11P06
Work, Energy and Power
11P06.1
Scalar Product and Work
11P06.1 Scalar Product and Work
Learning Objectives
Scalar Product
Work
Conservative and Non Conservative Force
11P06.1
CV 1
Scalar Product
11P06.1 Work
Scalar Product
Multiplication of Vector
11P06.1 Work
Scalar Product
Multiplication of Vector
With Scalar Quantity
11P06.1 Work
Scalar Product
Multiplication of Vector
With Scalar Quantity
With Vector Quantity
11P06.1 Work
Scalar Product
Multiplication of Vector
With Scalar Quantity
With Vector Quantity
Dot/Scalar Product
11P06.1 Work
Scalar Product
Multiplication of Vector
With Scalar Quantity
With Vector Quantity
Dot/Scalar Product
Denoted by (•)
11P06.1 Work
Scalar Product
Multiplication of Vector
With Scalar Quantity
With Vector Quantity
Dot/Scalar Product
Cross Product
Denoted by (•)
11P06.1 Work
Scalar Product
Multiplication of Vector
With Scalar Quantity
With Vector Quantity
Dot/Scalar Product
Cross Product
Denoted by (•)
Denoted by ( ╳ )
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
Scalar Quantity
θ
Scalar Product
Geometrical meaning of Dot Product:
Scalar Product
Geometrical meaning of Dot Product:
Scalar Product
Geometrical meaning of Dot Product:
ConcepTest
Ready for challenge
11P06.1 Work
Scalar Product
Question:
Solution:
Pause the Video
(Time Duration : 2 Minutes)
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
ConcepTest
Ready for challenge
11P06.1 Work
Scalar Product
Question:
Solution:
Pause the Video
(Time Duration : 2 Minutes)
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
When vectors are given in component form
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
When vectors are given in component form
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
When vectors are given in component form
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
When vectors are given in component form
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
When vectors are given in component form
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
When vectors are given in component form
11P06.1 Work
Scalar Product
Scalar Product/Dot product:
When vectors are given in component form
ConcepTest
Ready for challenge
11P06.1 Work
Scalar Product
Question:
Solution:
Pause the Video
(Time Duration : 3 Minutes)
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
11P06.1 Work
Scalar Product
Question:
Solution:
Scalar Product
Properties of Scalar Product:
Scalar Product
Properties of Scalar Product:
Scalar Product
Properties of Scalar Product:
Scalar Product
Properties of Scalar Product:
Scalar Product
CV-2
Work
Work
What is the work?
You are solving your homework problem in your mind
Is this a work ?
Work
What is the work?
A person carries buckets of water along a horizontal path while walking at constant velocity.
Is he doing Work?
Work
What is the work?
A Man holds a chair at arm’s length for several minutes.
Is he doing Work?
Work
What is the work?
No, These all are not doing any work according to the language of science
11P06.1 Work
Work
What is the work?
Work is said to be done when a force is applied on an object and there is a displacement of the point of application in the direction of the force or in the direction other than 90 degrees with the direction of force.
11P06.1 Work
Work
11P06.1 Work
Work
Work is a Vector Quantity or a Scalar Quantity?
11P06.1 Work
Work
Work is a Scalar Quantity
Work is a Vector Quantity or a Scalar Quantity?
11P06.1 Work
Work
What is the Unit and Dimension of Work ?
11P06.1 Work
Work
What is the Unit and Dimension of Work ?
Unit of work is N-m or Joule(J)
Dimension of work is [ML2T-2]
11P06.1 Work
Work
Nature of Work
11P06.1 Work
Work
0° ≤ θ < 90° cosθ>0
Nature of Work
Positive Work
11P06.1 Work
Work
Nature of Work
Negative Work
180°≥θ>90° cosθ<0
11P06.1 Work
Work
Nature of Work
Zero Work
Displacement = 0
11P06.1 Work
Work
Nature of Work
Zero Work
Displacement = 0
or θ = 90° cosθ=0
ConcepTest
Ready for challenge
11P06.1 Work
Work
Example: A Force of 15 N at angle 600 from horizontal is used to push a box along
the floor a distance of 3 meters. How much work was done?
Pause the Video
(Time Duration : 2 Minutes)
11P06.1 Work
Work
Example: A Force of 15 N at angle 600 from horizontal is used to push a box along
the floor a distance of 3 meters. How much work was done?
Solution:
11P06.1 Work
Work
Example: A Force of 15 N at angle 600 from horizontal is used to push a box along
the floor a distance of 3 meters. How much work was done?
Solution:
CV-3
Work Done by Variable Force
11P06.1 Work
Variable Force
Variable:Quantity Which changes with respect to any other quantity
11P06.1 Work
Variable Force
Variable Force: when magnitude or direction of force changes with time or displacement
11P06.1 Work
Variable Force
Variable Force: when magnitude or direction of force changes with time or displacement
11P06.1 Work
Variable Force
Variable Force: when magnitude or direction of force changes with time or displacement
F
t
F
X
11P06.1 Work
Work
Spring Force
11P06.1 Work
Work
Spring Force
11P06.1 Work
Work
Spring Force
(Hooke’s Law)
k = spring constant
k ∝ stiffness of spring
11P06.1 Work
Work
Spring Force
(Hooke’s Law)
k = spring constant
k ∝ stiffness of spring
FS
X
11P06.1 Work
Work done by a variable Force
Work done by a variable Force:
11P06.1 Work
Work
Work done by a variable Force
Work done by a variable Force:
11P06.1 Work
Work
Work done by a variable Force
Work done by a variable Force:
11P06.1 Work
Work
Work done by a variable Force
Work done by a variable Force:
11P06.1 Work
Work
Work done by a variable Force
Work done by a variable Force:
11P06.1 Work
Work
Work done by a variable Force
Work done by Spring:
FE
FS
xm
x=0
11P06.1 Work
Work
Work done by a variable Force
Work done by Spring:
FE
FS
xm
x=0
11P06.1 Work
Work
Work done by a variable Force
Work done by Spring:
FE
FS
xm
x=0
11P06.1 Work
Work
Work done by a variable Force
Work done by Spring:
FE
FS
xm
x=0
11P06.1 Work
Work
Work done by a variable Force
Work done by Spring:
ConcepTest
Ready for challenge
11P06.1 Work
Work
Work done by a variable Force
Question: Figure show the force F (in newton) acting on a body as a function of x.
Calculate the work done in moving the body from x = 0 to x = 4 m.
Pause the Video
(Time Duration : 3 Minutes)
11P06.1 Work
Work
Work done by a variable Force
Question: Figure show the force F (in newton) acting on a body as a function of x.
Calculate the work done in moving the body from x = 0 to x = 4 m.
Solution:
11P06.1 Work
Work
Work done by a variable Force
Question: Figure show the force F (in newton) acting on a body as a function of x.
Calculate the work done in moving the body from x = 0 to x = 4 m.
Solution:
11P06.1 Work
Work
Work done by a variable Force
Question: Figure show the force F (in newton) acting on a body as a function of x.
Calculate the work done in moving the body from x = 0 to x = 4 m.
Solution:
11P06.1 Work
Work
Work done by a variable Force
Question: Figure show the force F (in newton) acting on a body as a function of x.
Calculate the work done in moving the body from x = 0 to x = 4 m.
Solution:
11P06.1 Work
Work
Work done by a variable Force
Question: Figure show the force F (in newton) acting on a body as a function of x.
Calculate the work done in moving the body from x = 0 to x = 4 m.
Solution:
ConcepTest
Ready for challenge
11P06.1 Work
Work
Work done by a variable Force
Question: A force is given by function F=x2 calculate the work done by it for
displacement of body from x=3 to x=9.
Solution:
Pause the Video
(Time Duration : 3 Minutes)
11P06.1 Work
Work
Work done by a variable Force
Question: A force is given by function F=x2 calculate the work done by it for
displacement of body from x=3 to x=9.
Solution:
11P06.1 Work
Work
Work done by a variable Force
Question: A force is given by function F=x2 calculate the work done by it for
displacement of body from x=3 to x=9.
Solution:
11P06.1 Work
Work
Work done by a variable Force
Question: A force is given by function F=x2 calculate the work done by it for
displacement of body from x=3 to x=9.
Solution:
CV-4
Conservative and Non-Conservative Force
11P06.1 Work
Conservative and Non-Conservative Force
Conservative Force
Work done depends only on initial and final position of object.
Example:Gravitational force,Spring Force
11P06.1 Work
Conservative and Non-Conservative Force
Conservative Force
11P06.1 Work
Conservative and Non-Conservative Force
f
Work done depends on path rather than initial and final positions of objects.
Example:Friction force
Non-Conservative Force
11P06.1 Work
Conservative and Non-Conservative Force
Non-Conservative Force
f
f
f
Work done depends on path rather than initial and final positions of objects.
Example:Friction force
f
11P06.1 Work
Conservative and Non-Conservative Force
Non-Conservative Force
f
f
f
Work done depends on path
11P06.1 Work
Conservative and Non-Conservative Force
Non-Conservative Force
f
f
f
Work done depends on path
f
|Wf(ACB)| >|Wf(AB)|
ConcepTest
Ready for challenge
11P06.1 Work
Conservative and Non-Conservative Force
Question: A ball of mass m is thrown upwards from ground calculate the total work
done by gravity when it reaches back to the ground.
Solution:
Pause the Video
(Time Duration : 1 Minutes)
11P06.1 Work
Conservative and Non-Conservative Force
Question: A ball of mass m is thrown upwards from ground calculate the total work
done by gravity when it reaches back to the ground.
Solution: Gravity is a conservative force so for same initial and final point the total
work done by it will be zero.
11P06.1 Work
Conservative and Non-Conservative Force
Question: A ball of mass m is thrown upwards from ground calculate the total work
done by gravity when it reaches back to the ground.
Solution: Gravity is a conservative force so for same initial and final point the total
work done by it will be zero.
Or
Suppose ball went a height H upwards
Work done by gravity when ball is
Going upward
Work done by gravity when ball is
coming downward
ConcepTest
Ready for challenge
11P06.1 Work
Conservative and Non-Conservative Force
Question: Calculate the work done by friction when a box of mass 10 kg is moved
from A to B by Path AB and ACDB. 𝜇 for the surface is 0.2.
Take g=10 ms-2 .
Solution:
A
B
D
C
4 m
4 m
4 m
4 m
11P06.1 Work
Conservative and Non-Conservative Force
Question: Calculate the work done by friction when a box of mass 10 kg is moved
from A to B by Path AB and ACDB. 𝜇 for the surface is 0.2.
Take g=10 ms-2 .
Solution:
A
B
D
C
4 m
4 m
4 m
4 m
Pause the Video
(Time Duration : 3 Minutes)
11P06.1 Work
Conservative and Non-Conservative Force
Question: Calculate the work done by friction when a box of mass 10 kg is moved
from A to B by Path AB and ACDB. 𝜇 for the surface is 0.2.
Take g=10 ms-2 .
Solution:
A
B
D
C
4 m
4 m
4 m
4 m
11P06.1 Work
Conservative and Non-Conservative Force
Question: Calculate the work done by friction when a box of mass 10 kg is moved
from A to B by Path AB and ACDB. 𝜇 for the surface is 0.2.
Take g=10 ms-2 .
Solution:
A
B
D
C
4 m
4 m
4 m
4 m
11P06.1 Work
Conservative and Non-Conservative Force
Question: Calculate the work done by friction when a box of mass 10 kg is moved
from A to B by Path AB and ACDB. 𝜇 for the surface is 0.2.
Take g=10 ms-2 .
Solution:
A
B
D
C
4 m
4 m
4 m
4 m
11P06.1 Work
11P06.1 Summary
PSV 1
11P06.1 Scalar Product and Work
Question: A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (a) work done by the applied force in 10 s
(b) work done by friction in 10 s
(c) work done by the net force on the body in 10 s.
11P06.1 Work
11P06.1 Scalar Product and Work
Question: A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (a) work done by the applied force in 10 s.
Solution:
11P06.1 Work
11P06.1 Scalar Product and Work
Question: A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (a) work done by the applied force in 10 s.
Solution:
11P06.1 Work
11P06.1 Scalar Product and Work
Question: A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (a) work done by the applied force in 10 s.
Solution:
11P06.1 Work
11P06.1 Scalar Product and Work
Question: A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (a) work done by the applied force in 10 s.
Solution:
11P06.1 Work
11P06.1 Scalar Product and Work
Question: A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (a) work done by the applied force in 10 s.
Solution:
11P06.1 Work
11P06.1 Scalar Product and Work
Question: A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (a) work done by the applied force in 10 s.
Solution:
11P06.1 Work
11P06.1 Scalar Product and Work
Question:A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (a) work done by the applied force in 10 s
Solution: (a)
11P06.1 Work
11P06.1 Scalar Product and Work
Question:A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (b) work done by friction in 10 s
Solution: (b)
11P06.1 Work
11P06.1 Scalar Product and Work
Question:A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (c) work done by the net force on the body in 10 s.
Solution: (c)
11P06.1 Work
11P06.1 Scalar Product and Work
Question:A body of mass 2 kg initially at rest moves under the action of an applied
horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1
Compute the (c) work done by the net force on the body in 10 s.
Solution: (c)
11P06.2
Energy
11P06.2 Energy
Learning Objectives
Introduction to Energy
Forms of Energy
Kinetic Energy
Potential Energy
Conservation of Energy
CV-1
Introduction to Energy
Energy
Energy
Energy
Energy
Capacity of Doing Work or cause change
Energy
Energy
Energy
An object which does work losses energy
Energy
Capacity of Doing Work or cause change
Energy
An object which does work losses energy
Energy
An object on which work is done gains Energy
Capacity of Doing Work or cause change
Energy
Energy
Capacity of Doing Work
Work
Transfer of Energy
Energy
Energy
Capacity of Doing Work
Work
Transfer of Energy
Unit of Energy= Unit of Work=Joule(J)
CV-2
Forms of Energy
11P06.2 Energy
Energy
Forms of Energy
Electrical Energy
Heat Energy
Chemical Energy
Nuclear Energy
Mechanical Energy
11P06.2 Energy
Energy
Electrical Energy
11P06.2 Energy
Energy
Chemical Energy
11P06.2 Energy
Energy
Heat Energy
Steam Engine
11P06.2 Energy
Energy
Nuclear Energy
Nuclear Power Plant
11P06.2 Energy
Energy
Mechanical Energy
11P06.2 Energy
Energy
Mechanical Energy
It is energy in an object due to its motion or position.
11P06.2 Energy
Energy
Mechanical Energy
Kinetic Energy
Potential Energy
CV-3
Kinetic Energy
Kinetic Energy
Kinetic Energy:
Energy of a body by virtue of its motion
Kinetic Energy
Kinetic Energy:
Energy of a body by virtue of its motion
Kinetic Energy
Kinetic Energy:
Energy of a body by virtue of its motion
If an object is moving, then it is capable of doing work. It has energy of motion, or kinetic energy (KE)
Kinetic Energy
Kinetic Energy:
Energy of a body by virtue of its motion
If an object is moving, then it is capable of doing work. It has energy of motion, or kinetic energy (KE)
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
The net work done on an object is equal to its change in kinetic energy (W = KEf – KEi)
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
The net work done on an object is equal to its change in kinetic energy (W = KEf – KEi)
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
m
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
m
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
m
m
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
m
m
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
m
m
11P06.2 Energy
Kinetic Energy
Work Energy Theorem:
m
m
ConcepTest
Ready for challenge
11P06.2 Energy
Kinetic Energy
Question:A locomotive weighing 106 kg starts from rest and moves with a
constant acceleration of 0.5 m/s2. After travelling a distance of 900 m on
the track, what is the kinetic energy of the locomotive?
Solution:
Pause the Video
(Time Duration : 2 Minutes)
11P06.2 Energy
Kinetic Energy
Question:A locomotive weighing 106 kg starts from rest and moves with a
constant acceleration of 0.5 m/s2. After travelling a distance of 900 m on
the track, what is the kinetic energy of the locomotive?
Solution:
11P06.2 Energy
Kinetic Energy
Question:A locomotive weighing 106 kg starts from rest and moves with a
constant acceleration of 0.5 m/s2. After travelling a distance of 900 m on
the track, what is the kinetic energy of the locomotive?
Solution:
11P06.2 Energy
Kinetic Energy
Question:A locomotive weighing 106 kg starts from rest and moves with a
constant acceleration of 0.5 m/s2. After travelling a distance of 900 m on
the track, what is the kinetic energy of the locomotive?
Solution:
11P06.2 Energy
Kinetic Energy
Question:A locomotive weighing 106 kg starts from rest and moves with a
constant acceleration of 0.5 m/s2. After travelling a distance of 900 m on
the track, what is the kinetic energy of the locomotive?
Solution:
ConcepTest
Ready for challenge
11P06.2 Energy
Kinetic Energy
Question:A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches
the bottom if the incline is smooth?
Solution:
Pause the Video
(Time Duration : 2 Minutes)
11P06.2 Energy
Kinetic Energy
Question:A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches
the bottom if the incline is smooth?
Solution: Work done by the forces N and, which
are normal to the surface, is zero.
11P06.2 Energy
Kinetic Energy
Question:A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches
the bottom if the incline is smooth?
Solution: Work done by the forces N and, which
are normal to the surface, is zero.
Work done by the force mg sin θ =
11P06.2 Energy
Kinetic Energy
Question:A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches
the bottom if the incline is smooth?
Solution: Work done by the forces N and, which
are normal to the surface, is zero.
Work done by the force mg sin θ =
Work = change in kinetic energy
CV-4
Potential Energy
Potential Energy
Stored energy that results from the position or shape of an object is called Potential Energy
Potential Energy
Stored energy that results from the position or shape of an object is called Potential Energy
Potential Energy
Stored energy that results from the position or shape of an object is called Potential Energy
Potential Energy
Stored energy that results from the position or shape of an object is called Potential Energy
Potential Energy
Work done against conservative force is stored as potential energy
m
m
H
Potential Energy
Work done against conservative force is stored as potential energy
m
m
H
FE
FS
xm
x=0
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Potential Energy
Gravitational Potential Energy
Elastic Potential Energy
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Gravitational Potential Energy
Energy that is related to an object’s height with respect to earth's surface is called gravitational potential energy
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Gravitational Potential Energy
m
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Gravitational Potential Energy
m
m
H
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Gravitational Potential Energy
Work done against gravity=WE
m
m
H
m
m
H
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Gravitational Potential Energy
Work done against gravity=WE
Stored Potential Energy= V(H)=WE
m
m
H
m
m
H
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Gravitational Potential Energy
Work done against gravity=WE
Stored Potential Energy= V(H)=WE
m
m
H
m
m
H
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Gravitational Potential Energy
Work done against gravity=WE
Stored Potential Energy= V(H)=WE
m
m
H
m
m
H
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Gravitational Potential Energy
Work done against gravity=WE
Stored Potential Energy= V(H)=WE
Potential Energy= (Work done by conservative Force)
m
m
H
m
m
H
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Gravitational Potential Energy
Work done against gravity=WE
Stored Potential Energy= V(H)=WE
Potential Energy= (Work done by conservative Force)
m
m
H
m
m
H
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Generalised Formula For Potential Energy
(Work done by conservative Force) = Potential Energy
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Generalised Formula For Potential Energy
Generalised Formula For Potential Energy
(Work done by conservative Force) = Potential Energy
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Elastic Potential Energy
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Elastic Potential Energy
11P06.3 Potential Energy and Power
Potential Energy
Potential Energy For a Spring
11P06.3 Potential Energy and Power
Potential Energy
Potential Energy For a Spring
11P06.3 Potential Energy and Power
Potential Energy
Potential Energy For a Spring
11P06.3 Potential Energy and Power
Potential Energy
Potential Energy For a Spring
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Potential Energy is always defined relatively,absolute value of PE cannot be calculated.
11P06.3 Potential Energy and Power
Kinetic Energy
Potential Energy
Potential Energy is always defined relatively,absolute value of PE cannot be calculated.
Reference level:The place in a system where the PE is defined to be zero.
examples: A pendulum’s lowest point, Mean Position of spring,Bottom of a mountain etc.
CV-5
Conservation of Energy
11P06.3 Potential Energy and Power
Potential Energy
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy
The Total Mechanical Energy of a System is Conserved if the Forces, Doing Work are Conservative.
11P06.3 Potential Energy and Power
Potential Energy
Conservation of Energy
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy
11P06.3 Potential Energy and Power
Potential Energy
Conservation of Energy
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy
11P06.3 Potential Energy and Power
Potential Energy
Conservation of Energy
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy
11P06.3 Potential Energy and Power
Potential Energy
Conservation of Energy
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy
11P06.3 Potential Energy and Power
Potential Energy
Conservation of Energy
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a ball in gravitational field:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a ball in gravitational field:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a ball in gravitational field:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a ball in gravitational field:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a ball in gravitational field:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a ball in gravitational field:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a ball in gravitational field:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a ball in gravitational field:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a Spring:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Conservation of Mechanical Energy for a Pendulum:
11P06.3 Potential Energy and Power
Conservation of Energy
If Non-Conservative Forces are also Applying in system?
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Energy
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Energy
Energy can neither be created, nor destroyed.Total energy of an isolated system remains constant
ConcepTest
Ready for challenge
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: A small roller coaster starts at point A from rest on a curved track as shown in the figure. The friction between the roller coaster and the track is negligible and it always remains in contact with the track. What will be the speed of roller coaster at point D ?
Solution:
θ
Pause the Video
(Time Duration : 2 Minutes)
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: A small roller coaster starts at point A from rest on a curved track as shown in the figure. The friction between the roller coaster and the track is negligible and it always remains in contact with the track. What will be the speed of roller coaster at point D ?
Solution:
θ
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: A small roller coaster starts at point A from rest on a curved track as shown in the figure. The friction between the roller coaster and the track is negligible and it always remains in contact with the track. What will be the speed of roller coaster at point D ?
Solution:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: A small roller coaster starts at point A from rest on a curved track as shown in the figure. The friction between the roller coaster and the track is negligible and it always remains in contact with the track. What will be the speed of roller coaster at point D ?
Solution:
θ
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: A small roller coaster starts at point A from rest on a curved track as shown in the figure. The friction between the roller coaster and the track is negligible and it always remains in contact with the track. What will be the speed of roller coaster at point D ?
Solution:
θ
ConcepTest
Ready for challenge
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: What will be the maximum velocity for a block of mass m when it is
stretched xm from its mean position and released from rest ?
Solution:
xm
x=0
Pause the Video
(Time Duration : 2 Minutes)
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: What will be the maximum velocity for a block of mass m when it is
stretched xm from its mean position and released from rest ?
Solution:
xm
x=0
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: What will be the maximum velocity for a block of mass m when it is
stretched xm from its mean position and released from rest ?
Solution:
xm
x=0
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: What will be the maximum velocity for a block of mass m when it is
stretched xm from its mean position and released from rest ?
Solution:
xm
x=0
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: What will be the maximum velocity for a block of mass m when it is
stretched xm from its mean position and released from rest ?
Solution:
xm
x=0
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: What will be the maximum velocity for a block of mass m when it is
stretched xm from its mean position and released from rest ?
Solution:
xm
x=0
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: What will be the maximum velocity for a block of mass m when it is
stretched xm from its mean position and released from rest ?
Solution:
xm
x=0
ConcepTest
Ready for challenge
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J.
At what height the kinetic energy of the body becomes half of the original
value?
Solution:
θ
Pause the Video
(Time Duration : 2 Minutes)
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J.
At what height the kinetic energy of the body becomes half of the original
value?
Solution:
θ
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J.
At what height the kinetic energy of the body becomes half of the original
value?
Solution:
θ
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Question: A body of mass 5 kg is thrown vertically up with a kinetic energy of 490 J.
At what height the kinetic energy of the body becomes half of the original
value?
Solution:
θ
CV-6
Vertical Circular Motion
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Vertical Circular Motion
Vertical Circular Motion:
11P06.3 Potential Energy and Power
Conservation of Energy
Vertical Circular Motion
Vertical Circular Motion:
11P06.3 Potential Energy and Power
Conservation of Energy
Vertical Circular Motion
Vertical Circular Motion:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Vertical Circular Motion:
2L
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Vertical Circular Motion:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Vertical Circular Motion:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Vertical Circular Motion:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Vertical Circular Motion:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Vertical Circular Motion:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Vertical Circular Motion:
11P06.3 Potential Energy and Power
Conservation of Energy
Conservation of Mechanical Energy
Vertical Circular Motion:
11P06.1 Work
11P06.2 Summary
11P06.1 Work
11P06.2 Summary
PSV 2
θ
Question: A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches the
bottom if the coefficient of friction between the body and the incline is μ.
Solution:
Question: A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches the
bottom if the coefficient of friction between the body and the incline is μ.
Solution:
θ
Question: A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches the
bottom if the coefficient of friction between the body and the incline is μ.
Solution:
θ
θ
Question: A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches the
bottom if the coefficient of friction between the body and the incline is μ.
Solution:
θ
Question: A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches the
bottom if the coefficient of friction between the body and the incline is μ.
Solution:
θ
Question: A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches the
bottom if the coefficient of friction between the body and the incline is μ.
Solution:
θ
Question: A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches the
bottom if the coefficient of friction between the body and the incline is μ.
Solution:
θ
Question: A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches the
bottom if the coefficient of friction between the body and the incline is μ.
Solution:
Question: A body of mass ‘m’ starts from rest and slides down an inclined plane of
height 'h' and angle θ. What is the velocity of the body when it reaches the
bottom if the coefficient of friction between the body and the incline is μ.
Solution:
θ
11P06.3 Potential Energy and Power
11P06.2 Energy
Reference Questions
NCERT : 6.3,6.4,6.18,6.21,6.22,6.25
Work Book : 2,7,11,12,14,18,19
11P06.3
Power and Collision
CV 1
Power
Power
Power
Power
What is Difference in Walking and Running up the stairs?
Power
What is Difference in Walking and Running up the stairs?
In both walking and running up the stairs work done is same The difference between walking and running up these stairs is Power
Power
Power
The rate at which work is done or energy is transformed is called Power
Power
Power
The rate at which work is done or energy is transformed is called Power
Power
Power
The rate at which work is done or energy is transformed is called Power
Power
Power
The rate at which work is done or energy is transformed is called Power
Power
Power
The rate at which work is done or energy is transformed is called Power
Power
Power
Scalar Quantity
Si Unit- Watt
The rate at which work is done or energy is transformed is called Power
Conceptest
Ready for challenge
11P06.3 Potential Energy and Power
Power
Question:An elevator can carry a maximum load of 1800 kg (elevator +passengers)
is moving up with a constant speed of 2 ms–1. The frictional force
Opposing the motion is 4000 N. Determine the minimum power delivered
by the motor to the elevator in watts as well as in horse power.
Solution:
Pause the Video
(Time Duration : 2 Minutes)
11P06.3 Potential Energy and Power
Power
Question:An elevator can carry a maximum load of 1800 kg (elevator +passengers)
is moving up with a constant speed of 2 ms–1. The frictional force
Opposing the motion is 4000 N. Determine the minimum power delivered
by the motor to the elevator in watts as well as in horse power.
Solution:
1800 kg
F
mg
Ff
11P06.3 Potential Energy and Power
Power
Question:An elevator can carry a maximum load of 1800 kg (elevator +passengers)
is moving up with a constant speed of 2 ms–1. The frictional force
Opposing the motion is 4000 N. Determine the minimum power delivered
by the motor to the elevator in watts as well as in horse power.
Solution:
F = mg + Ff
1800 kg
F
mg
Ff
11P06.3 Potential Energy and Power
Power
Question:An elevator can carry a maximum load of 1800 kg (elevator +passengers)
is moving up with a constant speed of 2 ms–1. The frictional force
Opposing the motion is 4000 N. Determine the minimum power delivered
by the motor to the elevator in watts as well as in horse power.
Solution:
F = mg + Ff
= (1800 × 10 ) + 4000
11P06.3 Potential Energy and Power
Power
Question:An elevator can carry a maximum load of 1800 kg (elevator +passengers)
is moving up with a constant speed of 2 ms–1. The frictional force
Opposing the motion is 4000 N. Determine the minimum power delivered
by the motor to the elevator in watts as well as in horse power.
Solution:
F = mg + Ff
= (1800 × 10 ) + 4000
= 22000 N
11P06.3 Potential Energy and Power
Power
Question:An elevator can carry a maximum load of 1800 kg (elevator +passengers)
is moving up with a constant speed of 2 ms–1. The frictional force
Opposing the motion is 4000 N. Determine the minimum power delivered
by the motor to the elevator in watts as well as in horse power.
Solution:
F = mg + Ff
= (1800 × 10 ) + 4000
= 22000 N
Power supplied P = Fv
11P06.3 Potential Energy and Power
Power
Question:An elevator can carry a maximum load of 1800 kg (elevator +passengers)
is moving up with a constant speed of 2 ms–1. The frictional force
Opposing the motion is 4000 N. Determine the minimum power delivered
by the motor to the elevator in watts as well as in horse power.
Solution:
F = mg + Ff
= (1800 × 10 ) + 4000
= 22000 N
Power supplied P = Fv
= 22000 × 2
= 44000 W
11P06.3 Potential Energy and Power
Power
Question:An elevator can carry a maximum load of 1800 kg (elevator +passengers)
is moving up with a constant speed of 2 ms–1. The frictional force
Opposing the motion is 4000 N. Determine the minimum power delivered
by the motor to the elevator in watts as well as in horse power.
Solution:
F = mg + Ff
= (1800 × 10 ) + 4000
= 22000 N
Power supplied P = Fv
= 22000 × 2
= 44000 W
(746 W = 1 hp)
11P06.3 Potential Energy and Power
Power
Question:An elevator can carry a maximum load of 1800 kg (elevator +passengers)
is moving up with a constant speed of 2 ms–1. The frictional force
Opposing the motion is 4000 N. Determine the minimum power delivered
by the motor to the elevator in watts as well as in horse power.
Solution:
F = mg + Ff
= (1800 × 10 ) + 4000
= 22000 N
Power supplied P = Fv
= 22000 × 2
= 44000 W
(746 W = 1 hp)
P = | 44000 | = 59 hp |
746 |
CV 2
Introduction to Collision
11P06.3 Potential Energy and Power
Collision
Collision
Elastic Collision
11P06.3 Potential Energy and Power
Collision
Completely Inelastic Collision
Collision
Elastic Collision
11P06.3 Potential Energy and Power
Collision
Inelastic Collision
Completely Inelastic Collision
Collision
Elastic Collision
11P06.3 Potential Energy and Power
Collision
Elastic Collision
11P06.3 Potential Energy and Power
Collision
Elastic Collision
11P06.3 Potential Energy and Power
Collision
Elastic Collision
Total Momentum of System is Conserved
Total Kinetic Energy of System Is Conserved
11P06.3 Potential Energy and Power
Collision
Elastic Collision
Total Momentum of System is Conserved
Total Kinetic Energy of System Is Conserved
Deformation due to collision is completely relieved
11P06.3 Potential Energy and Power
Collision
Completely Inelastic Collision
11P06.3 Potential Energy and Power
Collision
Completely Inelastic Collision
11P06.3 Potential Energy and Power
Collision
Completely Inelastic Collision
Total Momentum of System is Conserved
Total Kinetic Energy of System Is Not Conserved
11P06.3 Potential Energy and Power
Collision
Completely Inelastic Collision
Total Momentum of system is conserved
Total Kinetic Energy of system Is not conserved
Deformation due to collision is not relieved
11P06.3 Potential Energy and Power
Collision
Inelastic Collision
11P06.3 Potential Energy and Power
Collision
Inelastic Collision
11P06.3 Potential Energy and Power
Collision
Inelastic Collision
Total Momentum of System is Conserved
Total Kinetic Energy of System Is Not Conserved
11P06.3 Potential Energy and Power
Collision
Inelastic Collision
Total Momentum of System is Conserved
Total Kinetic Energy of System Is Not Conserved
Deformation Due to collision is Partly Relieved
CV 3
Collision in 1-D
11P06.3 Potential Energy and Power
Collision in 1-D
Collision in 1-D/Head-on Collision
Before Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Collision in 1-D/Head-on Collision
Line of Contact
Before Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Collision in 1-D/Head-on Collision
Line of Contact
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Completely Inelastic Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Completely Inelastic Collision
m2
m1
u1
u2
Before Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Completely Inelastic Collision
m1
m2
m2
m1
u1
u2
vf
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Completely Inelastic Collision
m1
m2
m2
m1
u1
u2
vf
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Completely Inelastic Collision
m1
m2
m2
m1
u1
u2
vf
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Completely Inelastic Collision
m1
m2
m2
m1
u1
u2
vf
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Completely Inelastic Collision
m1
m2
m2
m1
u1
vf
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Completely Inelastic Collision
m1
m2
m2
m1
u1
vf
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Completely Inelastic Collision
m1
m2
m2
m1
u1
vf
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m2
m1
u1
u2
u1>u2
Before Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
v2
v1
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m1
m2
m2
m1
u1
v2
v1
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m
m
m
m
u1
u1
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m
m
m
m
u1
u1
Before Collision
After Collision
11P06.3 Potential Energy and Power
Collision in 1-D
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m2
m2
u1
Before Collision
After Collision
u1
m1
m1
11P06.3 Potential Energy and Power
Collision in 1-D
Elastic Collision
m2
m2
u1
Before Collision
After Collision
u1
m1
m1
11P06.3 Potential Energy and Power
Collision in 1-D
Conceptest
Ready for challenge
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
Pause the Video
(Time Duration : 2 Minutes)
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
11P06.3 Potential Energy and Power
Collision in 1-D
Question:
Solution:
v
2v
Conceptest
Ready for challenge
11P06.3 Potential Energy and Power
Collision in 2-D
Question:Two objects, each of mass 1.5 kg, are moving in the same straight line � but in opposite directions. The velocity of each object is 2.5 ms-1
before the collision during which they stick together. What will be the
velocity of the combined object after collision?
Solution:
Pause the Video
(Time Duration : 2 Minutes)
11P06.3 Potential Energy and Power
Collision in 1-D
Question:Two objects, each of mass 1.5 kg, are moving in the same straight line � but in opposite directions. The velocity of each object is 2.5 ms-1
before the collision during which they stick together. What will be the
velocity of the combined object after collision?
Solution:
By Momentum conservation
m1u1+m2u2=(m1+m2)v
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 1-D
Question:Two objects, each of mass 1.5 kg, are moving in the same straight line � but in opposite directions. The velocity of each object is 2.5 ms-1
before the collision during which they stick together. What will be the
velocity of the combined object after collision?
Solution:
By Momentum conservation
m1u1+m2u2=(m1+m2)v
1.5✕2.5ㄧ1.5✕2.5=(1.5+1.5)v
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 1-D
Question:Two objects, each of mass 1.5 kg, are moving in the same straight line � but in opposite directions. The velocity of each object is 2.5 ms-1
before the collision during which they stick together. What will be the
velocity of the combined object after collision?
Solution:
By Momentum conservation
m1u1+m2u2=(m1+m2)v
1.5✕2.5ㄧ1.5✕2.5=(1.5+1.5)v
0=3v ⇒ v=0
CV 4
Collision in 2-D
11P06.3 Potential Energy and Power
Collision in 2-D
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
u2
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
11P06.3 Potential Energy and Power
Collision in 2-D
Collision in 2D / Oblique Collision
When two equal masses undergo a oblique elastic collision with one of them at rest, after the collision, they will move at right angles to each other
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11P06.3 Potential Energy and Power
Collision in 2-D
Question:Body A with speed uA = 50 ms-1 collides elastically with Body B which is
initially stationary After the collision, body A is found to be moving at speed
vA = 25 ms-1 in a direction at 60° to its original direction of motion. Find the
Speed of body B after the collision
(Mass of A = mass of B = 2 kg)
Solution:
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(Time Duration : 2 Minutes)
11P06.3 Potential Energy and Power
Collision in 2-D
Question:Body A with speed uA = 50 ms-1 collides elastically with Body B which is
initially stationary After the collision, body A is found to be moving at speed
vA = 25 ms-1 in a direction at 60° to its original direction of motion. Find the
kinetic energy possessed by body B after the collision
(Mass of A = mass of B = 2 kg)
Solution:
A
B
11P06.3 Potential Energy and Power
Collision in 2-D
Question:Body A with speed uA = 50 ms-1 collides elastically with Body B which is
initially stationary After the collision, body A is found to be moving at speed
vA = 25 ms-1 in a direction at 60° to its original direction of motion. Find the
kinetic energy possessed by body B after the collision
(Mass of A = mass of B = 2 kg)
Solution:
A
B
11P06.3 Potential Energy and Power
Collision in 2-D
Question:Body A with speed uA = 50 ms-1 collides elastically with Body B which is
initially stationary After the collision, body A is found to be moving at speed
vA = 25 ms-1 in a direction at 60° to its original direction of motion. Find the
kinetic energy possessed by body B after the collision
(Mass of A = mass of B = 2 kg)
Solution:
A
B
11P06.3 Potential Energy and Power
Collision in 2-D
Question:Body A with speed uA = 50 ms-1 collides elastically with Body B which is
initially stationary After the collision, body A is found to be moving at speed
vA = 25 ms-1 in a direction at 60° to its original direction of motion. Find the
kinetic energy possessed by body B after the collision
(Mass of A = mass of B = 2 kg)
Solution:
A
B
11P06.3 Potential Energy and Power
Collision in 2-D
Question:Body A with speed uA = 50 ms-1 collides elastically with Body B which is
initially stationary After the collision, body A is found to be moving at speed
vA = 25 ms-1 in a direction at 60° to its original direction of motion. Find the
kinetic energy possessed by body B after the collision
(Mass of A = mass of B = 2 kg)
Solution:
A
B
11P06.3 Potential Energy and Power
Collision in 2-D
Question:Body A with speed uA = 50 ms-1 collides elastically with Body B which is
initially stationary After the collision, body A is found to be moving at speed
vA = 25 ms-1 in a direction at 60° to its original direction of motion. Find the
kinetic energy possessed by body B after the collision
(Mass of A = mass of B = 2 kg)
Solution:
A
B
11P06.3 Potential Energy and Power
Collision in 2-D
A
B
Question:Body A with speed uA = 50 ms-1 collides elastically with Body B which is
initially stationary After the collision, body A is found to be moving at speed
vA = 25 ms-1 in a direction at 60° to its original direction of motion. Find the
kinetic energy possessed by body B after the collision
(Mass of A = mass of B = 2 kg)
Solution:
ms-1
Summary
Elastic One-Dimensional Collision:
m1
m2
m2
m1
u1
u2
v2
v1
u1>u2
Before Collision
After Collision
Summary
Perfectly Inelastic One Dimensional Collision:
m1
m2
m2
m1
u1
u2
v
u1>u2
Before Collision
After Collision
11P06.3 Potential Energy and Power
11P06.3 Power and Collision
Reference Questions
NCERT : 6.8,6.15,6.16,6.17,6.23,6.24
Work Book : 15,17,20