Work and Energy

The Law of Conservation of Energy said that energy can only be converted from one form to another; it neither be created nor be destroyed.

The total energy of the system before and the transformation remains the constant.

The Law of Conservation of Energy is valid in all situations and for all kinds of transformation.

In the case of Free Fall the total Energy, i.e. Kinetic Energy plus Potential Energy is Constant

Let an object of mass m is set to free fall from a height, h

At the start the velocity of the object is zero, so the kinetic energy is also equal to zero (0)

The total Potential energy of the object thus, = mgh

If v is the velocity of the object at a given instant, the kinetic energy = ½ mv²

As the fall of object continues, the potential energy would decrease while kinetic energy increaease.

When, h = 0, the kinetic energy of the object is maximum while potential energy is lowest.

But, in all the situation, the sum of potential energy and kinetic energy remains constant.

That is, Potential Energy + Kinetic Energy = constant

Or, mgh + ½ mv² = constant.

Thus a continual transformation of gravitation potential energy into kinetic energy. But at every point the total energy is constant.

Rate of Doing Work is Power

Power is defined as the Rate of doing work. Or Rate of doing work is called power.

If an agent does a work W in time t, then power is given by

Unit of Power

The unit of power is watt.

The unit of watt for power is given in the honour of James Watt.

1 watt is the power of an agent, which does work at the rate of 1 joule lper second.

Or, the power is 1 W when the rate of consumption of energy is 1 W = 1 J s^–1

Larger unit of power is kilowatts. Kilowatts is denoted as "kW".

1 kilowatt = 1000 watts

1 kW = 1000 W

1 kW = 1000 J ^–1

Average Power

The power of an agent may vary with time.

This means an agent may do work at different rates at different interval of time.

Then, the average power is calculated.

The Average Power is obtained by dividing total energy consumed by the total time taken.

Average Power = Total Energy consumed/Total time taken

Commercial Unit of Energy

In house hold or factories, large unit of energy is used, which is called Commercial Unit of Energy. Because the unit joule is too small and hence is inconvenient to express large quantities of energy.

The bigger unit of Energy is kilowatt hour. And it is expressed as kW h

1 kW = 1000 J s^–1

If a machine which consumes energy of 1000 J s^–1 i.e. 1 kW per second and run for 1 hour, then the energy consumed is called 1 kW h.

This means, 1 kWh is the energy used in one hour at the rate of 1000 J s^–1 (or 1 kW)

1 kW h = 1 kW × 1 h

= 1000 W × 3600 s

= 3600000 J

1 kW h = 3.6 × 10⁶ J

The energy used in households, industries and commercial establishment are usually expressed in kilowatt hour.

In house hold electric power consumed in measured generally in 'units'.

Here, 1 unit means 1 kilowatt hour (1 kW h)

Example Problem (5) Rohit takes 50 second and Sonu takes 30 second to climb up a rope of 10 m height. If weight of Rohit is 50 N and weight of Sonu is 90 N find the power expended by both of the boys.

Solution

(a) Power of Rohit

Given, time taken to climb up = 50 s

Height of rope = 10 m

Weight of Rohit = 50 N

Then, Power, P = ?

We know that, Weight = mg = 50 N

Now, we know that, Power, P = Work done /Time taken

Thus, power expended by Rohit = 10 W

(b) Power of Sonu

Given, time taken to climb up = 30 s

Height of rope = 10 m

Weight of Sonu = 90 N

Then, Power, P = ?

We know that, Weight = mg = 90 N

Now, we know that, Power, P = Work done /Time taken

Thus, power expended by Sonu = 30 W and that of by Rohit = 10 W Answer

Example Question (6) A girl having weight of 70 N runs up a staircase of 30 steps in 10 s. If the height of each of the step of stair is 20 cm, find the power of girl.

Solution

Given, Weight of the girl = mg = 70 N

Height of one step of stair = 20 cm

Total number of steps in stair = 30 steps

Thus, total height of stair = 20 × 30 = 600/100 = 6 m

Now, time taken to climb up stairs = 10s

Thus, power, P = ?

Now, we know that, Power, P = Work done /Time taken

Thus, power of girl = 42 W Answer

Example Question (7) If an electric bulb of 40 W is used for 10 hours per day.Calculate the units of energy consumed in 30 days.

Solution

Given, power of electric bulb = 40 W

= 40/1000 = 0.04 kW

Time used in one day = 10 h

Thus, total time used in 30 days, t = 10 h × 30 = 300 h

Now, we know that, Energy = Power × time taken

= 0.04 kW × 300 h

= 12 kW h

= 12 units

Thus, energy consumed by bulb in given period of time = 12 units Answer

Example Question (8) If an object having mass of 20 kg has the gravitational potential energy of 500 J, then find the height of the object. [take g = 10 ms^–2]

Solution

Given, Mass of the Object = 20 kg

Potential energy, E_P = 500 J

Then, height of the object, h = ?

We know that, E_P = mgh

⇒ 500 J = 20 kg × 10 ms^–2 × h

Thus, height of the object = 2.5 m Answer

Summary

(1) Work can be defined as 'When an object is displaced by exerting a force on that object, then it is said that work is done. '

(2) There are two conditions must be satisfied for work to be done (a) A force should be act on an object, and (b) The object must be displaced.

If any one of the above two conditions does not exist, work is not done. This is the way we view work in scientific way.

(3) The product of the force and displacement is called the work.

Work done = force × Displacement

⇒ W = F s

Thus, work done can be defined as, work done by a force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the work.

Since, work done is the product of force applied on an object and displacement of the object. Thus, if any one of the two i.e. force or displace, be zero, then product will be zero. And work done will also become zero.

(4) The unit of work N m (Newton meter). It is also called Joule (J).

(5) 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the line of action of force.

(6) Work has only magnitude and no direction. Thus, work is a scalar quantity.

(7) Positive Work When force is exerted in the direction of displacement of the object, the work done is positive.

(8) Negative Work When the force is applied in the opposite direction of displacement, then work done is considered as negative.

(9) ENERGY is defined as the capability or capacity of doing work.

Or, capability of doing work is called ENERGY.

An object having a capability to do work is said to possess ENERGY.

The object which does the work loses energy and the object on which the work is done gains energy.

(10) SI unit of energy is joule (J)

(11) 1 J is the energy required to do 1 joule of work.

(12) Kilo joule (kJ) is the larger unit of energy. 1 kJ = 1000 J

(13) There are various forms of energy. For example mechanical energy, chemical energy, potential energy, kinetic energy, heat energy, light energy, sound energy, etc.

Potential energy and kinetic energy together can form mechanical energy.

(14) The word 'Kinetic' came from Greek word 'Kinesis' which means 'movement or to move or motion'. Consequently, the term 'Kinetic Energy' means energy due to motion or movement.

The energy possessed by an object due to its motion is called Kinetic Energy.

A moving object can do work. A faster moving object can do more work than an identical object moving slower.

(15) The Kinetic Energy of a body moving with a certain velocity is equal to the work done on it to make it acquire that velocity.

(16) Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is

(17) The Energy possessed by an object because of the position or configuration of the object is called POTENTIAL ENERGY.

In other word, the energy possessed by an object because of change in position or configuration is called POTENTIAL ENERGY.

(18) The energy possessed by an object at a point above the ground because of the work done in raising it from the ground to that point against gravity is called GRAVITATIONAL POTENTIAL ENERGY.

An object increases its energy when raised through a height. This happens because some work is done on the object against gravity while it is being raised. The energy present in such an object is called Gravitational Potential Energy.

(19) The Potential Energy (E_P) of the object, E_P = mgh

The work done by the gravity depends on the difference in vertical heights of the initial and final positions of the object and not on the path along with the object is moved.

(20) The Law of Conservation of Energy said that energy can only be converted from one form to another; it neither be created nor be destroyed.

The total energy of the system before and the transformation remains the constant.

The Law of Conservation of Energy is valid in all situations and for all kinds of transformation.

(21) Power is defined as the Rate of doing work. Or Rate of doing work is called power.

If an agent does a work W in time t, then power is given by, Power (P) = Work done (W) / Time (t)

(22) The Average Power is obtained by dividing total energy consumed by the total time taken.

Average Power = Total Energy consumed/Total time taken

(23) The bigger unit of Energy is kilowatt hour. And it is expressed as kW h

1 kW = 1000 J s^–1

If a machine which consumes energy of 1000 J s^–1 i.e. 1 kW per second and run for 1 hour, then the energy consumed is called 1 kW h.

1 kW h = 1 kW × 1 h

= 1000 W × 3600 s

= 3600000 J

1 kW h = 3.6 × 10⁶ J

The energy used in households, industries and commercial establishment are usually expressed in kilowatt hour.

In house hold electric power consumed in measured generally in 'units'.