Work And Energy

In science, we define Work as product of the Force(F) & the Displacement(s) moved along the direction of force

W = Force Displacement -- (i)

This formula for work used in only Translatory motion of the object.

Work has only Magnitude, no Direction. So, work is a Scalar quantity.

The SI unit of Force(F) is Newton(N) and Displacement(s) is meter(m).

Putting 1N and 1m in formula of work eq(i), work done comes out to be 1N-m.Hence unit of work is newton-meter(N-m) or joule(J).

Fig - Work done in moving a block through a distance ‘s’ and by appling force’F’

Example (i)- When a ball thrown upward the Gravitational force acts downward and the direction of motion of ball is upward as shown in Fig-(i).

Example (ii) when a ball rolls over a surface it slows down due to frictional force which acts opposite to the direction of motion of ball as shown in Fig-(ii).

Fig -(i) Fig-(ii)

a) Work and Energy have same unit joule(J),

Work is defined as W = Force Displacement ,its unit came out be Newton-metre or precisely Kg.--- (i)
Same thing with Energy , let us take Kinetic Energy ,it is given by the formula m

where m is mass of the object in kg

v is the velocity of the object in m/s,

now putting the value of m and v in SI units we will get Kinetic Energy Units as Kg

which is same as of the units of work given in Eq-(i) ,hence proved they have same units.

b) Work done by its weight is negative as the weight is acting downward and plane is going upward.

c) When we try to extend or compress spring we increases its energy and this energy is stored as potential energy and when we release spring it loses its potential energy to do some work.

d) External negative force acting on a system decreases it energy because it acts opposite to the direction of motion of object .for example when friction acts on a object it gradually lowers its velocity .

e) freely falling body loses its potential energy into kinetic energy. So, as potential energy decreases kinetic energy increases .

f) unit of power is joule/second(Watt). Power is defined as rate of change of energy per unit time.

Sum of kinetic energy and potential energy of an object is its mechanical energy.

The law states that energy can neither be created nor be destroyed, rather it can only be transferred from one form to another.

No, there is no violation of conservation of energy. When force is applied to lift the box ,it is moving along the direction of action of force so, the acting force increases its energy as potential energy. When box falls down it loses its potential energy into kinetic energy.

Nobody is wrong. Potential energy of an object depend upon the consideration of zero potential energy.

If we consider ground as zero potential energy lifting a 1kg object to a height of 3m taking g=10 brings the object to 20J potential energy , whereas considering the surface at a vertical height of 1 m above ground as zero potential lifting a 1kg object to 2m makes the potential to 30J.

a) Positive as the porter apply force on the suitcase in its direction of motion.

b) Positive as the gravity acts downward and suitcase is also falling downward

c) Zero Work is done as force exerted by its head on suitcase cause no motion.

d) Negative as the gravity acts downward and ball is moving upward.

e) Negative as the swimmer propels his hands back so as to get a forward displacement.

Potential energy of a body is its ability to do work, whereas gravitational potential energy of an body is its ability to do work in gravitational force.

Consider a object of mass ‘m’ raised to a height ‘h’ above the ground. The minimum force required to raise the object is mg. The object gains energy equal to work done on it.

W = Force Displacement

W =mgh

W = mgh

When apple falls it gains some speed due to action of gravitational force on it. It gains kinetic energy and loses it gravitational potential energy.

When it strike the ground the kinetic energy lost in various forms such as in breaking the apple some energy losses in heat energy and sound energy.

Work Done = Force Displacement

a) It doesn’t depend on the path taken because work done depends upon the displacement i.e Final Position and Initial Position.

b) It doesn’t depend upon time taken, work only depends upon force and displacement.

c) It does depend upon the weight of suitcase because the suitcase is raised against the gravitational force with a minimum force equal to the weight of body .

d) It doesn’t depend on my weight as while lifting the suitcase gravitational force doesn’t act against my weight and I don’t move against gravitational force.

Pushing up a bicycle and moving up the incline is done by my muscle ,So my muscle loses energy some of the lost energy goes into the potential energy of bicycle and myself.

The person standing is not doing any work externally but a lot of work is being done inside the body.

The muscle of body is stretched during standing and heart has to pump more blood to the muscle this leads to loss of energy inside body and thus he gets tired.

A body in motion posses kinetic energy

Let us assume that an object of mass(m) is at rest on a smooth horizontal plane as shown above . Let it be displaced through a distance ‘s’ from the point A to B by force(F) acting upon it in the direction of the displacement. In the horizontal direction the net force is equal to the applied force F.

The work done on the object by the net force W = Fxs ---(i)

Let the work done on the object cause a change in its velocity from ‘u’ to ‘v’ and the acceleration produced be ‘a’

The relation between initial velocity u, final velocity v, acceleration ‘a’ and displacement ‘s’ is given from the equation of motion as

---(ii)

By newton’s second law of motion

F = m x a --(iii)

From equation (i), (ii) (iii) ,we have

Note:- A Special case is when the object is initially at rest i.e u = 0 ,In that particular case ,Formula of Kinetic Energy comes to be K.E = .

As kinetic energy becomes zero on reaching the ground it gets converted into various forms of energy, Like heat energy due to impact with ground and due to air resistance with the object.

Given data,

mass(m)=25 kg

displacement(s) = 10 m

time taken(t) = 50 s

As the man is working against gravity so force(F) applied is

mg= 25 kg × 10 m/s² = 250 N

Power = work done/time taken

=(force×displacement)/(time taken)

=

=50 watt(w)

Given data

Mass of ball (m)= 10kg

Height(h) = 10m

(a) potential energy = mgh

= 10 (kg)× 10 (m/s²) × 10 (m)

=1000 (J)

(b)when the ball reaches the ground the gravitational potential energy changes to kinetic energy

So, kinetic energy gained= 1000(J)

If we neglect the air resistance

(c) We know that Kinetic Energy = and from above data we have kinetic energy as 1000 J and mass of ball (m) as 10kg ,hence on equating for velocity we will get velocity as

V = substituting Kinetic Energy = 1000 J and mass as 10 kg ,we have

Velocity = = = 14.14 m/s

Given Data:

Mass= 20kg

Height = 1m

Work is done against gravity so minimum force needed to lift the mass is (20×g), where g is acceleration due to gravity

Work done= force× displacement

=20 (kg) × 10(m/s²)× 1(m)

=200 (J)

Given Data:

kinetic energy= 5 J

velocity= 2 m/s

using the formula of kinetic energy

kinetic energy=

⇒

⇒

⇒

The energy required is kinetic energy of the cycle together with its rider

Given data :

mass (m) = 100kg

velocity (v) = 3 m/s

Kinetic Energy is given by the formula Putting the given values in the formula ,we have

100 = 450 J

B

Explanation: Because kinetic energy is directly proportional to square of speed

Kinetic Energy = --- (i)

If speed becomes doubled then V= 2v putting in the equation we have now new Kinetic Energy = --(ii)

Dividing Eq (ii) and (i) , We will get New Kinetic Energy as 4 times than the older one.

(a)

Explanation: Speed of both the bodies will be equal at any instant of time. According to equation of motion .

speed of free falling object doesn’t depend on mass of the object.

While the force of gravity, potential energy, kinetic energy depends upon the mass of object.

(a)

Explanation: Work done is positive because displacement is in the direction of the applied force.

(b)

Explanation : work done is negative because , gravitational force is the cause of weight and it acts downward on suitcase and displacement is upward.

The welfare of individuals, sustainable development of countries, and the life-supporting capacity of the global ecosystem depends on energy resources.

Energy supplies, particularly oil, are strategically important for industrial development and military weaponry. They help to increase national power. A nation endowed with sufficient energy resources can make its will prevail over the others.

Oil is a natural resource which is limited in quantity and is non-renewable in the economic sense. Alternatives to oil are being developed but they are not a viable replacement for oil. This creates economic interdependence between the nations.

The ability to obtain enough energy supplies at a reasonable cost is an important aspect of energy security.

In the future, energy resources may be in greater demand due to population and economic growth. This may lead to more conflicts.

The IEA which consists of 29 OECD member countries plays an important role in international energy cooperation. But its capacity to secure global cooperation is limited because the major developing countries are not its members. So there is a need for more collaboration and open markets in energy policy. Multilateral cooperation is extremely necessary for the stability of energy markets and a peaceful evolution of the international system.

Collaborated efforts to conserve energy in order to meet its increasing demand can go a long way in ensuring international peace and security.

We see various energy conversions in nature, for example

i) snow deposited at altitudes melts and the water so formed flows down to seas. In the process, its potential energy converted into kinetic energy. We convert the kinetic energy of water to electrical energy in hydroelectric power plants.

ii) Dead plans buried deep below the earth’s surface for millions of years get converted to fuels like petroleum and coal, which have chemical energy stored in them.

iii) The food we eat comes from plant sources or animal sources which in turn take plant parts as their food.

iv) When we eat food, several chemical processes take place and the chemical energy stored in food gets converted into various forms needed by the body. For example when we walk, run, exercise etc., the energy from food is used for kinetic energy.

Since Mechanical Energy is defined as Sum of Kinetic Energy and Potential Energy , It should be conserved at all points.

Let us consider a freely falling body ,It is at a height ‘H’ from the ground .

Let the Total Mechanical Energy be M.E joules

Considering its motion at three points A,B & C .

At A velocity v = 0 hence its Kinetic Energy is zero ,but its Potential energy = mgh

hence ,Mechanical Energy = Kinetic Energy + Potential Energy

M.E = mgh -- (i)

At B velocity v = v1 ,Kinetic Energy will be and Potential Energy will be mgh/2

hence, Mechanical Energy = Kinetic Energy + Potential Energy

M.E = + mg --(ii)

At C velocity v = v2 ,Kinetic Energy will be and potential Energy will be Zero

hence, Mechanical Energy = Kinetic Energy + Potential Energy

M.E = +0 -- (iii)

Since Mechanical Energy is Conserved , We can say that M.E at points A,B & C or Equations (i) ,(ii) & (iii) will be equal.