Physics Assignment
Group “A”Usman Abrar, Kamran Sharif,
Muneeba Idrees, Hassan Amjad, Ali Asad
Measurement
Motion in one Dimension&
Force and Newton’s Laws
Chapter # 01, 02, 03
Physical Quantities:- “Quantities which can be measured are called Physical
Quantities.” These require Magnitude, Unit and Sometime Direction
for their complete description. Here we will discuss SI( System International) for
measurements…
Chap#01 Measurement
For example Height of the girl, l = 1.55 m
Symbol of the physical
quantity
Numerical value for the magnitude of the physical
quantity
Unit of the physical quantity
Types of physical Quantities:- Base/ Basic Quantities . Derived Quantities.Basic Quantities:-
“ Quantities which are chosen as a base and many other measuring quantities are derived from them are called basic quantities and their units are called base units…”
They are :
System International:-
Derived quantities:-“All quantities other then “7” basic quantities are called Derived quantities because they are derived from Base
quantities and their units are called derived units.”For Example :-
Physical Quantities:-
Units:-“Units are symbol associated with every physical quantity whether its basic or Derived quantity….”
Like, Meter(m) for length ; kilogram(kg) for Mass and
second(s) for time etc…Standards:-“Physicals quantities must have a standard value so that
every calculation is accurate and scientist in different place can calculate things without any ambiguity…”
Some standards are discussed here...
System international
The Standard of time:-Anything which repeats its motion periodically can be set as time standard like Oscillating Pendulum, A mass-Spring system, a Quartz crystal etc… But in SI time standard is defined as:“The second is the duration of 9,192,631,770 vibrations of
(specific) radiation emitted by a Specific isotope Of the Cesium atom”
Fig shows the current national frequancy standard, so-called Cesium foundation clock.
System international
The Standard of length:
SI unit of length is Meter (m)… defined as: “The meter is the length of the path traveled
by light in vacuum during a time interval of 1/299,792,458 of a second”
Length is also measured in cm, km, miles, feets etc…The Standard of Mass: SI unit Base unit for Mass is “Kg”
“The SI standard of mass is a platinum-iridium cylinder kept at IBWM”
System international
Precision:-“An indication of the scale on the measuring device
that was used.”In other words, the more correct a measurement is, the more accurate it is. On the other hand, the smaller the scale on the measuring instrument, the more precise the measurement.
Fig illustrates difference b/w Precision and accuracy.
Precision And Significant Figures
“The significant figures (also known as significant digits, and often shortened to sig figs) of a number are
those digits that carry meaning contributing to its precision. This includes all digits”
except: leading and trailing zeros which are merely place
holders to indicate the scale of the number. spurious digits introduced, for example, by
calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.
Significant Figures
The rules for identifying significant figures when writing or interpreting numbers are as follows: All non-zero digits are considered significant. For example, 91 has two significant
figures (9 and 1), while 123.45 has five significant figures (1, 2, 3, 4 and 5).
Zeros appearing anywhere between two non-zero digits are significant. Example: 101.12 has five significant figures: 1, 0, 1, 1 and 2.
Leading zeros are not significant. For example, 0.00052 has two significant figures: 5 and 2.
Trailing zeros in a number containing a decimal point are significant. For example, 12.2300 has six significant figures: 1, 2, 2, 3, 0 and 0. The number 0.000122300 still has only six significant figures (the zeros before the 1 are not significant). In addition, 120.00 has five significant figures since it has three trailing zeros. This convention clarifies the precision of such numbers; for example, if a measurement precise to four decimal places (0.0001) is given as 12.23 then it might be understood that only two decimal places of precision are available. Stating the result as 12.2300 makes clear that it is precise to four decimal places (in this case, six significant figures).
Identifying significant figures
The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is precise to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. Various conventions exist to address this issue:
A bar may be placed over the last significant figure; any trailing zeros following this are insignificant. For example, 1300 has three significant figures (and hence indicates that the number is precise to the nearest ten).
The last significant figure of a number may be underlined; for example, "2000" has two significant figures.
A decimal point may be placed after the number; for example "100." indicates specifically that three significant figures are meant.
In the combination of a number and a unit of measurement the ambiguity can be avoided by choosing a suitable unit prefix. For example, the number of significant figures in a mass specified as 1300 g is ambiguous, while in a mass of 13 h g or 1.3 kg it is not.
Identifying significant figures
Kinematics:-“Kinematics is the branch of mechanics that describes the
motion of objects without necessarily discussing what causes the motion.”
By specifying the velocity, position and acceleration f a object, we can describe how this object moves, including the direction of its motion. How that direction changes with time, whether the object speeds up or slows down and so forth…
Position, velocity, acceleration etc… can be found using vectors.
Chapter # 02 Motion in one dimension
Vector:-“Vector is that quantity that requires
magnitude, unit as well as Direction for its complete description…”
For example: Displacement, velocity (v) etc… Vector is represented by straight line with an
arrow head on its either side… And vector quantities are represented either
in Bold or making an arrow on is symbol… A.
Vectors
Representation of a Vector:-
Properties of Vectors
x
and
z
θ
A
Ax
Aan
d
Az
θsenAAx cos
θsenAsenAy θcosAAz
222zyx AAAAA
kAjAiAA zyx
Sum of Vectors
BA
R
BA C
C
Law of the polygon
Sum of Vectors
BA
R
BA C
C
Law of the polygon
The resulting vector is one that vector from the origin of the first vector to the end of the last
Vectors Properties
A
Opposite-A
Null 0 = A + ()-A
Unit vector AA
μ
ˆAA
Properties of the sum of vectors
Commutative Law
ABBAR Associative
Law
C)BA)CBAR
((
Difference
B-AR
)B(-AR
A
B A
-BR
Commutative (Method parallelogram)
The vectors A and B can be displaced parallel to find the vector sum
B
R = A
+ B
A
B R = B
+ A
BR =
A +
B
Multiplication of a vector by a scalar
Given two vectors ByA
Are said to be parallel if BA
BAsi
0
BAsi
0BAsi
1
Dot product of two vectors
θABBA cos
cosθAAB Projection of A on B
cosθBBA
Projection of B on A
1ˆˆ ii1ˆˆ jj
0ˆˆ ji
0ˆˆ kj0ˆˆ ki
xAiA
1ˆˆ kk
yAjA ˆ
zAkA ˆ
ZZYYXX BABABABA
Vector product of two vectors BAC
θABC sen
0ii
0ˆˆ
jj
0ˆˆ
kk
kji ˆˆˆ ikj ˆˆˆ
jik ˆˆˆ
)kBjBiB()kAjAiA(BAC zyxzyx
YZZYX BABAC
zxxzy BABAC
xyyxz BABAC
Demonstrate:
Distance vs Displacement
Distance ( d ) Total length of the path travelled Measured in meters scalar
Displacement ( ) Change in position (x) regardless of path x = xf – xi
Measured in meters vector
d
Distance
Displacement
A
B
Finding displacement
hbwlarea 2
1
velo
city
time
vo
t
v
v – vo = at
atttvd o 2
1
20 2
1attvd
The displacement divided by the elapsed time.
timeElapsed
ntDisplaceme velocityAverage
ttt o
o
xxx
v
Average Velocity
SI units for velocity: meters per second (m/s)
sm4s 2
m 8 Slope
t
x
Finding velocity
The instantaneous velocity indicates how fast the car moves and the direction of motion at each instant of time.
tt
xv
0lim
Instantaneous Velocity & Speed
The instantaneous speed is the magnitude of the instantaneous velocity
Instantaneous Velocity
The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs.
Acceleration
ttt o
o
vvv
a
The difference between the final and initial velocity divided by the elapsed time
SI units for acceleration: meters per second per second (m/s2)
2sm6s 2
sm 12 Slope
t
v
Finding acceleration
Determine the average acceleration of the plane.
sm0ov
s 0ot
hkm260v
s 29t
s
hkm0.9
s 0s 29
hkm0hkm260
a
Example Acceleration and Increasing Velocity
o
o
tt
vv
a
s 9s 12
sm28sm13
o
o
tt
vva
Example Acceleration and Decreasing Velocity
2sm0.5a
It is common to dispense with the use of boldface symbols overdrawn with arrows for the displacement, velocity, and acceleration vectors (AP does not show arrows on given equations nor expect them on open-ended problems). We will, however, continue to convey the directions with a plus or minus sign. (AP calls elapsed time “t” where t = t – to)
t
vva o
Equations of Kinematics for Constant Acceleration
o
o
tt
vv
a
t
vva o
ovvat
atvv o
Equations of Kinematics for Constant Acceleration
AP Equation#1
atvv o vvt
xx
0
0
2
1
221 attvxx oo
Equations of Kinematics for Constant Acceleration
vvv o 2
1
t
xxv 0
tvvxx 00 2
1
If, a is constant:
tatvvxx ooo 2
1
AP Equation#2
a
vvvvxx o
oo 21
t
vva o
a
vvt o
a
vvxx oo 2
22
Equations of Kinematics for Constant Acceleration
tvvxx 00 2
1
022 2 xxavv o
AP Equation#3
In the absence of air resistance, it is found that all bodiesat the same location above the Earth fall vertically with the same acceleration. If the distance of the fall is smallcompared to the radius of the Earth, then the accelerationremains essentially constant throughout the descent.
This idealized motion is called free-fall and the accelerationof a freely falling body is called the acceleration due to gravity.
22
22
sft30sm10
sft2.32or sm80.9
org
g
Free Fall
Freefalling bodies
I could give a boring lecture on this and work through some examples, but I’d rather make it more real…
Use same kinematic equations just substitute g for aChoose +/- carefully to make problem as easy as possible
Free fall problems
Two types of forces◦ Contact force
Force caused by physical contact◦ Field force
Force caused by gravitational attraction between two objects
Force
Born 1642
Went to University of Cambridge in England as a student and taught there as a professor after
Never married
Gave his attention mostly to physics and mathematics, but he also gave his attention to religion and alchemy
Newton was the first to solve three mysteries that intrigued the scientists
◦ Laws of Motion◦ Laws of Planetary Orbits◦ Calculus
Isaac Newton
Newton’s Laws of Motion are laws discovered by Physicist and mathematician, Isaac Newton, that explains the objects’ motions depending on forces acted on them
◦ Newton’s First Law: Law of Inertia◦ Newton’s Second Law: Law of Resultant Force◦ Newton’s Third Law: Law of Reciprocal Action
Three Laws of Motion
An Object at rest remains at rest, and an object in motion continues in motion with constant velocity (that is, constant speed in a straight line), unless it experiences a net external force.
The tendency to resist change in motion is called inertia
◦ People believed that all moving objects would eventually stop before Newton came up with his laws
Newton’s First Law
A force that causes resistance to motion Arises from contact between two surfaces◦ If the force applied is smaller than the
friction, then the object will not move If the object is not moving, then
ffriction=Fapplied
◦ The object eventually slips when the applied force is big enough
Friction
Friction
Friction was discovered by Galileo Galilee when he rolled a ball down a slope and observed that the ball rolls up the opposite slope to about the same height, and concluded that the difference between the initial height and the final height is caused by friction.
Galileo also noticed that the ball would roll almost forever on a flat surface so that the ball can elevate to the same height as where it started.
Static Friction◦ Friction that exists
while the object is stationary
◦ If the applied force on an object becomes greater than the maximum of static friction, then the object starts moving
◦ Fstatic ≤ μstatic n
Kinetic Friction◦ The friction that exists
when an object is in motion
◦ F – fkinetic produces acceleration to the direction the object is moving
◦ If F = fkinetic, then the object moves at constant speed with no acceleration
◦ fkinetic= μkineticn◦ Kinetic friction and the
coefficient of kinetic friction are smaller than static friction and the static coefficient
Two types of Friction
Newton’s First Law
When there is no force exerted on an object, the motion of the object remains the same like described in the diagram
◦ Because the equation of Force is F=ma, the acceleration is 0m/s². So the equation is 0N=m*0m/s²
◦ Therefore, force is not needed to keep the object in motion, when
◦ The object is in equilibrium when it does not change its state of motion
The car is traveling rightward and crashes into a brick wall. The brick wall acts as an unbalanced force and stops the car.
The truck stops when it crashes into the red car.
But the ladder falls in front of the truck because the ladder was in motion with the truck but there is nothing stopping the ladder when the truck stops.
Inertial Frames
Any reference frame that moves with constant velocity relative to an inertial frame is itself an inertial frame
A reference frame that moves with constant velocity relative to the distant stars is the best approximation of an inertial frame
We can consider the Earth to be such an inertial frame, although it has a small centripetal acceleration associated with its motion
Newton’s First Law – Alternative Statement
In the absence of external forces, when viewed from an inertial reference frame, an object at rest remains at rest and an object in motion continues in motion with a constant velocity
Newton’s First Law describes what happens in the absence of a force Does not describe zero net force
Also tells us that when no force acts on an object, the acceleration of the object is zero
Inertia and Mass
“The tendency of an object to resist any attempt to change its velocity is called inertia”
“Mass is that property of an object that specifies how much resistance an object exhibits to changes in its velocity”
Masses can be defined in terms of the accelerations produced by a given force acting on them:
The magnitude of the acceleration acting on an object is inversely proportional to its mass
1 2
2 1
m am a
Mass vs. Weight
Mass and weight are two different quantities
Weight is equal to the magnitude of the gravitational force exerted on the object Weight will vary with location
Example: wearth = 180 lb; wmoon ~ 30 lb mearth = 2 kg; mmoon = 2 kg
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass
Newton’s Second Law
Fnet
Acceleration
Unbalanced Force and Acceleration
Force is equal to acceleration multiplied by mass
◦ When an unbalanced force acts on an object, there is always an acceleration
Acceleration differs depending on the net force
The acceleration is inversely related to the mass of the object
Force is a vector◦ Because it is a vector, the net force can be
determined by subtracting the force that resists motion from the force applied to the object.
◦ If the force is applied at an angle, then trigonometry is used to find the force
Net Force
Fnet
θR
R*cos θR*sin θ
θR
The force that exerts all objects toward the earth’s surface is called a gravitational force.
◦ The magnitude of the gravitational force is called weight
The acceleration due to gravity is different in each location, but 9.80m/s² is most commonly used
Calculated with formula w=mg
Gravitational Force
If two objects interact, the force exerted on object 1 by object 2 is equal in magnitude but opposite in direction to the force exerted on object 2 by object 1
Forces always come in pair when two objects interact
◦ The forces are equal, but opposite in direction
Newton’s Third Law
Fg
Fn
As the man jumps off the boat, he exerts the force on the boat and the boat exerts the reaction force on the man.
The man leaps forward onto the pier, while the boat moves away from the pier.
Newton’s Third Law
Newton’s Third Law
Flow backward
Foil deflected down
Foil deflected up
Engine pushed forward
Flow pushed backward
Foil deflected down
Applications of Newton’s LawAssumptions
Objects can be modeled as particles Interested only in the external forces acting
on the object can neglect reaction forces
Initially dealing with frictionless surfaces Masses of strings or ropes are negligible
When a rope attached to an object is pulling it, the magnitude of that force is the tension in the rope.