introduction - phys.ufl.edu

Introduction

Underlying Principles of PhysicsSignificant Figures

UnitsDimensional Analysis

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

2


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

3


Concept: Measurement

• physics is based on measurements

• fundamentally, a measurement is a comparison

• compare quantity of interest to standardized units [of mass, time ..]

4


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%

5


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

6


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


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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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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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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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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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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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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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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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


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)

16


Approximation

≈• 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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Motion Along A Line

• Distance vs Displacement

• Velocity - average and instantaneous

• Velocity vs Speed

• Acceleration - average and instantaneous

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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


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


End of Lecture 2 in Class

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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

=

23

average speed ≡distance traveled

total time


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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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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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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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


Instantaneous Velocity

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Δt

Δx


Δx

Δt



Δt

Δx

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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


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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Next Tuesday:

Chapter 2.4-2.6:

Linear Motion, Free Fall

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Supporting Materials

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Demonstrations

• Standards of Measurement

• Cart Motion Sensor

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