introduction - phys.ufl.edu
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Introduction
Underlying Principles of PhysicsSignificant Figures
UnitsDimensional Analysis
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
What is Physics?
• natural science
• method of collecting and analyzing empirical data about the natural (material) universe
• organized body of knowledge resulting from application of the scientific method
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Scientific Method
• observe a repeating pattern / effect
• construct model / theory of effect
• extrapolate model - predict new effect outside observed data
• perform measurement to confirm/disprove predicted effect
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Concept: Measurement
• physics is based on measurements
• fundamentally, a measurement is a comparison
• compare quantity of interest to standardized units [of mass, time ..]
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Significant Figures
• related to measurement uncertainty
• last digit implies measurement precision
• 201 cm vs 201.115 cm
• practical use in lab, difficult to use here
• for homeworks and exams, relevant: required precision of match ~3%
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Measurement Units
• “standard” units of comparison
• standards have been evolving over time
• have usually been culturally tied
• problems - always at the interface
• most popular interface: Imperial vs Metric systems
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
SI System of Units
• standardization of units
• reliability of measurements
• compatibility of results and devices
• we will be using the SI system of units in class7
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
SI in the USA
• Omnibus Trade and Competitiveness Act of 1988:“Industry in the United States is often at a competitive disadvantage when dealing in international markets because of its nonstandard measurement system, ...”
• “... designate the metric system of measurement as the preferred system of weights and measures for United States trade and commerce.”
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
SI Unit of Time
• 1 second [s]
• measurement of duration of an effect by comparing to periodic effects
• pendulum, quartz crystal, ...
• best precision so far: multiple periods of vibration of radiation emitted by an isotope of the Cesium atom
(9 192 631 770)
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
SI Fundamental Unit: Length
• 1 meter [m]
• originally defined as 1/10 000 000 distance from north pole to equator
• for a long time was a physical bar held in vacuum at 0 deg C in Paris
• nowadays - length traversed by light in vacuum during very short interval
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
SI Unit of Mass
• 1 kilogram [kg]• currently still a
physical piece of mass (weight)
• stored at NIST• only fund. unit to
incorporate power modifier
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Power Modifiers
centi (c) 10-2 pico (p) 10-12
mili (m) 10-3 kilo (k) 10+3
micro (μ) 10-6 mega (M) 10+6
nano (n) 10-9 tera (T) 10+9
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Important for Units
• when using values in formulas, all input values must be in the same units
• don’t forget about power modifiers
• once a common set of units is established, formulas apply
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Example 1• How far does light travel in one nanosecond (1 ns)?
The speed of light is 300, 000 km / s.
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Example 2
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• How fast is an object moving if it travels one furlong per fortnight? (in cm/s)
• one furlong = 201.168 m, one fortnight = 14 days
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Dimensional Analysis
• every physical quantity has a dimension
• some dimensions have fundamental units (mass, time, length)
• cross-check results
• derive properties (up to a point)
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Approximation
ť rough model will capture the general behavior;
specifics can be lost• not likely to have to pick models in PHY2053• technique is often used for quick estimates
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Motion Along A Line
• Distance vs Displacement
• Velocity - average and instantaneous
• Velocity vs Speed
• Acceleration - average and instantaneous
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Position, Displacementand Distance Traveled
• Reference point: “Origin”
• Displacement is the difference between final and initial positions
Δx = x2 - x1 = xfinal - xinitial
Important: Displacement is a signed quantity!
• Distance traveled is the sum of absolute values of all displacements, always positive definite
Distance traveled = Σi |Δxi|19
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Example 3:
A “perfect” ball is bouncing between two walls. The distance between the two walls is 0.5 m. Initially, the ball is by the left wall. It takes the ball 1 sec to travel the distance between the two walls. Assume the ball starts by the left wall at t = 0s.
What is the displacement of the ball and its distance traveled at t = 1s, t = 2s, t = 3s, ... , t = N s? (N > 0)
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension 21
x distancetraveled tfinal
0.0 m 0.0 m 0 sec
0.5 m 0.5 m 1 sec
0.0 m 1.0 m 2 sec
0.5 m 1.5 m 3 sec
0.0 m for evenvalues of N
N×0.5 m N sec0.5 m for oddvalues of N
N×0.5 m N sec
0.5 m
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
End of Lecture 2 in Class
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Average Velocity vs Average Speed
• Average Velocity is the change in position during a time interval
• Average Speed is the distance traveled during a time interval (hint: “car model”)
vav,x ≡Δx xf - xiΔt tf - ti
=
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average speed ≡distance traveled
total time
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Example 4:For the “perfect” ball from Example 3, what is the average velocity and average speed at
• t = 1 s, t = 2 s, t = 3 s?
• t = N s? (N > 0)
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Average Velocity, Constant
• The straight line indicates constant velocity
• The slope of the line is the value of the average velocity
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Average Velocity, Non Constant
• The motion is non-constant velocity
• The average velocity is the slope of the blue line joining two points
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Instantaneous Velocity• The limit of the average velocity as the time interval
becomes infinitesimally short, or as the time interval approaches zero
• The instantaneous velocity indicates what is happening at every point of time
• Instantaneous speed can be defined by analogy. It is the average speed as the total time becomes infinitesimally short. (= abs. value of instantaneous velocity)
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vx ≡ lim Δx xf - xiΔt tf - ti
= limΔt→0 tf →ti
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Instantaneous Velocity
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Δt
Δx
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension 29
Δx
Δt
Instantaneous Velocity
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension 30
Δx
Δt
Instantaneous Velocity
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Δt
Δx
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Instantaneous Velocity
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Average and Instantaneous Acceleration
• the rate of change of velocity has physical relevance• By analogy with velocity, define average acceleration:
• and instantaneous acceleration:
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aav,x ≡Δvx vx,f - vx,iΔt tf - ti
=
ax ≡ lim Δvx vxf - vxiΔt tf - ti
= limΔt→0 tf →ti
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Example 4:
A sports car goes from 0 to 60 mph in 4.1 seconds. What is the average acceleration over this period (in m/s2)?
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Next Tuesday:
Chapter 2.4-2.6:
Linear Motion, Free Fall
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Supporting Materials
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UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension
Demonstrations
• Standards of Measurement
• Cart Motion Sensor
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