message from prof. field - university of floridauf phy2053, lecture 2: introduction to physics,...

UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension

Message from Prof. Field(posted on PHY2053 main web page)

“PHY 2053 Discussion Section Mistake: I made two errors with the discussion sections: Section 3801 is MW 5 in 1101 NPB and 7835 is WF 5 in 1216 NPB. These sections were goofed up and the TA may not have showed up for the class. I have corrected the schedule at Instructors & TA's. Everything should be okay for next week. I am very sorry for the confusion.”

Other than that, discussion sections should be meeting1

http://www.phys.ufl.edu/courses/phy2053/fall11/instructors.html

http://www.phys.ufl.edu/courses/phy2053/fall11/instructors.html

Introduction

Underlying Principles of PhysicsSignificant Figures

UnitsDimensional Analysis


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

3


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

4


Concept: Measurement

• physics is based on measurements

• fundamentally, a measurement is a comparison

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

5


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%

6


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

7


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 class8


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.”

9


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)

10


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

11


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

12


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

13


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

14


Example 1• How far does light travel in one nanosecond (1 ns)?

The speed of light is 300, 000 km / s.

15


Example 2

16

• 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)

17


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

18


Motion Along A Line

• Distance vs Displacement

• Velocity - average and instantaneous

• Velocity vs Speed

• Acceleration - average and instantaneous

19


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|20


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)

21

UF PHY2053, Lecture 2: Introduction to Physics, Motion in One Dimension 22

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

23


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

=

24

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)

25


Average Velocity, Constant

• The straight line indicates constant velocity

• The slope of the line is the value of the average velocity

26


Average Velocity, Non Constant

• The motion is non-constant velocity

• The average velocity is the slope of the blue line joining two points

27


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)

28

vx ≡ lim Δx xf - xiΔt tf - ti

= limΔt→0 tf →ti


Instantaneous Velocity

29

Δt

Δx


Δx

Δt



Δt

Δx

32



Average and Instantaneous Acceleration

• the rate of change of velocity has physical relevance• By analogy with velocity, define average acceleration:

• and instantaneous acceleration:

33

aav,x ≡Δvx vx,f - vx,iΔt tf - ti

=

ax ≡ lim Δvx vxf - vxiΔt tf - ti

= limΔt→0 tf →ti


Example 4:

A Mustang GT500 goes from 0 to 60 mph in 4.1 seconds. What is the average acceleration over this period (in m/s2)?How many “g’s” is it pulling?

34


Next Tuesday:

Chapter 2.4-2.6:

Linear Motion, Free Fall

35


Supporting Materials

36


Demonstrations

• Standards of Measurement

• Cart Motion Sensor

37

message from prof. field - university of floridauf phy2053, lecture 2: introduction to physics,...

Documents