Mechanics

# Physics work energy and power Formulas with problems and solutions

## What is work?

“Work is a task or job  done when a force acts on a body and moves it in the direction of the force.”Generally ,it refers to perform some task or job.

## How to find work in physics?

In science ,work has precise meaning.For example,a man carrying a load is doing work but he is not doing work if he is not moving while keeping the load on his head,Scientifically,work is done only when an effort or force moves an object.When work is done,energy is used.Thus,work and energy are related to each other.The concept of energy is an important concept in physics.It helps us to identify the changes that occur when work is done.

## Work done by a constant force

Consider a particle acted on by a constant force F,and assume the simplest case in which the motion takes place in a straight line in the direction of the force.In such a situation we define the work W done by the force on the particle as the product of the magnitude of the force F and the magnitude of the displacement S through which the force acts.We write this as:

Work done = Force × displacement

or   W = F S

In a more general case,the constant force acting on a particle may not act in the direction in which the particle moves.In this case we define the work done by the force on the particle as the product of the component of the force along the line of motion and the magnitude of the displacement S.

Sometimes force and displacement do not have the same direction.

Here the force F is making an angle θ with the surface on which the body is moved.Resolving F into its perpendicular components Fand Fas:

F=F cosθ

Fy =F sinθ

In case when force and displacement are not parallel then only the x-component Fparallel to the surface causes the body to move on the surface and the y-component Fy.

Hence                        W= Fx  S

=(Fcosθ) S

=F S cosθ

## Unit of work

SI unit of work is joule (J).It is defined as:

“The amount of work is one joule when a force of one newton displaces a body through one meter in the direction of force.”

In the British system the unit of work is the foot pound.In the cgs systems the unit of work is 1 dyne centimeter ,called 1 erg.Using the relations between the newton,dyne,and pound ,and between the meter,centimeter,and foot,we obtain 1joule =10 7 ergs =0.7376 ft.1b.Work is a scalar,although the two quantities involved in its definition,force and displacement,are vectors.

A convenient unit of work when dealing with atomic or subatomic particles is the electron volt (abbreviation eV ),where 1eV = 1.60 ×10-19J. The work required to remove and outer electron from an atom has a typical magnitude of several electron volt (eV).The work required to remove a proton or a neutron from a nucleus has a typical magnitude of several M eV (106eV).

Work can be either positive or negative.If a force has a component opposite to the direction of the motion,the work done by that force is negative.This corresponds to  an obtuse angle between the force and displacement vectors.For example,when you lower an object by the upward force of your hand holding the object is negative.In this case θ is 180°,for F points up and S points down.The gravitational force in this case does positive work as the object moves down.

Although the force F is an invariant,independent in both magnitude and direction of our choice of inertial frames,the displacement S is not.Depending on the inertial frame from which the measurement is made,an observer could measure essentially any magnitude and direction for the displacement S.Thus observers in different inertial frames,who will agree on the forces that act on a body,will disagree in their evolution of the work done by the force acting on the body.Different observers might find the work to be positive,negative,or even zero.

Our special definition of the word “work” does not correspond to the colloquial usage of the term.This may be confusing.A person holding a heavy weight at rest in the air  may be working hard in the physiological sense,but from the point of view of physics that person is not doing any work on the weight.We say this because the applied force causes not displacement of the weight.

If,on the other hand,w consider the weightlifter to be a system of particles,we find that microscopically work is indeed being done a muscle is not a solid support and cannot sustain a load in static manner. They individual muscle fibers repeatedly relax and contract,and if we analyse the situation in this manner we would find that work is done in each contraction.That is why the weightlifter becomes tired in supporting the weight.

If there are number of forces acting on the body,then work done is separately calculated for each force.Then the net work will be the sum of work done by all separate forces.

### Case 1: If the displacement is produced in the direction of the force i.e,θ = 0°,then work done will be:

W = FS cos0°

we know that cos 0°=1

So:

W = F S (1)

W=FS

Thus ,when a horizontal force moves a body horizontally or when a vertical force lifts a body vertically,then the work done is the product of force and distance covered by the object.

### Case 2(If θ = 90°):

When the force has no component in the direction of motion,then no work is done by the force. W =FS cos(90°)

W=FS cos(0)

W=0

Thus,if a person carrying a weight walks horizontally, then the force exerted by the man is perpendicular to the horizontal displacement.So,no work is done.The examples of forces which don’t work are:

• Centripetal force
• Tension in the string of vibrating pendulum
• Weight and normal force don’t work because they are perpendicular to the displacement

### Case 3(if θ =180°):

When the force has a component opposite to the direction of displacement,then the work done by the force is: W =FS cos(180°)

W =FS (-1)

W=-FS

The force of friction is opposite to the direction of motion,so the work done by the force of friction on the object is zero.

## What is energy?

“Energy is the ability of a body to do work.”

The quantity that is the measure of the capacity of a body or a system for doing work .When a body does work ,W, its energy decreases by an amount equal to W.The energy of a body upon which it does work increases by exactly the same amount so that total energy of the system does not change.This is the principle of conservation of energy .The interaction of two bodies causes the transfer of energy between them.The kind of energy may be unchanged,or it may be partially or wholly changed.If two bodies are at different temperatures ,it is possible for energy,Q,to be transferred from that at high temperatures to that at lower without any apparent forces and displacements by which work could be done.This is the process heat,which involves work on the the molecular scale.

Energy makes change possible.We use it while doing things.It moves cars along the road and boats over the water.It cooks our food and keeps ice frozen in the freezer.It plays our favorite songs on the radio and lights our homes.It also needed our body to grow. In an avalanche,a mass of loose snow,soil,or rock suddenly gives away and slides down the side of a mountain.The avalanche releases a great amount of energy.

Unit of energy is joule.It is represented by J.The unit of energy is same as that of work.One joule is defined as the amount of work done when a body covers distance of one meter in the in the direction of one newton force.

1 J =1 Nm

In the study of energy ,we would like you to keep five important aspects of this concept in mind:

1. Energy brings about changes in the world.
2. Energy can be transferred from one place to another.
3. Energy can be converted from one form to another.
4. In energy conversations and transfers ,the total amount does not change.
5. Some forms of energy are more useful than other.

## What is Power?

The definition of work makes no reference to the passage of time.If you lift a barbell weighing 100 N through a vertical distance of 1.0 m at constant velocity,you do (100 N)(1 m)=100 J of work whether it takes you 1 second,1 hour,or 1 year to do it.But often we need to know quickly work is done.We describe this in terms of power.In ordinary conversation the word “power” is often synonymous with “energy” or “force”.In physics we use a much more precise definition.Power is the time rate at which work is done.Like work and energy,power is a scalar quantity.

## Unit of power

Since work is a scalar quantity,therefore,power is also a scalar quantity.SI unit of power is watt (W).It is defined as:”The power of a body is one watt if it does work at the rate of 1 joule per second (1 J s-1).”Sometimes ,for example,in the electrical measurements,the unit of work is expressed as watt second.However,a commercial unit of electrical energy is kilowatt hour.One kilowatt hour is the work done in one hour by an agency whose power is one kilowatt.

## Work energy and power problems and solutions

• A machine does 20 joule of work in 4 seconds.Find its power.

Solution:

Given data:  time=t= 4s

Work =W = 20J

Power =P=?

Formula= P =W/t

P=20J/4s

P=5 W

• A man has pulled a cart through 35m by applying a force of 300 N.Find the work done by the man.

Solution:

Given data: Distance =S =35 m

Force =F=300 N

Work = ?

Formula:   Work = Force × distance

W= F × S

W = 35 × 300

W=10500 J