Course 1

Tim Teaching Fisika Mekanika & Thermodinamika

Academics year: 2020-2021

ENCV611001: Physics (Mechanics and Thermodynamics)

18/09/2020 1
ENCV611001 - Physics (Mechanics and Thermodynamics)
Week
Course Learning Outcome 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
CLO 1 : Measurements, Vectors, and Kinematics
CLO 2 : Newton's laws and applications
CLO 3 : Energy and Linear momentum
CLO 4 : Rotation
CLO 5 : Oscilation and Gravitation
CLO 6 : Equilibrium, Elasticity and Fluids
CLO 7 : Laws of thermodynamics I and II
CLO 8 : The Kinetic Theory of Gases
CLO 9 : Conservation of mass and energy

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ENCV611001 - Physics (Mechanics and Thermodynamics)

• Quiz 1 : CLO 1 and 2

• Midterm : CLO 3 and 4
• Quiz 2 : CLO 5, CLO 7.1 (Law Therm. I) and CLO 8
• Finals : CLO 6, CLO 7.1 (Law Therm. II) and CLO 9
• Individuals assignment

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Outline
1. Introduction
2. Measurement
3. Motion in a straight line
4. Motion in Two and Three Dimensions

Reference:
• Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of physics Extended. John Wiley & Sons.H
• Giancoli, Douglas C. (2016) Physics: principles with applications. Boston: Pearson

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Introduction
Academics year: 2020-2021
ENCV611001: Physics (Mechanics and Thermodynamics)

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1. Introduction
The Nature of Science
• The principal aim of all sciences,
including physics, is generally
considered to be the search for
order in our observations of the
world around us.
• The other side is the invention or
creation of theories to explain
and order the observations.
• Observations may help inspire a
theory, and theories are accepted
or rejected based on the results of
observation and experiment.

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1. Introduction
Physics and its Relation to Other Fields
• Civil engineer: Understanding Forces and material behavior of law.
• Zoologist: Understanding animal can live underground without suffocating
• Physical therapist: principles of center of gravity and the action of forces within the
human body
• Etc.

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Measurement
Academics year: 2020-2021
ENCV611001: Physics (Mechanics and Thermodynamics)

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2. Measurement: Units
• Units is particular standard for quantifying of measurement
• The International System of Units or SI (Système International)
Quantity Unit Name Unit Symbol
Length meter m
Time second s
Mass kilogram kg
Electric current ampere A
Temperature kelvin K
Amount of subtance mole mol
Luminous intensity candela cd

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2. Measurement : Units
• SI derived units are based from base units
Example:
Units of power : watt (W)
1 watt = 1 W = 1 kg • m²/s3
• Scientific notation using power of 10
Example:
3 560 000 000 m = 3.56 × 109 m or 3.56E9
0.000 000 492 s = 4.92 × 10-7 s or 4.92E-7
*E = exponent of ten

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2. Measurement : Converting Units
• Conversion factor
Example

1 so

2 𝑁 106 𝑚𝑚2 𝑁
1 𝑃𝑎 = 1 𝑁/𝑚2 so 1 𝑁/𝑚𝑚2 =1 ∙ 6
= 10 2 = 1 𝑀𝑃𝑎
𝑚𝑚2 1 𝑚2 𝑚
1 𝑚2 = 106 𝑚𝑚2

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2. Measurement : Significant Figures and Decimal Places
• Significant figures
Example
11.3516 → round to three significant: 11.4
11.3279 → round to three significant: 11.3
• Decimal places
35.6 mm = three significant and one decimal
3.56 m = three significant and two decimal
0.00356 m = three significant and five decimal

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Exercise
1. The micrometer (1 mm) is often called the micron. (a) How many microns make
up 1.0 km? (b) What fraction of a centimeter equals 1.0 mm? (c) How many
microns are in 1.0 yd? *1 yd = 3 ft and 1 ft = 0.3048

Answer:
(a) Since 1 km = 1 × 103 m and 1 m = 1 × 106 μm
6
3 3
10 𝜇𝑚
1.0 𝑘𝑚 = 10 𝑚 = 10 𝑚 ∙ = 109 𝜇𝑚
1𝑚
The given measurement is 1.0 km (two significant figures), which implies our result
should be written as 1.0 × 109 𝜇𝑚.

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Exercise
(b) We calculate the number of microns in 1 centimeter. Since 1 cm = 10 -2 m,
6
−2 −2
10 𝜇𝑚
1.0 𝑐𝑚 = 10 𝑚 = 10 𝑚 ∙ = 104 𝜇𝑚
1𝑚
We conclude that the fraction of one centimeter equal to 1.0 𝜇𝑚 is 1.0 × 10-4.

(c) Since 1 yd = (3 ft)(0.3048 m/ft) = 0.9144 m,

106 𝜇𝑚
1.0 𝑦𝑑 = 0.91 𝑚 ∙ = 9.1 × 105 𝜇𝑚
1𝑚

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Exercise
2. Antarctica is roughly semicircular, with a radius of 2000 km. The average
thickness of its ice cover is 3000 m. How many cubic centimeters of ice does
Antarctica contain? (Ignore the curvature of Earth.)

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Exercise
Water is poured into a container that has a small leak. The mass m of the water is
given as a function of time t by m = 5.00t0.8 - 3.00t + 20.00, with t ≥ 0, m in grams,
and t in seconds.
(a) At what time is the water mass greatest
(b) what is that greatest mass?
In kilograms per minute, what is the rate of mass change at (c) t = 2.00 s and (d) t =
5.00 s?

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Motion in a
straight line
Academics year: 2020-2021
ENCV611001: Physics (Mechanics and Thermodynamics)

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3. Motion in a straight line
⚫ Kinematics is the classification and comparison of motions
⚫ For this chapter, we restrict motion in three ways:
1. We consider motion along a straight line only
2. We discuss only the motion itself, not the forces cause it
3. We consider the moving object to be a particle
⚫ A particle is either:
⚫ A point-like object (such as an electron)
⚫ Or an object that moves such that each part travels in the same
direction at the same rate (no rotation or stretching)

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3. Motion in a straight line: Position, Displacement, and Average Velocity
• Position
Position is determined on an axis that is marked in units of length (here meters) and
that extends indefinitely in opposite directions. The axis name, here x, is always on
the positive side of the origin

• Displacement
A change from position x1 to position x2 → Δx

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3. Motion in a straight line: Position, Displacement, and Average Velocity

⚫ Average velocity is the ratio of ∆x to ∆t

o ∆x = a displacement
o ∆t = the time interval in which the displacement occurred
o Average velocity has units of (distance) / (time) meters per second, m/s

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3. Motion in a straight line: Position, Displacement, and Average Velocity

⚫ Average speed is the ratio of total distance to ∆t

⚫ Total distance = The total distance covered.
⚫ ∆t = The time interval in which the distance was covered.
⚫ Average speed is always positive (no direction)
Example A particle moves from x = 3 m to x = -3 m in 2 seconds.
• Average velocity = -3 m/s; average speed = 3 m/s

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3. Motion in a straight line: Instantaneous Velocity and Speed
• Instantaneous velocity, or just velocity, v, is:
• At a single moment in time
• Obtained from average velocity by shrinking ∆t
• The slope of the position-time curve for a particle at an instant (the derivative of position)
• A vector quantity with units (distance) / (time)
• The sign of the velocity represents its direction
• Speed is the magnitude of (instantaneous) velocity
• Example: A velocity of 5 m/s and -5 m/s both have an associated speed of 5 m/s.

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3. Motion in a straight line: Instantaneous Velocity and Speed
Example
• The graph shows the position and velocity
of an elevator cab over time.
• The slope of x(t), and so also the velocity v,
is zero from 0 to 1 s, and from 9s on.
• During the interval bc, the slope is
constant and nonzero, so the cab moves
with constant velocity (4 m/s).

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3. Motion in a straight line: Acceleration
• Acceleration is a change in a particle's velocity
• Average acceleration over a time interval ∆t, aavg is

• Instantaneous acceleration (or just acceleration), a, for a single moment in time

is:

• Acceleration is a vector quantity:

• Positive sign means in the positive coordinate direction
• Negative sign means the opposite
• Units of (distance) / (time squared)

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3. Motion in a straight line
• Example
• The graph shows the velocity and
acceleration of an elevator cab over time.
• When acceleration is 0 (e.g. interval bc)
velocity is constant.
• When acceleration is positive (ab) upward
velocity increases
• When acceleration is negative (cd) upward
velocity decreases.
• Steeper slope of the velocity- time graph
indicates a larger magnitude of
acceleration: the cab stops in half the time
it takes to get up to speed.

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3. Motion in a straight line: Constant Acceleration
⚫ In many cases acceleration is constant,
or nearly so.
⚫ For these cases, 5 special equations
can be used.
⚫ Note that constant acceleration means
a velocity with a constant slope, and a
position with varying slope (unless a =
0).

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3. Motion in a straight line: Constant Acceleration
First basic equation Second basic equation
• When the acceleration is constant, the • Rewrite and Rearrange
average and instantaneous accelerations
are equal

• As we know
• so

• This equation reduces to v = v0 for t = 0

• Its derivative yields the definition of a, dv/dt

Additional useful forms

1 2 3

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3. Motion in a straight line: Free-Fall Acceleration
• Free-fall acceleration is the rate at
which an object accelerates downward
in the absence of air resistance
• Varies with latitude and elevation
• Written as g, standard value of 9.8
m/s2
• Independent of the properties of
the object
• The equations of motion in Table 2-1
apply to objects in free-fall near Earth's
surface
• In vertical flight (along the y axis)
Where air resistance can be
neglected
• The free-fall acceleration is
downward (-y direction) so Value -g
in the constant acceleration
equations

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3. Motion in a straight line: Relative Motion in One Dimension
• Measures of position and velocity depend on
the reference frame of the measurer
• How is the observer moving?
• Our usual reference frame is that of the ground

• Read subscripts “PA”, “PB”, and “BA” as “P as

measured by A”, “P as measured by B”, and “B
as measured by A"
• Frames A and B are each watching the
movement of object P

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3. Motion in a straight line: Relative Motion in One Dimension
• Positions in different frames are related by: • Example
• Frame A: x = 2 m, v = 4 m/s
• Frame B: x = 3 m, v = -2 m/s
• Taking the derivative, we see velocities are • P as measured by A: xPA = 5 m, vPA = 2 m/s, a = 1
related by: m/s2
• So P as measured by B:
• xPB = xPA + xAB = 5 m + (2m – 3m) = 4 m
• But accelerations (for non-accelerating
• vPB = vPA + vAB = 2 m/s + (4 m/s – -2m/s) = 8 m/s
reference frames, aBA = 0) are related by
• a = 1 m/s2

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Exercise
• While driving a car at 90 km/h, how far do you move while your eyes shut for 0.50 s during a hard
sneeze?
• The speed (assumed constant) is v = (90 km/h)(1000 m/km) / (3600 s/h) = 25 m/s. Thus, in 0.50 s,
the car travels a distance d = vt = (25 m/s)(0.50 s) = 13 m.

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Exercise: Instantaneous Velocity and Speed
• An electron moving along the x axis has a position given by 𝑥 = 4 − 12𝑡 + 3𝑡 2 (where t
is in seconds and x is in meters),
a) what is its velocity at t = 1s?
b) Is it moving in the positive or negative direction of x just then?
c) What is its speed just then?
d) Is the speed increasing or decreasing just then? (Try answering the next two questions without
further calculation.)
e) Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer no.
f) Is there a time after t = 3 s when the particle is moving in the negative direction of x? If so, give
the time t; if not, answer no.

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Exercise: Instantaneous Velocity and Speed (solution)

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Exercise: Acceleration
• The position of a particle moving along an x axis is given by 𝑥 = 12𝑡 2 − 2𝑡 3 ,
where x is in meters and t is in seconds. Determine
a) the position,
b) the velocity, and
c) the acceleration of the particle at t = 3.0 s.
d) What is the maximum positive coordinate reached by the particle and
e) at what time is it reached?
f) What is the maximum positive velocity reached by the particle and
g) at what time is it reached?
h) What is the acceleration of the particle at the instant the particle is not moving (other than at t =
0)?
i) Determine the average velocity of the particle between t=0 and t =3 s.

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Exercise: Acceleration (Solution)

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Exercise: Acceleration (Solution)

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Motion in Two
and Three
Dimensions
Academics year: 2020-2021
ENCV611001: Physics (Mechanics and Thermodynamics)

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4. Motion in Two and Three Dimensions: Positions
• A position vector locates a • Example : Position vector (-3m, 2m, 5m)
particle in space
• Extends from a reference
point (origin) to the particle

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4. Motion in Two and Three Dimensions: Displacement
• Change in position vector is a displacement

• We can rewrite this as:

• Or express it in terms of changes in each coordinate:

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4. Motion in Two and Three Dimensions: Velocity
⚫ Average velocity is a displacement divided by its time interval

• Instantaneous velocity is the velocity of a particle at a single point in time and the limit of avg.
velocity as the time interval shrinks to 0

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4. Motion in Two and Three Dimensions: Acceleration
⚫ Average acceleration is a change in velocity divided by its time interval

• Instantaneous velocity is again the limit t → 0:

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4. Motion in Two and Three Dimensions: Projectile Motion
• A projectile is
• A particle moving in the vertical plane
• With some initial velocity
• Whose acceleration is always free-fall acceleration (g)
• Therefore we can decompose two- dimensional motion
into 2 one-dimensional problems

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4. Motion in Two and Three Dimensions: Projectile Motion
• Horizontal motion: • Vertical motion:
• No acceleration, so velocity is constant • Acceleration is always -g

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4. Motion in Two and Three Dimensions: Projectile Motion
• The projectile's trajectory is • In these calculations we assume air
• Its path through space (traces a parabola) resistance is negligible
• Found by eliminating time • In many situations this is a poor
assumption:

• The horizontal range is:

• The distance the projectile travels in x by
the time it returns to its initial height

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4. Motion in Two and Three Dimensions: Uniform Circular Motion
• A particle is in uniform circular motion if • Acceleration is called centripetal
• It travels around a circle or circular arc acceleration
• At a constant speed • Means “center seeking”
• Since the velocity changes, the particle • Directed radially inward
is accelerating!
• Velocity and acceleration have:
• Constant magnitude • The period of revolution is:
• Changing direction • The time it takes for the particle go around
the closed path exactly once

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3. Motion in a straight line: Relative Motion in Two Dimension
• The same as in one dimension, but now with vectors:
• Positions in different frames are related by:

• Velocities:

• Accelerations (for non-accelerating reference frames):

• Again, observers in different frames will see the same

acceleration

⚫ Frames A and B are both observing the motion of P

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