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Unit-3
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Science
Unit 3.1 b
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Lecture # 1
Unit 3.1 b
• Contents:
1.
2.
3.
4.
5.
6.
7.
Fundamental and Derived units
Table 1. SI base units
Table 2. Examples of SI Derived units
Prefixes of the SI system
Volume, Area & Length
Difference between Area & Volume
Practice of L, A & V
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Fundamental and Derived units
FUNDAMENTAL UNITS:
Seven well-defined, dimensionally independent, fundamental units
(or base units) that are assumed irreducible by convention.
(meter, kilogram, second, ampere, Kelvin, mole, and candela).
DERIVED UNITS:
A large number of derived units formed by combining fundamental
units according to the algebraic relations of the corresponding
quantities.
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Table 1. SI base units
BASE QUANTITY
Length
Mass
Time
Electric current
Thermodynamic
temperature
Amount of substance
Luminous intensity
SYMBOL FOR
QUANTITY
l
m
t
I
T
n
lʋ
NAME
SYMBOL
meter
m
kilogram
kg
second
s
ampere
A
Kelvin
K
mole
mol
candela
cd
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Table 2. Examples of SI derived units
DERIVED QUANTITY
NAME
SYMBOL
Area
square meter
m2
Volume
cubic meter
m3
Speed
meter per second
m/s
Velocity
meter per second
m/s
Acceleration
meter per second squared
m/s2
Force
newton
N
Pressure
Pascal OR newton per meter squared
Pa or N/m2
Torque
newton meter
N-m
Work
joule OR newton meter
J or N-m
Energy
joule OR newton meter
J or N-m
Power
Watt OR joule per second
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W or J/s
Prefixes of the SI system
PREFIX
mega
kilo
FACTOR
106
103
SYMBOL
M
k
milli
10−3
m
micro
10−6
µ
nano
10−9
n
pico
10−12
p
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• LENGTH
• the linear extent in space from one end to the other; In
geometric measurements, length most commonly refers to the
longest dimension of an object.
• The unit of length is “meter” (m) in SI system.
• AREA
• Area is a quantity that expresses the extent of a two-dimensional
surface or shape in the plane.
• A roughly bounded part of the space on a surface; a region.
• The unit of area is “square meter (m2) in SI system.
• VOLUME
• the amount of 3-dimensional space occupied by an object
• Volume is how much three-dimensional space a substance (solid,
liquid, gas, or plasma) or shape occupies or contains.
• The unit of volume is “cubic meter (m3) in SI system.
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Difference between Area & Volume
• Length is a measure of one dimension, whereas area is a
measure of two dimensions (length squared) and volume is a
measure of three dimensions (length cubed).
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PRACTICE OF L, A & V
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Science
Unit 3.2 b
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Lecture # 2
Unit 3.2 b
• Contents:
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2.
3.
4.
5.
6.
7.
8.
9.
Mass
Force
Moment
Equilibrium
Static equilibrium
Relationship between mass, force & acceleration
Vectors
Resultant of two Coplanar forces
Head & tail Rule
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Mass
The quantity of matter in a given body is the mass of the body and
it can be measured from the equation.
m= F/a
The property of a body that causes it to have weight in a
gravitational field
According to Newton's second law of motion, if a body of fixed
mass m is subjected to a force F, its acceleration a is given by F/m.
The SI unit of mass is the kilogram (kg).
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Force
• Force is an agent which changes or tends to change the state of
rest or the motion of a body.
• In physics, a force is any influence that causes a free body to
undergo a change in speed, a change in direction, or a change in
shape.
• Force is a vector. The SI unit for force is the Newton (N). One
Newton of force is equal to 1 kg * m/s2.
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Moment
• Moment of force (often just moment) is the tendency of a force
to twist or rotate an object.
• The turning effect of a force is called torque or moment of the
force. Moment of a force or torque may rotate an object in clockwise or anti-clock-wise direction.
τ =f.r
• The unit of Torque in SI units is Newton meter(N-m).
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Equilibrium
•
The state of a body or physical system at rest or in un
accelerated motion in which the resultant of all forces acting on
it is zero and the sum of all torques about any axis is zero.
• A state of equal balance between weights, forces etc.
• Two conditions for equilibrium are that the net force acting on
the object is zero, and the net torque acting on the object is zero.
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Static equilibrium
• Any system in which the sum of the forces, and torque, on each
particle of the system is zero; mechanical equilibrium.
• According to Newton’s second law of motion, we know that if the
net force acting on an object is zero the object has zero
acceleration. If an object that is at rest or moves with a uniform
velocity then the equilibrium is defined as “an object is in
equilibrium when the object has zero acceleration.”
ΣFX = o
ΣFy= o
• This is the 2=1st condition of equilibrium.
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Relationship between mass, force & acceleration
• According to Newton's Second Law, an object will move with constant
velocity until a force is exerted on the object. Or from a different angle,
force effects acceleration.
•
•
The acceleration produced by a particular force acting on a body is directly
proportional to the magnitude of the force and inversely proportional to the
mass of the body.
The relationship between the force applied and the acceleration produced in
an object can be mathematically expressed as
aαF
(for a constant mass)
a α 1/m
( for a constant force)
i.e.
a α F/m
Which can e written as
a = K.F/m
Where K is a constant.
In SI units F must have units of kilogram times meter per second squared if K
has a value of 1.
Therefore
a = 1.F/m
Or
F=ma
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The SI unit of force is the Newton ( N = kg-m/sec2) and it is denoted by N.
Vectors
• Physical quantities which require not only magnitude but also
direction for their complete description. The directional
quantities, are called vector quantities or simply vectors.
• e.g. Velocity, force, acceleration and momentum etc.
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Resultant of two Coplanar forces
To calculate the resultant of the force system shown above, move
force A so that it's tail meets the head of force B. Now forces A and
B form a "Head-to-Tail" arrangement. The resultant R is found by
starting at the tail of B (the point of intersection of forces A and B)
and drawing a vector which terminates at the head of the
transposed A. Note that if force B had been transposed instead of
force A, the resultant would have started from the tail of A and
terminated at the head of force B. Again, this process could be
repeated for any number of force vectors.
• The resultant is described by the vector's magnitude and direction.
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These are determined by scaling the length and angle respectively.
Head & tail Rule
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Lecture # 3
Unit 3.2 b
• Contents:
1.
2.
3.
4.
5.
6.
7.
Examples of Force
Moment or torque formula
Examples of torque
Force and torque
Forces about a point
Simple Beams
Types of beams
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Examples of Force
Example#1: (Resultant of two forces)
A boy walks 10m towards west, then 20m north and finally 20m
east of north at an angle of 60°. Find the resultant displacement.
Example#2: (Resultant of 03 or more forces)
A certain body is acted upon by forces of 30,60,40 and 70N. The
direction of these forces make angles of 0°,60°,90° and 150°
respectively with the x-axis. Find the resultant force acting on the
body.
Example#3: An object of mass 20 kg is moving with an
acceleration of 3 m/s2. Find the force acting on it.
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Moment or Torque formula
• Objects which can rotate about an axis will start rotating under
the action of a suitable force. The turning effect of a force is
called torque or moment of the force.
• Moment of force or torque may rotate an object in clock-wise or
anti-clock-wise direction.
• The symbol for torque is typically τ, the Greek letter tau. When it
is called moment, it is commonly denoted M.
• The magnitude of torque depends on three quantities: First, the
force applied; second, the length of the lever arm connecting the
axis to the point of force application; and third, the angle
between the two. In symbols:
where
τ is the torque vector and τ is the magnitude of the torque,
r is the displacement vector (a vector from the point from which torque is measured to the
point where force is applied), and r is the length (or magnitude) of the lever arm vector,
F is the force vector, and F is the magnitude of the force,
θ is the angle between the force vector and the lever arm vector.
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Example of Torque
• Example#1 : A force of 20N is applied at the edge of a wheel of
radius 10cm. Find the torque acting on the wheel?
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Force and Torque
How are force and torque related?
moment arm
A force can
create a torque by
acting through a
moment arm.
…produces a
torque here.
A force here...
The relationship is t = F x r.
r is the length of the moment arm
(in this case, the length of the wrench).
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Forces about a point
if all the forces are added together as vectors, then the resultant
force (the vector sum) should be 0 Newton. (Recall that the net
force is "the vector sum of all the forces" or the resultant of adding
all the individual forces head-to-tail.) Thus, an accurately drawn
vector addition diagram can be constructed to determine the
resultant. Sample data for such a lab are shown below.
The resultant was 0 Newton (or at
least very close to 0 N). This is what we
expected - since the object was at
equilibrium, the net force (vector sum
of all the forces) should be 0 N.
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Simple Beams
A beam is generally considered to be any member subjected to
principally to transverse gravity or vertical loading.
The term transverse loading is taken to include end moments.
There are many types of beams that are classified according to their
size, manner in which they are supported, and their location in any
given structural system.
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Types of beams
Types of Beams Based on the Manner in Which They are
Supported.
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Science
Unit 3.3 b
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Lecture # 4
Unit 3.3 b
• Contents:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Displacement & Displacement
Example of Distance & Displacement
Speed
Examples of Speed
Velocity
Examples of Velocity
Acceleration
Examples of Acceleration
Vectors
Scalars
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Displacement & Distance
• Suppose a body is initially at position A. Let it move to
position D. There may be various Paths along which we
can move the body from A to D. This is called distance.
• But the directed distance form A to D is called
displacement AD.
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Example of Distance & Displacement
• A body travels from A to D along a rectangular path ABCD. Find
the total distance covered and its displacement.
AB = CD = 1m
BC = 3m
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SPEED
• Speed is a distance covered per unit time. It is scalar. The
direction does not matter. If you are on the highway whether
traveling 100 km/h south or 100 km/h north, your speed is still
100 km/h.
• Speed(V) = total distance (S) covered/total time (t).
V = S/t
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Example of Speed
• Example : You drive a car for 2.0 h at 40 km/h, then for another
2.0 h at 60 km/h. What is your average speed?
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Velocity
• Velocity is a vector. Both direction and quantity must be stated.
It one train has a velocity of 100km/h north, and a second train
has a velocity of 100km/h south, the two trains have different
velocities, even though their speed is the same.
• Average velocity = displacement / time.
V = S/t
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Example of velocity
• Example# 1 if a person walked 400 m in a straight line in 5 min,
that person's velocity would be (400 m [forward])÷(5 min) = 80
m/min [forward] .
Example#2 If the same person walked 100 m
[North] then 300 m [South] in 5 minutes, we
first find their displacement.
displacement = 200 m [S]
velocity = 200÷5 = 40 m/min [S]
Example#3
• If that person walked 100 m [E] in .75 min, 100 m [N] in 1.50 min,
100 m [W] in 1.00 min and finally 100 m [S] in 1.75 min, find 38its
velocity?
Acceleration
Acceleration is a vector when it refers to the rate of change of
velocity. Acceleration is scalar when it refers to rate of change of
speed. A car slowing down to stop at a stop sign is accelerating
because its speed is changing. We might refer to this type of
acceleration as deceleration or negative acceleration. A car going at
a constant speed around a curve is still accelerating because its
direction is changing.
acceleration = (change in velocity) ÷ time.
a = (vf - vi)/t
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Examples of Acceleration
Example#1 : A box with a mass of 40 kg sits at rest on a
frictionless tile floor. With your foot, you apply a 20 N force in a
horizontal direction. What is the acceleration of the box?
As we know
F=mxa
or
F/m=a
A = 20 N / 40 kg
Acceleration = a = 0.5 m / s2
Example#2 : A pitcher delivers a fast ball with a velocity of 43 m/s
to the south. The batter hits the ball and gives it a velocity of 51m/s
to the north. What was the average acceleration of the ball during
the 1.0ms when it was in contact with the bat?
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Vectors
• Physical quantities which require not only magnitude but also
direction for their complete description. The directional
quantities, are called vector quantities or simply vectors.
• e.g. Velocity, force, acceleration and momentum etc.
Force
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Scalars
Those quantities which are completely specified by their
magnitude expressed in suitable units. They do no require any
mention of direction for their representation. Scalars are added,
subtracted, multiplied and divided according to ordinary
arithmetical rules.
• e.g. volume, mass, length, speed, time, work and density etc.
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Lecture # 5
Unit 3.3 b
• Contents:
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2.
3.
4.
5.
6.
7.
8.
1st Equation Of Linear Motion For Constant Linear Acceleration
Example of Equation # 1
2nd Equation of Linear Motion for Constant Linear Acceleration
Example Of Equation # 2
3rd Equation of Linear Motion for Constant Linear Acceleration
Example of Equation # 3
Distance, Time graph
Velocity, Time graph
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1st Equation Of Linear Motion For Constant
Linear Acceleration
• If an object is moving with uniform acceleration a and its velocity
changes from initial velocity vi to final velocity vt in time interval
t, then change in velocity,
Δv = vf - vi
Average acceleration = change in velocity / time
For uniform accelerated motion average acceleration is equal to
uniform acceleration
Therefore
a = Δv / t =(vf – vi ) / t
eq#1
a = (vf - vi )/ t or at = vf - vi
vf = vi + at
eq#2
This is the relationship between a, t, vi, and vf if any three of
these are known then we can calculate the fourth one.
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EXAMPLE OF EQUATION # 1
Example: A motor car is moving with a uniform acceleration and
attains the velocity of 36 km/h in 2 minutes. Find the acceleration
of the car.
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2nd Equation Of Linear Motion For Constant
Linear Acceleration
Suppose a body starts with an initial velocity vi and moves for t
seconds with an acceleration a so that its final velocity becomes vf .
We can find the distance covered by it as follows:
The average velocity is given by the relation.
Vav = (vi + vf )/ 2
Also the total distance covered by the body
S = Vav x t
Substituting the value of Vav , we get
= (vi + vf ) x t / 2
eq#3
Since
vf = vi + at
Therefore
S = (vi + vi + at) x t / 2
Or
S = vit + ½ at2
eq#4
Equation#4 establishes the relationship between distance, initial
velocity, acceleration and time.
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Example Of Equation # 2
• Example: A car is moving with a velocity of 72 km/h. When
brakes are applied it comes to rest after three seconds. Find the
distance travelled by it before coming to rest.
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3rd Equation Of Linear Motion For Constant
Linear Acceleration
The third equation of motion is relating, the initial velocity, the
final velocity, the acceleration and the distance travelled. It can
be obtained by eliminating t from the equation.
vf = vi + at
Therefore
t = (vf – vi ) / a
By substituting the value of t in eq#3, we have,
s = (vi + vf )/ 2 + (vf – vi ) / a
2as = vf 2 - vi2
eq#5
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Example Of Equation # 3
• Example: A motorcyclist is moving with velocity of 72 km/h on a
straight road. After applying brakes it comes to rest after
covering a distance of 10m. Calculate its acceleration.
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Distance Time graph
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Velocity Time graph
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Science
Unit 3.4 b
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Lecture # 6
Unit 3.4 b
• Contents:
1.
2.
3.
4.
5.
6.
7.
Work
Examples of work
Energy
Examples of Energy
Power
Examples of Power
Law of Conservation of energy
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Work
• When a force acts upon an object to cause a displacement of the
object, it is said that work was done upon the object. There are
three key ingredients to work - force, displacement, and cause. In
order for a force to qualify as having done work on an object,
there must be a displacement and the force must cause the
displacement.
• Mathematically, work can be expressed by the following
equation.
The Joule is the unit of work.
1 Joule = 1 Newton * 1 meter
1J=1N*m
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WORK cont.
• Scenario A: A force acts rightward upon
an object as it is displaced rightward. In
such an instance, the force vector and the
displacement vector are in the same
direction. Thus, the angle between F and
d is 0 degrees.
• Scenario B: A force acts leftward upon an
object that is displaced rightward. In such
an instance, the force vector and the
displacement vector are in the opposite
direction. Thus, the angle between F and
d is 180 degrees.
• Scenario C: A force acts upward on an
object as it is displaced rightward. In such
an instance, the force vector and the
displacement vector are at right angles to
each other. Thus, the angle between F
and d is 90 degrees.
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Work cont.
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Example of work
• Example#1
Find the work done when a force of 400N acting at an angle of
60° with the ground, moves an object 10m along the ground.
• Exmaple#2
Waiter who carried a tray full of meals above his head by one
arm straight across the room at constant speed. Find the work
done.
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Energy
Any body which can do work is said to posses energy.
Energy may be defined as the capability of doing work.
Energy can take a wide variety of forms.
Thus, energy and work are measured in the same units i.e.. joules,
but in many fields other units, such as kilowatt-hours and
kilocalories, are customary.
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Example of energy
• A boy pushes a 5.00 kg cart in a circle, starting at 0.500 m/s and
accelerating to 3.00 m/s. How much work was done on the cart?
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Power
• The rate at which work is performed or energy is converted.
• The quantity work has to do with a force causing a displacement.
• The standard metric unit of power is the Watt (joules/second).
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Examples of power
• Example#1 :
When doing a chin-up, a physics student lifts her 42.0-kg body a
distance of 0.25 meters in 2 seconds. What is the power
delivered by the student's biceps?
• Example#2 :
An escalator is used to move 20 passengers every minute from
the first floor of a department store to the second. The second
floor is located 5.20 meters above the first floor. The average
passenger's mass is 54.9 kg. Determine the power requirement
of the escalator in order to move this number of passengers in
this amount of time.
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Law of conservation of energy
• Within an isolated system, one type of energy can be transformed into
another type of energy, but the total of all energies in the system is
constant. The energy of a system changes by the work done on or by
the system and the heat that enters or leaves the system.
• Energy can be neither created nor destroyed by ordinary means.
• The five main forms of energy are:
– Heat
– Chemical
– Electromagnetic
– Nuclear
– Mechanical
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Lecture # 7
Unit 3.4 b
• Contents:
1.
2.
3.
4.
5.
Potential Energy
Example of Potential Energy
Kinetic Energy
Examples of Kinetic Energy
Distance, Time graph
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Potential energy
• Stored energy of position is referred to as potential energy.
Potential energy is the stored energy of position possessed by an
object.
• potential energy is the energy stored in a body or in a system
due to its position in a force field or due to its configuration. The
SI unit of measure for energy and work is the Joule (symbol J).
• PE = mass x g x height
• PE = m x g x h
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Example of Potential Energy
• Example #1: Consider a body of mass 2kg placed on a table 1m
high, which is placed on a platform of height 2m.
Find potential energy of the body with respect to platform, and
ground.
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Kinetic Energy
• Kinetic energy is the energy of motion. An object that has motion
- whether it is vertical or horizontal motion - has kinetic energy.
There are many forms of kinetic energy - vibrational (the energy
due to vibrational motion), rotational (the energy due to
rotational motion), and translational (the energy due to motion
from one location to another).
• Work needed to accelerate a body of a given mass from rest to
its stated velocity. Having gained this energy during its
acceleration, the body maintains this kinetic energy unless its
speed changes. The same amount of work is
done by the body in decelerating from its current
speed to a state of rest.
where m = mass of object
v = speed of object
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Example of Kinetic Energy
• Example #1: What is the kinetic energy of a body having mass 5
kg moving at a speed of 2 m/s.
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Kinetic energy cont.
• The faster an object moves, the more kinetic energy it has.
• The greater the mass of a moving object, the more kinetic energy
it has.
• Kinetic energy depends on both mass and velocity.
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Force Distance graph
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