PHYSICS

Class 9TH (KPK)

Chapter # 6

Work and Energy

NAME: __________________________

F.NAME: _________________________

CLASS:___________ SECTION: ________

ROLL #: _____ SUBJECT: ____________

ADDRESS: ___________________________________

__________________________________________

SCHOOL: _____________________________________

https://web.facebook.com/TehkalsDotCom/

https://tehkals.com/
 1
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
Chapter # 06
Work and Energy
COMPREHENSIVE QUESTIONS
Q1: Define work and explain how work is calculated if force is applied at an angle.
Ans: Work:
Work is said to be done when a force displaces a body in its own direction.
Or
The product of force and displacement is called work.
Explanation:
In our daily life, when someone hold a body in state of rest no work is done because it does not cover any
displacement. In the scientific sense, work is said to be done, when a force acts on a body, there must be
motion or displacement by a body in the direction of the force.
Mathematically:
When an object moves distance “S” in the direction of applied force “F” then work done is given as:
Work = force × Displacement

W=F×S
Or W = FS

Force making at Angle 𝜽:

Sometime force is not perfectly applied in the direction of motion.
In that case, the direction of force and the direction of motion of a body is
not same. So, when a body is moving in horizontal direction and force “F”
is applied making certain angle “𝜃” with the horizontal. In such situation,
the force is resolved into its rectangular components. According to
definition of work, horizontal component of force “Fx” i-e cos𝜃 displaces
a body through distance “S” horizontally. So, mathematically work done
can be written as:
W = Fx x S :. Fx = Fcosθ
W = Fcosθ x S
Or, W= FScosθ
Quantity and Unit of work:
Work done is a scalar quantity and the SI unit of work is Joule, denoted by “J” and can be defined as:
W = FS
So, 1J = 1N .1m
Or, 1J = 1Nm

Q2: Define Kinetic Energy. Derive the expression used for kinetic energy.
Ans: Kinetic Energy:
The energy possessed by a body due to its motion is called kinetic energy.
Examples:
All moving objects have kinetic energy i-e.
1. Moving car or train
2. Blowing wind
3. Flowing water etc.
 2
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
Explanation:
The object mass and its speed are contributing to its kinetic energy. When the body is at rest, there is
no kinetic energy present in it. It means the velocity of a body is zero, its kinetic energy is also zero. So,
greater the mass or velocity of a body, greater will be the kinetic energy. It is denoted by “EK”.
Mathematical Form:
Mathematical, kinetic energy is one half the product of an object’s mass “m” and the square of its
velocity “v”.
𝟏
Ek = 𝟐 mv2
Quantity and Unit:
Kinetic energy is a scalar quantity and the SI unit of “Ek” is Joule (J)
Derivation of formula:
Consider a body of mass “m” which is placed on a smooth surface. As the body is at rest, so its initial
velocity “vi” is zero. A force “F” is applied on the body and the body moves from point “A” to “B” after
covering the distance “S”. At point “B” final velocity “vf” of the body becomes “v”.
We know that when a force “F” is applied on a body and it covers some distance “S” then work “W” can be
written as:
W=FxS
This is the work done by the body due to its motion. So, it appears as the kinetic energy i-e.
W = EK
F x S = Ek
Or EK = F x S -------------eq (i)
According to Newton’s second law of motion
F = ma
In order to find distance “S” covered by the body, we use third equation of motion.
2aS = vf2 − vi2
As vf = v & vi = 0, By putting the values
2aS = (v2) – (0)2
2aS = v2 – 0
2aS = v2
Divide “2a” on both sides
2𝑎𝑆 𝑣2
= 2𝑎
2𝑎
𝒗𝟐
s = 𝟐𝒂
Now, putting the value of “F” And “S” in Eq (i)
Ek = F x S
𝑣2
Ek = ma x 2𝑎
𝟏
Or Ek = 𝟐 mv2
This equation shows the relation between kinetic energy of a moving object with its mass and velocity.

Q3: What is potential Energy? Prove that gravitational potential energy of a body of mass “m” at a
height “h” above the surface of earth is given by mgh.
Ans: Potential Energy:
The energy possessed by a body due to its position or configuration in a force field is called
potential energy.
Explanation:
Potential energy can be produced by changing the position of a body horizontally or vertically
that is said to be elastic potential energy. For example, doing work on an elastic band by stretching it stores
 3
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
potential energy in the elastic bond. Also a battery contains both chemical and electrical potential energy.
When an object raised above the ground, it has gravitational potential energy due to its raised position.
Gravitational Potential Energy:
When a body is taken to a height with respect to earth, here work is done against the force of gravity
then potential energy stored in a body will be termed as gravitational potential energy. It is denoted by “EGP.E”.
If we release the body from that height, it will accelerate and gain kinetic energy as its velocity increases.
Thus “EGP.E” can be released and have the ability to do useful work.
Mathematical Form:
Mathematically, gravitational potential energy is the product of mass “m”, the acceleration due to
gravity “g” and the change in height “h”.
EGP.E = mgh
Derivation of Gravitational Potential Energy:
Consider a body of mass “m” is taken to certain height “h” due to applied force “F”. The work
done can be written as.
W=FxS ----------------- (i)
This is the work done by the body due to its height. So, it is considered as gravitational potential
energy then eq (i) becomes
W = EGPE
F x S = EGPE
Or, EGPE = F x S
As we know that,
Force “F” is equal to weight of body i-e F = W and S = h
EGPE = W x h
As we know, W = mg
EGPE = mg x h
Or, EGPE = mgh

Q4: State the law of conservation of energy and mass energy conversion relation.
Ans: Law of Conservation of Energy:
Statement:
The law of conservation of energy states that:
“Energy can neither be created nor destroyed in any process. It can be converted from one from to
another but the total amount of energy remains constant”.
Examples:
• In radio, electrical energy is converted into sound energy.
• In light bulb, electrical energy is converted into heat and light energy.
• In electric motor, electrical energy is converted into mechanical energy.
Mass Energy Equivalence / Equation:
According to Einstein’s mass energy equation “The energy “E” of a physical system is
numerically equal to the product of its mass “m” and the speed of light “c” squared. It is also known as mass
energy equivalence.
Mathematical Form:
Mathematical, mass energy equation can be written as:
Energy = mass X the speed of light squared
E = m x c2
Or E = mc2
Where the speed of light is constant having value of 3 X 108 ms-1, however this value needs to be
squared.
This equation shows the relationship between mass and energy that mass and energy are same physical entities
and can be changed into each other.
 4
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6

Q5: Explain briefly major sources of energy. Such fossil fuels, wind, solar, biomass, nuclear and
thermal energy.
Ans. Major sources of energy:
The major sources of energy are described below:
1. Fossil Fuels:
Coal, oil and natural gas are called fossil fuels because they are non – renewable resources that formed
when prehistoric plants and animals died and were gradually buried by layers of rock. Over million of years,
different types of fossil fuels i-e coal, oil or gas are formed.
Coal is most abundant fossil fuel in world, with an estimated reserve of one million metric tons.
Crude oil is refined into many different types of energy products i-e gasoline, jet fuel and heating oil.
Oil produces more energy than same amount of Coal.
Natural gas is often a byproduct of oil; it is the mixture of gases the most common of which is methane.
The main advantage of natural gas is that it is easy to transport.
Most of the energy that we use comes from fossil fuels which are burned in power stations, factories,
homes and vehicles etc. It is consumed in more than 80 % of the world demand for energy. The disadvantage
is that burning of fossil fuels caused atmospheric pollution.

2. Wind Energy:
The kinetic energy of the wind is currently used in many parts of the world to generate electricity. It is
a renewable resource that can be used again and again. It is ecofriendly source of energy but require very large
open space.

3. Solar Energy:
Solar energy is the energy obtained from sunlight. The energy from direct sun light can be used to
produce electricity. Today, solar cells are used to power everything from calculators and watches to small
cities. The energy obtained from sunlight is 100% free and very eco-friendly. It doesn’t cause any pollution.
However, just like wind energy, huge land area is required to produce electricity.

4. Bio – mass:
“Bio” means life so bio – mass is the energy from living things. The term “bio mass” refers to the
material from which we get bio-energy. Biomass is produced when the sun’s solar energy is converted into
plant matter (carbohydrates) by the process of photosynthetic. Only green plants and photosynthetic algae,
containing chlorophyll, are able to use solar energy. The simplest process employed to make use of this energy
is eating. In this way, we are taking advantage of the energy stored as biomass.

5. Geothermal Energy:
Geo means “earth” and thermal means “heat”. So, geothermal energy is the heat energy obtained from
earth’s core. The thermal energy contained within Earth’s core result from energy trapped almost 5 billion
years ago during the formation of planets. It is a natural renewable resource and doesn’t cause any pollution.
In many countries, geothermal energy is used to generate electricity.

6. Nuclear Energy:
Nuclear fission is the process of splitting large atoms i-e uranium into two or more pieces, which releases
a huge amount of energy in the form of radiation or heat. The heat is used to boil water that is further used to
produce electricity, In nuclear reactor, small quantities of fuel produce large amount of energy (E=mc2). The
advantage is that major portion of heat energy is used for useful purpose while some part of energy is wasted
that can cause pollution and it is harmful for the humans.
 5
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
Q6: Define and explain efficiency.
Ans. Efficiency:
Efficiency is the ratio of useful energy or work output to the total energy or work input.
Or
It is the ratio between work done by the machine and work done on the machine.
Mathematical Form:
𝑢𝑠𝑒𝑓𝑢𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑤𝑜𝑟𝑘
Efficiency =
𝑖𝑛𝑝𝑢𝑡 𝑤𝑜𝑟𝑘
𝑾𝟎
Efficiency =
𝑾𝒊
or
𝑢𝑠𝑒𝑓𝑢𝑙 𝑒𝑛𝑒𝑟𝑔𝑦 𝑜𝑢𝑡𝑝𝑢𝑡
Efficiency =
𝑒𝑛𝑒𝑟𝑔𝑦 𝑖𝑛𝑝𝑢𝑡
𝑬𝒐
Efficiency =
𝑬𝒊
Percentage efficiency:
Efficiency is always expressed in percentage. It is defined as the ratio of useful energy provided
by a device to the energy required to operate the device or machine. Mathematically the percentage efficiency
is calculated as follow.
𝑬
Efficiency = 𝑬𝒐 X 100%
𝒊
Or
𝑾𝒐
Efficiency = X 100 %
𝑾𝒊
Efficiency has no unit.
Explanation:
The efficiency of any machine describes the extent to which it converts the energy given as an input into the
required form of energy obtained from a machine as an output. As we know, energy can neither be created
nor destroyed. Like a light energy. While the bulb is transforming potential energy (Stored in it) into the
required form of energy i.e. light energy while some part of its energy is lost or wasted. That lost energy is
transformed into heat energy.
Thus it is not possible to have a machine with 100% efficiency because friction lowers the efficiency
of a machine. So, work output is always less than work input.
Examples:
1. In light bulb 5% of the electrical energy transforms into light energy while the rest of given energy is
wasted in the form of heat energy. So we say, the efficiency of light bulb is only 5% out of 100%.
2. If a petrol engine does 25 joule of useful work for every 100 joule of energy supplied to it, then its
efficiency will be 25%.

Q7. Define and explain power.

Ans. POWER:
Power is defined as the time rate at which work is done or time rate at which energy is converted.
Mathematical Form:
Mathematically, power can be written as:
𝑤𝑜𝑟𝑘
Power = 𝑡𝑖𝑚𝑒

𝑾
P= 𝒕
 6
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
Or (in terms of energy)
𝐸𝑛𝑒𝑟𝑔𝑦
Power =
𝑡𝑖𝑚𝑒
𝑬
P= 𝒕
EXPLANATION:
As we know, power is a measure of how fast work is done or how fast energy is being converted from one
form to another. Let suppose, there are two persons ‘A’ and ‘B’. They both are having equal masses. Person
‘A’ runs 5 meters in 1 min while person ‘B’ also runs 5 meter in 3 mins. So, it shows that person ‘A’ is more
powerful than person ‘B’ because both have performed the same work but person ‘A’ takes less time to cover
a distance of 5 m than person ‘B’ and he has performed work faster than ‘B’. Also his energy is quickly
converted from one form to another. So, we relate work or energy with time which shows how much power
is consumed in given time period.

QUANTITY AND UNIT:

Power is a scalar quantity. The SI unit of power is watt (W) where as 1 watt is equal to 1 Joule (J) per
1 second (s). i-e
1 W = 1Js-1
OTHER UNITS OF POWER:
A larger unit is often used for power is the “horse power (hp)” where as one horse power is equal to
746 W. i-e
1hp = 746 W
Another commercial unit of power is “kilowatt hour (kWh)” where as one kilowatt hour is the energy
converted or consumed in 1 hour at constant rate of 1000 Js-1 or 1kW. I-e
1kWh = 1000 x 3600
1kWh = 3600000
or 1kWh = 3.6 x 106 J

TOPIC WISE QUESTIONS

Q1: Define energy and explain different types of energy.
Ans: Energy:
Energy is defined as the ability to do work.
SI Unit:
The SI Unit of energy is Joule (J).
Types / Forms of Energy:
There are different types of energy which are as follow:
1. Kinetic Energy:
The energy possessed by a body due to its motion is called kinetic energy. If an object is moving, it
has kinetic energy i.e. a person running, a river flowing, or a car traveling on a road are the examples of kinetic
energy.

2. Potential energy:
The energy possessed by a body due to the position, arrangement or state of the object is called potential
energy. It is the energy that is stored in an object that has potential to do work. So, when the position,
arrangement or state of the object changes, the stored energy will be released.
For example, chemical potential energy is stored in the food you eat or the energy stored in stretched elastic
band.
 7
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
3. Chemical Energy:
Chemical energy is the stored energy in the bonds of chemical compounds such as atoms and molecules.
These bonds can take many different forms, like it is the energy stored in food, gasoline in chemical
combination. For example, striking a match stick or breaking light sticks releases chemical energy.

4. Heat Energy:
Heat energy is also known as thermal energy. Heat is a transfer of energy from one part of a substance to
another or from one object to another due to difference in temperature. For example, burning of fire transfer
the energy to keep room warm.

5. Electrical Energy:
The energy produced by electrons moving through a substance is called electrical energy. We mostly see
electric energy in batteries and from the outlets in our homes. It lights our homes, and runs all our appliances.
Electrical energy is major source of energy that is used in homes, offices, schools, industries etc.

6. Sound Energy:
Sound energy is produced when an object is made to vibrate. Sound energy travels out as waves in all
directions. Sound needs a medium to travel through such as air, water, Woods etc. For example, voices,
whistles, horns and musical instruments produced sound energy.

7. Nuclear Energy:
Nuclear energy is the energy that is released when the nuclei of atoms are spilt (fission) or fused together
(fusion). Nuclear energy is used in nuclear power plants to generate electricity. It is also used in sun and
atomic bonds.

8. Radiant energy:
Radiant energy is a combination of heat and light energy. It travels as an electromagnetic wave. Light
energy like sound energy travels in all direction in waves. For example, the microwave cooks food on the
basis of radiant energy. Other examples of radiant energy are the glowing coils on a toaster, the sun and even
headlights on cars.

CONCEPTUAL QUESTIONS:
1. Can a centripetal force ever do work on an object? Explain.
Ans. The centripetal force is always perpendicular to the direction of motion of an object. Only the component
of the force in the direction of motion can do work. The centripetal force has no such component, so it can
never do work on an object.

2. What happens to the kinetic energy of a bullet when it penetrates into a sand bag?
Ans: When a bullet penetrates into a sand bag its kinetic energy works against the frictional force of sand
particles up to a short distance and becomes in state of rest. In this the energy of the bullet is transferred to
sand particles, some energy is converted into heat and sound energy.

3. A meteor enters into earth’s atmosphere and burns. What happens to its kinetic energy?
Ans: When meteor enters into earth’s atmosphere its kinetic Energy works against the frictional force of gases
therefore the meteor burns and its kinetic energy is converted into light and heat energy.

4. Two bullets are fired at the same time with the same kinetic energy. If one bullet has twice the mass
of the other which has the greater speed and by what factor? Which can do the most work?
Ans: Kinetic energy of a particle is
 8
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
1
EK = 2 mv2
Kinetic energy of the first bullet is,
1
EK1 = 2 m1v12
Here m1 is the mass of first bullet and v1 is the speed of the first bullet.
Kinetic energy of the second bullet is,
1
EK2 = 2 m2 v2 2
Here m2 is the mass of the second bullet and v2 is the speed of the second bullet.
Since, kinetic energy of both the bullets are same.
E K1 = E K2
1 1
m1v12 = 2 m2v22 (i)
2
Since mass of one bullet is twice the mass of the other bullet. So, put m1 = 2m2 in eq (i)
1 1
(2m2) v12 = m2v22
2 2
Rearrange the equation
1
m2v12= 2 m2v22
1
=> v12 = 2 v22
Multiplying 2 on both sides
1
2v12 = 2 × 2 v22
2v12 = v22
=> v22 = 2v12
Taking square root on both sides
√𝑣22 = √2𝑣1 2
v2 = √𝟐v1
Thus, the second bullet travels with greatest speed with a factor of √2. Both the bullets have the same kinetic
energies therefore they can do the same work.

5. Can an object have different amounts of gravitational potential energy if it remains at the same
elevation?
Ans: We know that
Ep = mgh (i)
Eq (i) shows that gravitational potential energy is directly proportional to the mass of object and height of
object.
If the objects have same masses and remain at the same elevation then gravitational potential energy of the
objects remains same.
If the objects have different masses and remains at the same elevation then object with greater mass has
greater potential energy and the object with lighter mass has less gravitational potential energy.

6. Why do roads lead to the top of a mountain wind back and forth?
Ans: The reason is that most vehicles don’t have the ability to exert enough force, fast enough to climb up a
steep slope. By making vehicle go up a longer, but less steep slope, the vehicle has to exert less power over a
longer period of time.
Also, going down those steep slopes may cause more accidents that the winding mountain road. Therefore, to
reduce the incline of the road, we make road longer by putting curves in it.
 9
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
7. Which would have a greater effect on the kinetic energy of an object, doubling the mass or doubling
the velocity?
Ans. We know that
1
Ek = 2 mv2
If m = 2m

Then
1
EK1 = 2 (2m) v2
1
= (2)𝑚𝑣2
2
1
EK1 = 2 (2 mv2)
𝐄𝐊𝟏 = 2 Ek (i)
Eq (i) shows that if we double the mass the kinetic energy will also be double
Now
1
EK2 = 2 mv2
If v = 2v
Then
1
EK2 = 2m(2v)2
1
= 2 m (4v2)
1
= 4 (2mv2)
𝐄𝐊𝟐 = 4Ek ---------- (ii)
Eq(ii) shows that if we double the velocity the kinetic energy will be increases four times.
Therefore, doubling the velocity has greater effect on the kinetic energy of the object than doubling the mass.

8. If the speed of a particle triples, by what factor does its kinetic energy increases?
Ans. As we know that
1
Ek=2 mv2
If v = 3v
Then
1
EK1 = 2 m (3v)2
1
= 2 m (9)v2
1
= 9 (2mv2)
𝐄𝐊𝟏 = 9 Ek - (i)
Eq (i) shows that if we triple the speed of the particle then the kinetic energy of the particle increases the
factor nine.

9. The motor of a crane uses power P to lift a steel beam. By what factor must the motor’s power
increase to lift the beam twice as high in half the time.
Ans. We know that
𝑾
P = 𝒕 --------------- (i)
Here work done is due to gain in potential energy. So,
W = mgh
Eq (i) becomes
 10
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
𝑚𝑔ℎ
P= 𝑡
1
If h = 2h and t = 2 t
𝑚𝑔(2ℎ)
P= 1
𝑡
2
2𝑚𝑔ℎ
= 1
𝑡
2
2×2𝑚𝑔ℎ
= 𝑡
4𝑚𝑔ℎ
P= 𝑡
𝑚𝑔ℎ
P = 4( 𝑡 )
P = 4 P – (ii)
Eq (ii) shows that power ‘P’ will increases by factor 4, if we lift the beam twice as high in half the time.

ASSIGNMENTS
6.1 During a tug – of – war, team A pulls on team B by applying a force of 1100 N to the rope between
them. The rope remains parallel to the ground. How much work does team A do if they pull team B
towards them a distance of 2.0 m?
Given data:
Force = F = 1100N
Distance = S = 2m
Find:
Work done = W = ?
Solution:
As we know that
W=F×S
= 1100 × 2
W = 2200 J
Or W= 2.2 × 103J

6.2 A bullet of mass 30g travels at a speed of 400ms-1. Calculate its kinetic energy.
Given Data:
Mass = m = 30g
30
= 1000 𝑘𝑔
= 0.03 kg
Speed = v = 400m/s
Find:
Kinetic Energy = Ek = ?
Solution:
As we know that
𝟏
Ek = 𝟐 mv2
Putting values
1
= 2 (0.03)(400)2
Ek = (0.5)(0.03)(400)2
Ek = 0.5 × 0.03 × 160000
Ek = 2400 J
 11
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
6.3 An object of mass 10 kg is lifted vertically through a height of 5m at a constant speed. What is the
gravitational potential energy gained by the object?
Given Data:
Mass = m = 10 kg
Height = h = 5m
Acceleration due to gravity = g = 9.8 m/s2

Find:
Gravitational potential energy = Ep = ?
Solution:
As we know that
Ep = mgh
Putting values
Ep = 10 × 9.8 × 5
Ep = 490 J

6.4 How much energy is generated when mass of 1 g is completely converted into energy?
Given Data:
Mass = m = 1 g
1
= 1000 kg
= 0.001 kg
Speed of light = c = 3 ×108 m/s
Find:
Energy = E = ?
Solution:
By Einstein equation
E = mc2
Putting value
E = (0.001)(3×108)2
= 0.001×9×1016
= 0.009 × 1016
= 9 × 10-3 × 1016 J
= 9 × 10-3+16 J
E = 9 × 1013 J

6.5 An electric heater is heated at 250W. Calculate the quantity of heat generated in 10 minutes.
Given Data:
Power = P = 250 W
Time = t = 10 min
= 10 × 60 sec
= 600 sec
Find:
Quantity of heat is work done = W = ?
Solution:
As we know that
𝑊
P= 𝑡
or W = P ×t
Putting values
W = 250 ×600 J
 12
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
= 150000 J
= 150 × 103 J
W = 150 kJ
NUMERICALS
1.Determine the work done in each of the following cases:
a.Kicking a soccer ball forward with a force of 40 N over a distance of 15 cm.
Given data:
Force = F = 40 N
15
Distance = S = 15 cm = 100m = 0.15 m
Find:
Work done = W = ?
Solution:
As we know that
W=F×S
= 40 × 0.15
W = 6J
b. Lifting a 50 kg barbell straight up 1.95 m
Given data:
Mass of barbell = m = 50 kg
Acceleration due to gravity = g = 9.8 m/s2
Distance = S = 1.95m
Find:
Work done = W = ?
Solution:
By using formula
W = F ×S – (i)
As we know that
F = mg
Putting value
= 50 ×9.8
F = 490 N
Now putting values in eq (i)
W=F×S
= 490 × 1.95
W = 955.5J
= 9.55 × 102 J
W = 9.6 × 102 J

2.Calculate the velocity of a 1.2 kg falling star (meteorite) with 5.5 × 108 J of energy.
Given data:
Mass = m = 1.2 kg
Energy = E = 5.5 × 108 J
Find:
Velocity = v = ?
Solution:
As we know that
𝟏
EK = 𝟐 mv2
Rearranging the formula
 13
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
2 EK = mv2
2𝐸𝑘
= v2
𝑚
2𝐸𝑘
or v2 = 𝑚
Taking square root on both sides
2𝐸𝑘
√𝑣 2 = √ 𝑚
𝟐𝑬𝒌
v= √ 𝒎
Putting values
2×5.5×108
=√ 1.2
11×108
=√ 1.2
11
= √1.2 × 108
= √9.16 × 108 m/s
v = 3.02 × 104 m/s
or
v = 3 × 1𝟎𝟒 m/s

3. Calculate the gravitational potential energy of a 2000 kg piano.

a.Resting on the floor.
Given data:
Mass = m = 2000 kg
Height = h = 0 m
Acceleration due to gravity = g = 9.8 m/s2
Find:
Gravitational potential energy = Ep = ?
Solution:
As we know that
Ep = mgh
Putting value
= 2000 × 9.8 × 0
Ep = 0 J

b. With respect to the basement floor, 1.9m below.

Given data:
Mass = m = 2000 kg
Height = h = 1.9m
Acceleration due to gravity = g = 9.8 m/s2
Find:
Gravitational potential energy = Ep = ?
Solution:
As we know that
Ep = mgh
Putting values
= (2000) × 9.8 × 1.9
Ep = 37240 J
 14
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
Ep = 3.7 × 1𝟎𝟒 J

4.An elevator weighting 5000 N is raised to a height of 15.0m in 10.0s, how much power is developed?
Given data:
Weight of elevator = W= mg = 5000 N
Height = h = 15 m
Time = t = 10 Sec
Find:
Power = P = ?
Solution:
As we know that
𝑬
P = 𝒕𝑷 ---------- (1)
For finding𝐸𝑃 , we know that
Ep = mgh
= 5000 × 15
Ep = 75000 J
Putting value of 𝐸𝑃 in eq 1
𝑬
P = 𝒕𝑷
75000
= 10 W
P = 7500 W

5.What power is required for a ski – hill chair lift that transports 500 people (average mass 65 kg) per
hour to an increased elevation of 1200 m?
Given data:
Average mass of one person = 65 kg
Mass of 500 peoples = m = 500 × 65 kg
m= 32500 kg
Height = h = 1200m
Acceleration due to gravity = 9.8 m/s2
Time = 1 hour
= 1 × 60 × 60 sec
= 3600 sec
Find:
Power = P = ?
Solution:
As we know that
𝑬
P = 𝒕𝑷 ------- (i)
So,
Ep = mgh
= 32500 × 9.8 × 1200
Ep = 382200000 J
Eq(i) =>
𝐸
P = 𝑡𝑃
Putting values
382200000
= W
3600
= 106166.6 W
 15
https://web.facebook.com/TehkalsDotCom
https://tehkals.com
Chapter # 6
= 1.06166 × 105 W
P = 1.06 × 105W

6.How long will it take a 2750 – W motor to lift a 385 – kg sofa set to a sixth - story window 16.0 m
above?
Give Data:
Power = P =2750 W
Mass = m = 385 Kg
Height = h = 16.0m
Acceleration due to gravity = g = 9.8 m/s2
Time = t = ?
Solution:
As we know that
𝑾
P = ------------------(i)
𝒕
Here
W = Ep = mgh
Putting values
W = 385 × 9.8 × 16 J
W = 60368 J
Now eq (i) becomes
𝑊
P= 𝑡
𝐖
⇒𝐭= 𝐏
Putting Value
60368
t = 2750 sec
= 21.9 Sec
Or
t = 22 Sec

7. How much work can a 2.0 hp motor do in 1.0h?

Data:
Power = P = 2hp
= 2 × 746 W :. 1hp = 746 W
= 1492 W
Time = t= 1 hour
= 1 hour
= 1 × 60 × 60 Sec
= 3600 Sec
Find:
Work done = W = ?
Solution:
As we know that
𝑾
P= 𝒕
or W = P×t
= 1492×3600
= 5371200 J
= 5.37×106J
W = 5.4 × 106 J