Transcript A x - Soran University

General Physics
Muna salah al-deen
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General Physics
week1
Contents
A. Mechanics
1 .Physics and measurement
2. Motion and dimensions
3. Vectors
4. Motion in two dimensions
5. Laws of motion
6. Circular motion
7. Energy
8. Potential energy
9. Linear momentum and collision
10. Rotation
11. Angular momentum
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B. Properties of Matter
12. Static and Elasticity
13. Universal gravitation
14. Fluid mechanics
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1 .Physics and measurement
1.1 SI prefixes for power of ten
1.2 The Greek Alphabet
1.3 Standard Abbreviations and Symbols for Units
1.4 Mathematical Symbols and their meaning
1.5The Fundamental SI units
1.6 Dimensional Analysis
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1.5 The Fundamental SI units
The Fundamental SI units
quantity
unit
abbreviation
kilogram
kg
Length
meter
m
Time
second
s
Temperature
kilvin
K
Electric current
ampere
A
Luminous intensity
candela
cd
mole
mol
Mass
Amount of substance
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Motion in one dimension
week2 •
2.1 Position, velocity, and speed
2.2 Instantaneous velocity and speed
2.3 Acceleration
2.4 One-Dimensional motion with constant acceleration
2.5 Freely Falling Objects
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The displacement of a particle is defined as its change in position in
some time interval.
∆x = xf – xi …………. (2.1)
Instantaneous velocity
The instantaneous velocity is vx equals the limiting value of the 
ratio ∆x / ∆t as ∆t approaches zero:
vx = lim (∆x / ∆t) = dx /dt ……….. (2.4)

∆t---------0
The instantaneous velocity can be positive, negative, and zero. 
Instantaneous speed
Instantaneous speed of a particle is defined as the
magnitude of its instantaneous velocity
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One-Dimensional motion with constant acceleration
week3 •
A simple type of one-dimensional motion is that in which the acceleration is constant.
In this case the average acceleration āx over any time interval is numerically equal to
the instantaneous acceleration ax at any instant within the interval, and the velocity
changes at the same rate through the motion (āx = ax ).
If ti = 0 and tf any later time t, we find that
ax = (vxf – vxi) / (t – 0)
or
vxf = vxi + ax t (for constant ax) ……… (2.7)
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3. Vectors
Week4 •
3.1 Coordinate systems
3.2 Vector and scalar quantities
3.3 Some properties of vectors
3.4 Components of a vector and unit vectors
3.5 Vector product (multiplication)
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Coordinate systems
(a) Cartesian coordinate
This system of coordinate 
is represented by two or
three dimensions, i.e.,
plane or space.
In two dimensions

(see the figure), the
vector from the origin O =
(0,0) to the point A = (2,3)
is simply written
as
a = (2,3)
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3.2 Vector and scalar quantities
1. The scalar and vector quantities
The scalar quantity is that quantity

determines by magnitude only, such as,
temperature T and energy E.
The vector quantity is that quantity

determines by magnitude and direction,
such as, displacement x, velocity v, and
force F.
A vector is a geometric entity

characterized by a magnitude (in
mathematics a number, in physics a
number times a unit) and a direction.
In rigorous mathematical treatments, a

vector is defined as a directed line
segment, or arrow, in a Euclidean space.
Week5
•
The Addition and subtraction of vectors
A and B are two vectors, their sum is R ,
i.e., R = A + B
Vectors can be subtracted, i.e.,
if A and B are two vectors then their
subtraction is
C = A – B = A + (-B)
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3.4 Components of a vector and unit
vectors
Components of a vector
The components of the vector A in
two dimensions are the vectors
Ax and Ay, in such a way that:
A = Ax + Ay
Ax = A cos θ
Ay = A sin θ
A = [(Ax)2 + (Ay)2]½
tan θ = Ay / Ax
θ = tan-1 (Ay / Ax)
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Week6
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Unit vectors
Another way to express a vector in three
dimensions is to introduce the three
standard basis vectors:
e1 = (1,0,0) , e2 = (0,1,0) , e3 = (0,1,0)
These have the intuitive interpretation as
vectors of unit length pointing up the
x, y, and z axis of a Cartesian
coordinate system, respectively, and
they are sometimes referred to as
versors of those axes.
In terms of these, any vector in three
dimensions space can be expressed
in the form:
(a,b,c) = a(1,0,0) + b(0,1,0) +
c(0,0,1)
= ae1 + be2 + ce3
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These three special vectors are often
instead denoted i, j, k , the versors
of the three dimensional space (or
) , in which the hat symbol (^)
typically denotes unit vectors
(vectors with unit length).
The notation ei is compatible with the
index notation and the summation
convention commonly used in higher
level mathematics, physics, and
engineering.
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Vectors product (multiplication)
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4. Motion in two dimensions
Week7
4.1 The position, Velocity, and Acceleration
Vectors
4.2 Two-dimensional motion with constant
acceleration
4.3 Projectile motion
4.4 Uniform circular motion
4.5 Tangential and radial acceleration
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4.1 The position, velocity, and acceleration vectors
We describe here the motion of a particle in two dimensions,
i.e., motion in xy-plane.
The description of the position of a particle is by position vector
r.
The displacement vector ∆r is defined as the difference
between its final position vector and its initial position vector:
Displacement vector
∆r ≡ rf – ri ………………….. (4.1)
The direction of ∆r is shown in the Figure below.
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Two-dimensional motion with
constant acceleration Week8
4.2 Two-dimensional motion with constant acceleration
The position vector for a particle moving in the xy-plane can be written
as
r = xi + yj ………………. (4.6)
where x, y and r change with time as the particle moves.
From the Equations 4.3 and 4.6 the velocity of the particle can be
obtained as
v =dr/dt
=dx/dt i +dy/dt j
= vx i + vy j ………….. (4.7)
Because the acceleration is constant, its components ax and ay are
also constants.
Therefore, the equations of kinematics to the x and y components of
the velocity vector can be applied.
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4.4 Uniform circular motion
4.4 Uniform circular motion
Week9
The movement of an object in a circular path with constant speed v is
called uniform circular motion.
Even though an objects move at constant speed in circular path, it still
has acceleration.
The acceleration depends on the change in the velocity vector.
The acceleration depends on the change in the magnitude of the
velocity and / or by a change in the direction of the velocity.
The change in the direction of the velocity occurs for an object moving
with constant speed in a circular path.
The velocity vector is always tangent to the path of the object and
perpendicular to the radius of the circular path.
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Laws of motion (Particle’s dynamics)
]
5.1 The concept of the Force
Week10 •
An object accelerates due to an external force.
The object accelerates only if the net force acting on it is not equal zero.
The net force acting on an object is defined the vector sum of all forces acting
on the object.
The net force is the total force, the resultant force, or the unbalanced force.
If the net force exerted on an object is zero, the acceleration is zero and its
velocity remains constant.
Definition of equilibrium
When the velocity of an object is constant (including when the object is at
rest), the object is said to be in equilibrium.
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5.2 Newton’s first law
“In the absence of external force, when viewed from an
inertial reference frame, an object at rest remains at
rest and an object in motion continues in motion with
constant velocity”.
That is to say, when no force acts on an object, the
acceleration of the object is zero.
From the first law, we conclude that any isolated object
(one that does not interact with its environment) is
either at rest or moving with constant velocity.
Definition of inertia
The tendency of an object to resist any attempt to change
its velocity is called inertia
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5.3 Mass
Definition of mass
“Mass is an inherent property of an object and is independent of the
object’s surrounding and of the method used to measure it”.
Mass is a scalar quantity
Mass and weight are two different quantities
The weight of an object is equal to the magnitude of the gravitational
force exerted on the object and varies with location.
For example, a person who weight 900 N on the Earth weights only
150 N on the Moon.
The mass of an object is the same everywhere: an object having a
mass of 2 kg on the Earth also has a mass of 2 kg on the Moon.
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5.5 The Gravitational force and weight
Week11
The attraction force exerted by the Earth on an object is called the gravitational force
Fg.
This force is directed toward the center of the Earth, and its magnitude is called the
weight of the object.
Freely falling object experience an acceleration g acting toward the center of the
Earth.
Applying Newton’s second ΣF = ma to the freely falling object of mass m, with a = g
and ΣF = Fg, we obtain
Fg = mg …………………… (5.4)
Thus, the weight of an object, being defined as the magnitude of Fg , is equal to mg,
and g = 9.8 m/s2.
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5.6 Newton’s third law
Newton’s third law states that:
If two objects interact, the force F12 exerted by object 1 on object 2 is equal in
magnitude and opposite in direction to the force F21 exerted by object 2 on
object 1:
F12 = - F21 …………… (5.5)
The force that object 1 exerts on object 2 is called the action force and the force
of object 2 on object 1 the reaction force.
Either force can be labeled the action or reaction force.
In general, “The action force is equal in magnitude to the reaction force and
opposite in direction”.
The action and reaction forces act on
different objects
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5.7 Some applications of Newton’s laws
Objects in Equilibrium
Week12
If the acceleration of an object is zero; the particle is in equilibrium. If apply the
second law to the object, noting that a = 0 , we see that because there are no
forces in the x direction, ΣFx = 0
The condition ΣFy = may = 0 gives
ΣFy = T – Fg = 0
or T = Fg
The forces T and Fg are not an action-reaction pair because they act on the same
object.
The reaction force to T is T’, the downward force exerted by the object on the
chain.
The ceiling exerts on the chain a force T” that is equal in magnitude to the
magnitude of T’ and points in the opposite direction.
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Work and Energy
Week13
6.1 Work done by a constant force
If an object undergoes a displacement Δr under the action of a constant force
F, the work done, W , by the force is,
W = F Δr cos θ ………. (6.1)
From Equation 6.1, the work done by a force on a moving object is zero when
the force applied is perpendicular to the displacement of its point of
application, i.e., θ = 90o ,then W = 0 because cos 90o = 0.
W = F Δr cos 90o
If the applied force F is in same direction as the displacement Δr, then θ = 0
and cos θ = 1. In this case, Equation 6.1 gives W = F Δr
Work is scalar quantity, and its units are force multiplied by length.
The SI unit of work is the newton . meter (N.m), this unit is called joule (J).
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6.2 Work done by a varying force
Consider a particle being displaced along the x axis under the action of a force, Fx , that
varies with position, x.
We can express the work done by Fx as the particle moves from xi to xf as
W = ∫ Fx dx………. (6.2)
This equation reduces to Equation 6.1 when the component
Fx = F cos θ is constant
If more than one force acts on a particle, the total work done on the system is the work
done by the net force.
If the net force in the x direction is Σ Fx then the total work, or net work, done as the
particle moves from
xi to xf is
Σ W = Wnet = ∫ (∑ Fx )dx ………….. (6.3)
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6.3 Kinetic energy and the Work–Kinetic energy
Theorem
6.3 Kinetic energy and the Work–Kinetic energy Theorem
Consider a system consisting of a single object.
The figure below shows a block of mass m moving through a
displacement directed to the right under the action of a net force ΣF.
From Newton’s second law that the block moves with an
acceleration a.
If the block moves through a displacement
Δr = Δxi = (xf - xi)i
the work done by the net force ΣF is
Week14
W   (  F )dx.............................( 6.8 )
xf
xi
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6.5 Potential energy of a system
Week15
We introduced the concept of kinetic energy associated with motion of objects. Now
we introduce potential energy, the energy associated with the configuration of a
system of objects that exert forces on each other.
Potential energy
Consider a system consists of an object and the Earth, interacting via the gravitational
force.
We do some work on the system by lifting the object slowly through a height Δy = yb –
ya .
While the object was at the highest point, the energy of the system had the potential to
become kinetic energy, but did not do so until the book was allowed to fall.
Thus, the energy storage mechanism before
releasing the object is called potential energy.
In this case, the energy is
gravitational potential energy.
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7. Linear momentum and collision
Week16
The momentum of an object is related to both its mass and its velocity.
The concept of momentum leads us to second conservation law, that of conservation
of momentum.
We introduce a new quantity that describes motion, linear momentum.
Consider two particles interact with each other.
According to Newton’s third law, F12 = – F21 and then
F12 + F21 = 0
m1a1 + m2a2 = 0
and
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7.2 Impulse and Momentum
Week17
Assume that a single force F acts on a particle and that
this force may vary with time.
According to Newton’s second law, F = dp/dt, or
dp = Fdt …………………… (7.7)
If the momentum of the particle changes from pi at time
ti to pf at time tf , then
The quantity
is called the Impulse of the force F
acting on a particle over the time interval Δt = tf –ti
Impulse is a vector defined by
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pf
tf
pi
ti
p   dp  p f  p i   Fdt ............( 7.8 )
tf
I   Fdt ............( 7.9 )
ti
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7.3 Collisions in One Dimension
Week18 
We use the law of conservation of linear momentum to describe
what happens when two particles collide.
There are two types of collision, elastic and inelastic.
An elastic collision between two objects is one in which the total
kinetic energy (as well as total momentum) of the system is
the same before and after the collision.
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Fluid Statics
Week19
Fluid statics: study of fluids at rest
Different from fluid dynamics in that it concerns pressure
forces perpendicular to a plane (referred to as
hydrostatic pressure)
If you pick any one point in a static fluid, that point is going
to have a specific pressure intensity associated with it:
P = F/A where
P = pressure in Pascals (Pa, lb/ft3) or Newtons (N, kg/m3)
F = normal forces acting on an area (lbs or kgs)
A = area over which the force is acting (ft2 or m2)
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Bernoulli’s Equation
Week20
Z1 + (P1/) + (V12/2g) = Z2 + (P2/) + (V22/2g)
Wow! Z = pressure head, V2/2g = velocity head (heard of
these?), 2g = (2)(32.2) for Eng. System
If we’re trying to figure out how quickly a tank will drain,
we use this equation in a simplified form: Z = V2/2g
Example: If the vertical distance between the top of the
water in a tank and the centerline of it’s discharge pipe
is 14 ft, what is the initial discharge velocity of the
water leaving the tank? Ans. = 30 ft/s
Can you think of any applications for this?
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Stagnation Point: Bernoulli Equation
Stagnation point: the point on a stationary body in every flow where V= 0
Stagnation Streamline: The streamline that terminates at the stagnation point.
Symmetric:
Stagnation Flow I:
Axisymmetric:
If there are no elevation effects, the stagnation pressure is largest
pressure obtainable along a streamline: all kinetic energy goes into a
pressure rise:
p
Stagnation Flow II:
2
Total Pressure with Elevation:
p
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V 2
1
V 2  z  pT  cons tan t on a streamline
2