Work And Energy

 Mind Maps

Class IX - science: Work and Energy
Q) 1 kJ equals to how many joules?

Q) What is the biggest natural source of energy to us?

Q) The kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is?

Q) The sum of kinetic energy and potential energy of an object is its total?

Q) If an electric appliance consumes 1000 joule of energy in one minute and runs for one hour, then it will consume how much unit of electricity?

Q) The unit of work is?

Q) Find the energy possessed by an object of mass 10kg when it is at a height of 6m above te ground? Given g=9.8ms-2.

Q) Which energy is the energy possessed by an object due to its motion?

Q) Which form of energy does the flowing water possess?

Q) Write a short note on the direction of force?

Q) Explain about Work done by Constant Force?

Q) Explain about Rate of Doing Work?

Q) Write a short note on Law of Conservation Of Energy?

Q) Explain the Work done by Constant Force?

Q) Explain about different types of Energy?

Q) Explain the Commercial Unit Of Energy?

Q) Explain difference between kinetic and potential energy?

Introduction

All living beings need food. Living beings have to perform several basic activities to survive. We call such activities 'life processes'.
The energy for these processes comes from food.We need energy for other activities like playing,singing, reading,writing,thinking,jumping,cycling and running.Activities that are strenuous require more energy.

Example
Push a pebble lying on a surface. The pebble moves through a distance. You exerted a force on the pebble and the pebble got displaced. In this situation work is done.
A girl pulls a trolley and the trolley moves through a distance. The girl has exerted a force on the trolley and it is displaced.
Therefore, work is done.

Work done by Constant Force

Let a constant force, F act on an object. Let the object be displaced through a distance, s in the direction of the force. Let W be the work done.
We define work to be equal to the product of the force and displacement.
Work done = force * displacement
W = F s

Thus, 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 force.
Work has only magnitude and no direction.
Here the unit of work is newton metre (N m) or joule (J).
Thus 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 the force.

Example1:

A force of 5 N is acting on an object. The object is displaced through 2 m in the direction of the force. If the force acts on the object all through the displacement,
then work done is 5 N * 2 m =10 N m or 10 J.

Consider a situation in which an object is moving with a uniform velocity along a particular direction. Now a retarding force F, is applied in the opposite direction. That is, the angle between the two directions is 180°.
Let the object stop after a displacement s. In such a situation, the work done by the force, F is taken as negative and denoted by the minus sign.

The work done by the force is F * (-s) or (-F * s).
Work done is negative when the force acts opposite to the direction of displacement. Work done is positive when the force is in the direction of displacement.

Energy

The Sun is the biggest natural source of energy to us. Many of our energy sources are derived from the Sun. We can also get energy from the nuclei of atoms, the interior of the earth, and the tides. The energy possessed by an object is thus measured in terms of its capacity of doing work.
The unit of energy is the same as that of work that is, joule (J).
1 J is the energy required to do 1 joule of work.
Sometimes a larger unit of energy called kilo joule (kJ) is used.
1 kJ equals 1000J.

The various forms include mechanical energy (potential energy +kinetic energy), heat energy, chemical energy, electrical energy and light energy.

Kinetic Energy

A moving object can do work.An object moving faster can do more work than an identical object moving relatively slow. A moving bullet,blowing wind,a rotating wheel,a speeding stone can do work. Objects in motion possess energy. We call this energy kinetic energy.
Kinetic energy is the energy possessed by an object due to its motion. The kinetic energy of an object increases with its speed.

 v^2 - u^2 = 2a s
s=(v^2 -u^2)/(2a)
w =ma
w= ma (v^2-u^2)/(2a)
or  w= 1/2m (v^2 - u^2)

If the object is starting from its stationary position, that is, u = 0, then
W=1/2 m v^2
The kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is
Ek =1/2 mv^2

Example:

An object of mass 15 kg is moving with a uniform velocity of 4 m s-1 . What is the kinetic energy possessed by the object?
Solution:

Mass of the object, m = 15 kg,
velocity of the object, v = 4 m s^-1.
Ek =1/2 mv^2
=1/2** 15 kg ** 4 m s^-1 ** 4 m s^-1
= 120 J
The kinetic energy of the object is 120 J.

Potential Energy

Activity:

• Take a slinky as shown below.
• Ask a friend to hold one of its ends. You hold the other end and move away from your friend. Now you release the slinky.
The energy transferred to the spring inside is stored as potential energy. The potential energy possessed by the object is the energy present in it by virtue of its position or configuration.

Activity

• Take a bamboo stick and make a bow.
• Place an arrow made of a light stick on it with one end supported by the stretched string.
• Now stretch the string and release the arrow.
• Notice the arrow flying off the bow. Notice the change in the shape of the bow.
• The potential energy stored in the bow due to the change of shape is thus used in the form of kinetic energy in throwing off the arrow.
Potential Energy Of An Object At A Height

The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.

Let the work done on the object against gravity be W.
That is, work done,
W = force * displacement
Work done on the object is equal to mgh, an energy equal to mgh units is gained by the object.
This is the potential energy (EP) of the object. Ep = mgh.
In a case where a block is raised from position A to B by taking two different paths.

Let the height AB = h. In both the situations the work done on the object is mgh.

#### Example: Find the energy possessed by an object of mass 10 kg when it is at a height of 6 m above the ground. Given, g = 9.8 m s^-2.

Solution: Mass of the object, m = 10 kg
displacement (height), h = 6 m
and acceleration due to gravity, g = 9.8 m s^-2
Potential energy = mgh
= 10 kg ** 9.8 m s^-2 ** 6 m = 588 J.
The potential energy is 588 J.

Law Of Conservation Of Energy

According to this law, energy can only be converted from one form to another, it can neither be created nor destroyed. The total energy before and after the transformation remains the same. The law of conservation of energy is valid in all situations and for all kinds of transformations.

The sum of the potential energy and kinetic energy of the object would be the same at all points.
That is, potential energy + kinetic energy = constant
Or mgh + 1/2 mv^2 = constant
The sum of kinetic energy and potential energy of an object is its total mechanical energy.

Rate of Doing Work

Power measures the speed of work done, that is, how fast or slow work is done. Power is defined as the rate of doing work or the rate of transfer of energy.

Power = work/time
or P = W/t
The unit of power is watt.
1 kilowatt = 1000 watts
1 kW = 1000 W
1 kW = 1000 J s^-1

Example: A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm, find his power. Take g = 10 m s^-2.
Solution:

Weight of the boy, mg = 50 kg ** 10 m s^-2 = 500 N
Height of the staircase, h = 45 ** 15/100 m
= 6.75 m
Time taken to climb, t = 9 s.
P = Work done/time taken
P =(mgh)/t
P =(500N**6.75m)/(9s)
P =375 W
Power is 375W.

Commercial Unit Of Energy

The unit joule is too small and hence is inconvenient to express large quantities of energy. We use a bigger unit of energy called kilowatt hour (kW h).

1 kWh =1 kW *1 h
1 kWh = 1000 W * 3600 s
1 kWh = 3600000 J
1 kWh = 3.6 ** 10^6 J

Example: An electric bulb of 80 W is used for 8 h per day. Calculate the 'units' of energy consumed in one day by the bulb.
Solution:

Power of electric bulb = 80 W = 0.06 kW.
Time used, t = 8 h
Energy = power * time taken
= 0.06 kW * 8 h
= 0.48 kW h
= 0.48 units.
The energy consumed by the bulb is 0.48 units.

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