rsz si — **Seven SI Base Unit** (Image Credit: Dono via Wikipedia)

The base units are the fundamental units and are considered the system’s building blocks, where all the others are derived from the base units known as derived units.

The derived units can be stated with the collection of base and derived unit.

What is the SI Unit of Force and Work?

SI unit of force is Newton (abbreviated N)

As per Newton’s second law of motion,

“A force of 1 newton (N) act on the object is equal to the mass of the object (m) times its acceleration (a).”

$F = m \\ast a$

Hence, Newton(N) is the SI-derived unit of force.

Similarly, Joule(J) derived from the SI-derived unit of force and SI base unit of displacement.

Therefore, Joule(J) is the SI-derived unit of Work.

Unit of Work in CGS System

CGS unit of Work is Erg (abbreviated erg).

What is a CGS system?

CGS, a variant of the metric system; means centimetre gram second system of units.

Relation between Joule and Erg

Joule is the SI unit, and Erg is the CGS unit of Work.

Relation between Joule and Dyne

Since $1 N = 10^5 dyne$

And $1m = 100cm = 10^2 cm$

Hence, $1 J = 1 N \\ast 1 m$ becomes,

$1 J = 10^5 * 10^2$

Relation between Joule and Dyne given by,

$1 J = 10^7 dyne*cm$

Conversion of Joule to Erg

Since, $1 dyne*cm = 1 erg$

Hence, Relation between Joule and Erg is,

$1 J = 10^7 erg$

What are other Units used to measure Work?

Some normally different utilized units of work are

HP-hr
Newton-meter
kW-hr
ft-pound
litre-atm.

Units of Work Crossword Clue

The possible crossword solution for the “Work units” is given by:

ERG

Clue: The CGS kind of ‘unit’ of ‘work’

JOULE

Clue The SI kind of ‘unit’ of ‘work’

MANHOUR

Clue: A time ‘unit’ used in industry for measuring ‘work’

What is the Dimensional Formula of Work?

What is Dimensional Formula?

When a quantity “X” depends on the base dimensions like Mass(M), Length(L), Time(T), Temperature, current electricity, and luminous intensity with respective powers a,b and c, its dimensional formula is represented as:

$[M^a L^b T^c]$

And the exponents a, b, and c here are called the dimensions of “X”.

How to find a Dimensional Formula?

E.g., Dimensional Formula for displacement is $[M^0 L^1 T^0]$ as it only has one dimension in length.

Where, dimension of force are mass(M)=1, length(L)=1, and time(T)=– 2.

Dimensional formula of force is = $[M^1 L^1 T^{-2}]$

Since, Work = Force * Displacement

Dimensional Formula for Work units calculated as

$[M^1 L^1 T^{-2}] \\ast [M^0 L^1 T^0] = [M^1 L^2 T^{-2}]$

What are the Units of Work and Energy?

SI and CGS unit of Energy

SI unit of Energy is Joule (J)

The name “Joule” is given to the unit of Energy after the English scientist James Prescott Joule (1818–1889), who the first person to understand the properties of Energy.

CGS unit of Energy is Erg (erg).

Read more about energy: Energy Basics || Energy Types || Energy Units

Why are Energy and Work measured using the similar Units?

Relation between Work, Force, and Energy

An applied force can cause work on an object and change in its energy which shows that work and energy are closely related to the concepts of force.

Therefore, the object’s energy measures its capacity of work.

Hence, the energy and work measured using the same Joule(J) or Erg (erg) work units.

Application of Units of Work and Energy

In physics you can see this applications everywhere if any force utilized and if any workdone.

What is Ac Units?

Ac units is known as Air Conditioner units. As the name propose, the Ac units is used to cool the air.

What are Ac Units components?

An outdoor ac unit that houses a condenser coil, fan, and compressor.
An indoor ac unit that mount the evaporator coil and fan for circulation of coolair.
A thermostat to controls complete Ac units operation.
A copper tubing that passes refrigerant to flow between the indoor and outdoor ac units
The duct work permit air to circulate from the indoor ac unit to the other living spaces and backspace.
An expansion valve to regulates the amount of refrigerant going into the evaporator coil

Working Principle of Ac Units

Principles of Air Conditioning

Ac units working principle is based on a thermodynamic cycle called the refrigeration cycle:

rsz 1heatpumpsvg — **Refrigeration Cycle:** 1) Condenser Coil 2) Expansion Valve 3) Evaporator Coil 4) Compressor. (Image Credit: Inkscape by Ilmari Karonen via Wikipedia)

The refrigeration cycle is done by varying the pressure and also the state of the refrigerant to absorb or release heat. The refrigerant then absorbed heat from the interior and then pumped it outside.

The Conservation of Energy

“Energy can neither be created nor destroyed – only converted from one form to other form of energies”

This energy of conservation is implemented in ac working as,

‘if you have some unwanted energy in your room, you can’t get rid of it completely. But all you can do is change this unwanted energy into another form or move it to the outside of the room.’

How do Ac Units work?

Ac Units Working

Firstly, when the thermostat senses that air temperature needs to lower and sends signals to both indoor and outdoor ac units to turn on, the cooling process starts. Further air conditioning process involves two actions that co-occur from indoor and outdoor ac units:

Indoor Ac unit working: This is also called the “hot side” of the Ac units.

The indoor ac unit fan first pulls hot air from inside through return air ducts.
Air further pass through filter where dust collected.
Filtered, warmed inside air is further absorbed by the cool evaporator coil.
Indoor blower fan will pump the chilled air.

Outdoor Ac unit working: This is also called the “cold side” of the Ac units.

The refrigerant gas from indoor ac units is further compressed before entering a sizable condenser coil in the outdoor ac unit.
Inside warm air is released outside as liquid.
A sizable outdoor ac unit fan pulls outside air through the condenser coil rejecting the inside warm air that is absorbed.

As a final result, inside warm air or humidity exits to the outside, and refreshing cold air returns to the inside after removal or continuous cycle of warm air from indoor air.

Types of Ac Units

There are six different types of Ac units and each designed for an additional space/reason:

Basic central Ac units
Ductless Ac units
Window Ac units
Portable unit Ac units
Hybrid Ac units
Geothermal Ac units

What is Window AC Units?

Window AC units is sometimes referred to as ‘Room Ac units’ as well. It is the simplest form of Ac units that can be moved from one window to another.

The Window Ac units is a single box enclosed with all of the components with a thermostat gauge fitted at the window.

How do Window Ac Units work?

A window ac unit includes the same essential components and uses the same principles as the primary type of Ac units. The significant difference is that it can be installed inside a wall.

What is Portable Ac Units?

Portable Ac units is similar mainly to Window Ac units, but the difference is that it is a self-contained system and can stand on the room floor without external support to move from anywhere.

How do Portable Ac Units work?

The primary function of the Portable Ac units is to pull inside warm air and then process it to the set temperature by eliminating inside warm air the heat and releasing the fresh cooled air back to inside.

Portable Ac Units Working Principle

Portable ac unit work by pull the hot air from the interior into the ac unit and motor will cool the air for circulation.

How to fix common problems of Ac Units?

If the Ac Units not cooling or working:

Check if the fuse is blown or tripping of the circuit breaker occurs.
Make sure that the complete ac units are plugged in. Check the outdoor ac unit to determine if the condenser of the units is working well.
Check whether the thermostat is set correctly or make the thermostat set to cool to see if that is the problem or not.
If the Ac units still not cooling, a coil of units may be frozen, or there might be a problem with that motor or compressor.

Inside Ac Unit not working

Ac Units Fan not working

If the breaker hasn’t been tripped, then check if the inside air filter is blocked or not.
If you find a block of ice on the evaporator coil or refrigerant lines, allow it to melt completely. If the inside fan is still not working, there may be a chance that the coil gets frozen.
A frozen coil requires a service call to repair the contacts inside the fan parts, such as the fan relay, the fan belt, or the motor itself.

Outside AC unit not working

Outside Ac Unit Fan not working

If the outside unit fan isn’t spinning, first check the breaker or fuse box.

If resetting the complete ac units doesn’t fix the issues, there may be possibilities of a couple of problems:

Start capacitor not working: If the unit’s compressor is working well, there may be a problem with capacitor ie, dirt or rust may have caused the fan to get stuck. You can try to run or clean the fan by pushing it with wooden sticks, but do not use your hand to start the fan. Also, do not try hard to run the fan as there may be chances of burning the compressor, which is a costly repair in ac units. If a still problem occurs, you need to replace the start capacitor of the units by calling a local technician.

What is the Units of Work and Power?

SI and CGS Unit of Power

The SI Unit of Power is Watts (abbreviated W).

How do Units of Work and Power Compare?

“Power defined as the amount of object’s workdone divided by the time it will take to perform that work.”

Power (watts) = Work (joules)/Time (seconds)

$P = W / t$

Hence, CGS unit of Power is Erg per Second (erg/t)

Dimensional Formula for Power is calculated as

$[M^1 L^2 T^{-2}] \\ast [M^0 L^0 T^{-1}] = [M^1 L^2 T^{-3}]$

What is Watt-Hour?

Watt, a unit of measurement of the power; is defined as the consumption of 1J of work in 1 sec.

1 watt of Power = (1 joule of Work) / (1 second of time)

Also, the work required to produce one watt of power for one second or say ‘one watt-second (W⋅s),’ which can define the one joule.

Application of Units of Work and Time

Duration Units Work Formula

Let’s see there is a relationship between the duration (D), the Work (W), and its assignment units (U).

Using the Scheduling formula,

Duration * Assignment Units = Work

E.g.

Suppose for completion of any new project; ten days are equal to 80 hours. When we assigned task 5 to a resource named Raj, the project applied 100% of Raj’s working time to this task.

80 hrs (task duration) * 100% assignment units = 80 hrs of work

Application of Units of Work, Time, and Power

How to Calculate your Electricity Bill?

The measurement unit of electrical Power is Kilowatt (kW).

Since energy is the ability to work done, work has the same units as energy – Joule.

Hence, the equation of Power that can be written in terms of Energy is:

Energy (Joules) = Power (Watts) * Time (Seconds)

This critical equation allows us to calculate how much Energy is consumed in the electricity meter of our home.

How is electricity measured?

To calculate electricity usage of any particular appliance or electronic device, you’ll need to find out the following three figures:

The wattage of the appliance
The average hours you use the appliance per day
The price you pay per kilowatt-hour (kWh) of electricity

rsz 1aid1165263 v4 728px read an electric meter step 2 version 4 — **How to read Electricity Meter**. (Image Credit: wikiHow)

Let, A 150W television with watch-time 5 hr/day, it take up power-consumption 750W-hr/day $(150 \\ast 5 = 750)$ .

Note that a joule is a unit for Energy, and it is also measured in other units of (power * time).

Here, (power * time), also known as ‘kilowatt-hour(kWh), the unit of Energy appears on our electricity bill $(750 \\ 1000 = 0.75)$ .

If your electricity rate is 20%/kWh, that costed 15 %/day to use your television $(0.75 \\ast 0.2 = 0.15 )$ .

Finally, the monthly electric bill calculated as $0.15 \\ast 30 = 4.5$ kwh/month or 4.5 units/month.

What is a TENS Unit?

TENS stands for Transcutaneous Electrical Nerve Stimulation.

What does a TENS Unit do?

A TENS unit is a battery-operated pain relief device that works by passing the mild electrical current through electrodes with adhesive pads that connect the device to a human body. These transmitted small electrical pulses to the body are like little electric shocks which can help to ease the pain.

TENS therapy is effective for:

Bursitis
Arthritis
Tendonitis
Surgery
Headaches

TENS Unit Working Principle

When you have any injuries to your body, rubbing that body area can temporarily reduce the pain.

The gate control theory proposes a gate based process in-between brain and spinal cord nerve.

The electrical impulses generated at a high rate of 90-130 Hz by the TENS device are transferred into the human body. This transmitted electric current stimulates specific non-pain-carrying nerves to modify the human body’s perception of pain by blocking its transmission to the brain. In effect, rather than more painful signals That the body receives when we have injuries, the brain is busy dealing with the pain signals that it gets quickly from the TENS device.
The electrical impulses generated at a low rate of 2-5 Hz by the TENS raise the level of endorphins, the body’s natural pain-killing chemical. This endorphin acts a bit like morphine to stop the perception of pain signal that the body receives during injuries.

TENS Unit Side Effects

TENS is a low-risk pain relief therapy but note that it isn’t safe for everyone. Do not use TENS without medical prescription if:

You have a heart problem or major disease.
You have an electrical/metal implant.
You’re pregnant/might be pregnant.

FREQUENTLY ASKED QUESTIONS (FAQ)

What is the ratio of Units of Work in the SI and CGS systems?

Ans: Relation between Joule and Erg is 1 Joule = 107 Erg unit of Work.

What is 1 Joule Formula?

Ans: $1N \\ast 1m = 1J$

One newton of force causing a displacement of one meter is equivalent to one joule of work.

What is the Units of Work, whether the Units of Work is a Fundamental or Derived Unit?

Ans: Unit of Work is derived unit because it is derived from the SI-derived unit of force and SI base unit of displacement.

What is Dimensional Formula for Work, Pressure and Energies?

Ans:

Dimensional Formula for Work = $[M^1 L^2 T^{-2}]$

Dimensional Formula for Energy = $[M^1 L^2 T^{-2}]$

Pressure = Force / Area

Dimensional Formula for Force = $[M^1 L^1 T^{-2}]$

Dimension for Area is = $[M^0 L^2 T^0]$

Hence, Dimensional Formula for Pressure = $[M^1 L^{-1} T^{-2}]$

How does Work affect an object’s Energy?

Ans: Object’s energy measures its capacity of work. When work is done on the object, it receives energy and if work is done by the object on another, it transfers its energy to another object.

Ans: A force on the object can cause that work done by changing its energy. Also, the object that possesses energy can exert a force on other, energized to other object.

What is the Displacement Work Unit Formula?

Ans: Duration(D) * Assignment Units(U) = Work(W).

What is the relationship between Work and Power?

Ans: 1 watt of Power = (1 joule of Work) / (1 second of time)

How do you calculate energy from power?

Ans: Since work has the same units as energy, the equation of Power that can be written in terms of energy is:

Energy (Joules) = Power (Watts) * Time (Seconds)

How to convert kW to Unit?

Ans: If bulb of 100-Watt (W) kept on for 10 hours, then it will consume: [latex](100 \ast 10 = 1000)[/latex] Watt-Hour = 1 Kilowatt-Hour (kWH) = 1 Unit (on your meter).

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Manish Naik

Hello, I’m Manish Naik completed my MSc Physics with Solid-State Electronics as a specialization. I have three years of experience in Article Writing on Physics subject. Writing, which aimed to provide accurate information to all readers, from beginners and experts.
In my leisure time, I love to spend my time in nature or visiting historical places.
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