PHYS 1A - Lecture notes 1-10 PDF

Preview

Summary

Philbert Tsai...

Description

Chapter 1: The Nature of Science and Physics Thursday, September 26, 2019 12:30 PM

I.

Introduction a.

b. b. c. d.

I.

Scientific method: experiments to make truth i. Observation and question ii. Hypothesis: test in various methods iii. Test and data iv. Evaluation and Conclusion Physics: interactions between energy, matter, space and time i. DESCRIPTION OF NATURE BASED ON OBSERVATION AND EVIDENCE Models: simple representation of system Theories: explanations supported by scientific evidence (why it happened) Laws: concise descriptions that are supported by scientific evidence (what happens)

Science and the Realm of Physics a. Realm of Physics: understanding mechanisms/functions behind everything in nature

I.

Applications of Physics a. Used in everything field: engineering, chemistry, biology b. Basic laws of physics + analytical methods of application

I.

Models, Theories, and Laws; Role of Experimentation a. Physics: discovering and understanding laws of physics (cannot be changed by humans) b. Model: represents something too hard to display directly; need to be justified with proof c. Theory: EXPLANATION supported by experience and verified many times by researchers; cannot be proven true i. Complex and dynamic b. Law: language to DESCRIBE pattern in nature i. Concise but general statement b. Principles: less broadly applicable statements i. Enables scientists to make predictions

I.

Scientific Method a. Observation/Question→Research→Hypothesis→Data/Experiment→Analyze/Conclusions

I.

Evolution of Natural Philosophy into Modern Physics a. PHYSICS = NATURE b. Classical Physics: Renaissance to 19th century i. CONDITIONS: 1. Matter move at speed less than 1% of light speed 2. Objects large enough to see under microscope 3. Only weak gravity can be involved b. Modern Physics: 20th century scientific advancements

c. Moderns help visualize in "human terms"

a. Limits on Laws of Classical Physics i. ii.

Exception of high speeds, gravity, small objects Rejected or modified through technology but give accurate description of universe

b. Modern Physics i.

Relativity: object travelling faster than 1% of speed of light or experiences strong gravitational field Quantum Mechanics: objects so small cannot be seen under microscope Relativistic Quantum Mechanics: combining two theories 1. Small objects travelling super fast or has strong gravitational field

ii. iii.

Chapter 2: Units, Accuracy, and Approximation Thursday, September 26, 2019 12:30 PM

I.

Introduction a. b.

Fundamental Units: time, mass, length Derive Units: units of physical quantities described in terms of fundamental units

c. d. e. f. g.

I.

Order of Magnitude: KHDUDCM Conversion Factors: ratio from one unit to another Accuracy: close measurement is to actual/true value Precision: closely measurement is repeated; quantities agree with each other Significant Figures: reflection of confidence in measurement

Physical Quantities and Units a. b.

Connect measured values to physical quantities Expression of vast ranges of physical properties through quantitative observation (numerical) c. LENGTH, MASS, TIME, ELECTRIC CURRENT d. Units: measurement of physical quantities e. SI System: standardized units

I.

SI Units: Fundamental and Derived Units a. b.

Common units that are used: m, kg, sec Derived units can be in terms of fundamental units such as newtons, pascal, joules

I.

Units of Time, Length, and Mass: Second, Meter, Kilogram a.

I.

Electric Current: Amps

Metric Prefixes

a.

Factors of 10

Tera

10^12

Giga

10^9

Mega

10^6

Kilo

10^3

Deci

10^-1

Centi

10^-2

Milli

10^-3

Micro

10^-6

Nano

10^-9

Pico

10^-12

Femto

10^-15

I.

Accuracy and Precision of Measurement

a. b.

a.

Accuracy: close measurement is to true value Precision: close measurement is similar to others when repeated (spread/range)

Measurement Uncertainty

a.

Uncertainty: measured value deviates from true/expected value How confident can you be in your measurement that it represents the expected value ii. Measures PRECISION b. Indicate range that the value falls under; small = more precise i.

A±δA a. b.

b.

b.

a.

TRUE/BEST ESTIMATE ± UNCERTAINTY Contributors a. Limitations of measuring device b. Care when making measurement c. Irregularities in objects measured d. Other factors (depending on situation) Absolute Uncertainty: reporting magnitude of uncertainty is not INFORMATIVE a. Depending on situation: 0.1 m could be a lot or very small b. Cannot change Percent Uncertainty: more INFORMATIVE a. Change depending on the information given

Uncertainties in Calculations a. Add/Subtract = ABSOLUTE UNCERTAINTY i. Numerical a.

Multiply/Divide = RELATIVE UNCERTAINTY a. Percentage

a.

Formulas give exact solution if: a. Measurements are independent b. Individual uncertainties have a normal distribution If not, then it gives APPROXIMATION

b.

a.

Precision of Measuring Tools and Significant Figures a. Tool Precision i. ii.

Smallest increments that tool can measure; ex. Tick marks on ruler Smaller difference in length or metric prefix = more precise

b. Significant Figures i. ii.

Tools limit precision based on how close it can measure Last digit is an estimation or first digit with uncertainty

b. Zeros i.

Before decimal and non-zero number = not significant (placeholder)

0.056 a.

2 sig fig

Internal zeros = significant 10.056

5 sig fig

i. Trailing Zero = depends on written connotation 1.20x10^5

3 sig fig

120000

2 sig fig

i. Prevent ambiguity by writing in scientific notation

a.

Significant Figures in Calculations i.

a.

Sig fig in answer follows measurement with least precision (placeholder or # of sig fig) 1. MULTIPLICATION/DIVISION a. Same number of sig fig as measurement with least sig fig 2. ADDITION/SUBTRACTION a. Same place as measurement with least precision (least decimal place)

Approximation i. ii.

I.

Guesstimates: save time to determine best instrument of measurement Does not have to be very precise/accurate; rough estimate

Unit Conversion and Dimensional Analysis a.

Unit Conversions i. ii.

Conversion factor: from one to another through ratio 80 m to x km

i.

d. Dimensional Analysis i. ii.

ALWAYS!!! Include units to cross check Dimension = physical characteristic (length, mass, time) described by unit

iii. iv.

[L,M,T]: UNIT DIMENSIONS Combine units through multiplication and division, even exponential

EX. Suppose that you drive the 10.0 km from your university to your home in 20.0 min. Your average speed is defined as distance traveled divided by the time (speed = d/t) . Calculate average speed in kilometers per hour and in meters per second (m/s) Average Speed 10.0 km 20.0 min = 0.500 km/ min 0.500 km min (60 min - hr =30 0.500 km

tossed 1000m min T, min

.okm/hr

114m =8.33m/sec

EX. A grocery store sells 5-lb bags of apples. You purchase four bags over the course of a month and weigh the bags each time. You obtain the following measurements:  Week 1 weight: 4.6 lb  Week 2 weight: 5.3 lb  Week 3 weight: 4.7 lb  Week 4 weight: 5.4 lb You determine that the weight of the 5-lb bag has an absolute uncertainty of ±0.4lb. What is the percent uncertainty of the bag’s weight?

RANGE: 5 lb ± 8%

0.0009

1 sig fig

15,450.0

6 sig fig

6×103

1 sig fig

87.990

5 sig fig

30.42

4 sig fig

Chapter 3: 1D Kinematics: Motion Along a Line Tuesday, October 1, 2019 12:30 PM

I. Introduction: HOW THINGS MOVE a. b. c. d. b.

b. c. d. e. f.

Scalars: number/measurement with no direction (magnitude) Vectors: number/measurement with direction Position: location of object Displacement: net change in position (INITIAL TO FINAL) i. Nothing about the amount of [L] traveled Distance: TOTAL path traveled by object i. Opposition of displacement ii. Takes into consideration path taken Vector Addition: combining magnitude and direction of vectors Duration: change in time from start to end of event Speed: actual rate of change in position Velocity: object's net rate of change in position over time Acceleration: rate of change in velocity over time

a. Motion in a Straight Line i.

II.

Kinematic Equation 1. Time: how long 2. Position: where from beginning to end 3. Velocity: how position changes over time (magnitude and direction) 4. Acceleration: how velocity change over time 5. Displacement curve: x - x0 = v0t +1/2at^2 6. Definition of acceleration: V = v0 + at

Position a. Describe at any particular time relative to a reference frame b. Reference frame: item or location selected as stationary i. Ex. Earth when measuring the position of the teacher ii. Ex. The place when measuring the position of reclining chair

II.

Displacement a. b. c. d.

II.

Def: change in position (movement) of object in comparison to reference frame Delta (Δ) = change Unit Dimension - [L] in meters +/- is based on person determining; sign doesn’t matter but interpretation of number is IMPORTANT

Distance a. Scalar value: does not care about the direction or path take b. POSSIBLE: i. Same displacement but different distance via versa

II.

Vectors and Scalars a. Scalar can be negative i. Value is less than reference chosen to be zero b. Vector cannot be negative i. Minus sign indicates a spatial direction ii. Usually represented with arrows

II.

Time and Duration

a. Unit Dimension: [T] in seconds b. Elapsed time/duration: beginning to end (Δt)

II.

Velocity a. b. Speed: how FAST object is moving (scalar quantity)

I. a. Does not give info on what happens within time frame

I.

Instantaneous Velocity a. At any point in time and space b. Break duration into multiple smaller intervals (increase details about motion = accuracy)

I.

Graphically equivalent to slope of displacement: x(t) a. Can be zero when slope does not change eg. at max/min

I.

Instantaneous Velocity vs Average Velocity a. Speedometer = instantaneous velocity i. Displacement over specific time interval b. Average velocity: how long to get from one place to another if instantaneous velocity varies c. NEGATIVE VELOCITY = GOING BACKWARDS

I.

Speed a. Scalar quantity describing how fast an object is going i. Always position b. Average Speed: distance traveled over duration i. Can be greater than average velocity ii. Not necessarily magnitude of velocity b. Instantaneous Speed: magnitude of velocity i. Need to change sign when velocity is negative

II.

Acceleration a. Def: rate of change of instantaneous velocity over time

I.

Average Acceleration: change in velocity over duration (m/s²)

II.

Vector: velocity changes in magnitude, direction, or both

a.

Deceleration vs. Negative Acceleration i. ii.

b.

Motion Diagrams i. ii.

a.

Deceleration: acceleration in the opposite direction to SLOW DOWN 1. Does not depend on direction defined as positive Negative Acceleration: depend on which direction of positive axis Def: visualize position, velocity, and acceleration Accelerating: when opposite moves at different speed; not CONSTANT

Instantaneous Acceleration i.

Def: acceleration at specific instant in time

a. b. c.

Same sign = speeding up Opposite sign = slowing down

I. Simplifying Assumption: Constant Acceleration a.

Average acceleration = instantaneous acceleration

a. Equations of Motions for Constant Acceleration in 1D a.

b.

Describe motion of object in terms of displacement, velocity, acceleration, duration

Kinematic Equations: Summary List of equations:

a.

Calculate final position of object going at constant acceleration given starting and ending velocities during certain time

a.

Calculate final velocity of object if given initial velocity, acceleration constant, and duration of acceleration

b.

a. b. c.

Calculate final position if given initial position, initial velocity, and duration at constant acceleration If a(t) is non-zero, displacement depends quadratically on duration If a(t) is zero, displacement depends linearly on duration

a.

Use for calculating final velocity and rearrange to find displacement

b.

a.

Problem-Solving Basics for 1D Kinematics a. b. b. c. d.

b.

b.

Unreasonable Results a.

a.

One premise or more is unreasonable which produces an unreasonable final value i. Not just about manipulating math equations STEP 1: SOLVE problem STEP 2: CHECK answer for reasonability a. Sign, magnitude, direction, units STEP 3: If unreasonable, IDENTIFY premise leading to it

Falling Objects and Gravity a. b. c. d. e.

b.

EXAMINE to determine which physical properties are given i. Maybe sketch to visualize LIST of given and inferred values i. Stop/at-rest = 0 IDENTIFY what needs to be found (unknown values) DETERMINE equation to use SUBSTITUTE the knowns with proper units into equation i. Position/Displacement: m ii. Duration/Time: s iii. Velocity: m/s iv. Acceleration: m/s2 CHECK answer to ensure reason (magnitude and sign) i. Accurately describe nature and phenomena

Air resistance and friction are negligible; all objects fall towards center of Earth at constant acceleration (9.80 m/s2) independent of mass In vacuum, acceleration is the same for ALL despite varying mass Free Fall: object solely under the influence of gravity Acceleration due to Gravity: acceleration of free-falling objects Direction = downwards (may be negative depending on labeling system)

1D Motion Involving Gravity a. b.

Assume velocity is vertical; no air resistance and friction Same kinematics equations but acceleration is replaced with -g

Position (m)

Time (5)

EX. Given the position-versus-time graph of the below figure, find the average velocity of the object in each of the three time windows : (a) 0.0 s to 0.5 s , (b) 0.5 s to 1.0 s , and (c) 1.0 s to 2.0 s.

= 1.0 m/s

= 0 m/s

= -0.5 m/s

EX. A particle is in motion and is accelerating. The functional form of the velocity is v(t) = 20t 5t² m/s a. Find the functional form of the acceleration. a(t) = 20 - 10t

b. Find the instantaneous velocity at t = 1.0 s , 2.0 s , 3.0 s , and 5.0 s. v(1) = 20(1) - 5(1)² 20 - 5 15 m/s v(2) = 20(2) - 5(2)² 40 - 20 20 m/s

c. Find the instantaneous acceleration at t = 1.0 s , 2.0 s , 3.0 s, and 5.0 s. a(1) = 20 - 10(1) 20 - 10 10 m/s² a(2) = 20 - 10(2) 20 - 20 0 m/s²

d. Interpret the results of (c) in terms of the directions of the acceleration and velocity vectors. When the time is equal to 1 s, the particle is moving to the right and speeding up since v(1) and a(1) are both positive. When the time is equal to 2 s, the particle is moving to the right at constant speed. It is traveling at maximum velocity. When the time is equal to 3 s, the particle is moving to the right and slowing down because v(3) and a(3) are opposite signs. When the time is equal to 5s, the particle is moving to the left and speeding up since v(5) and a(5) are both negative v(3) = 20(3) - 5(3)² 60 - 45 15 m/s v(5) = 20(5) - 5(5)² 100 - 125 -25 m/s a(3) = 20 - 10(3) 20 - 30 -10 m/s² a(5) = 20 - 10(5) 20 - 50 -30 m/s²

EX. A person accelerates starting a foot race accelerates at 0.40 m/s2 for 100 s, what will be his final speed? a(100) = 0.40 m/s2 T = 100 s Vi = 0 m/s Vs = ? 0 m/s + 0.40 m/s2(100s) 40 m/s Around 89 mph NOT REASONABLE: PERSON CANNOT RUN 40 m/s FOR 100 S



Unreasonable because of duration of velocity 0.4 m/s2 means velocity is increasing by value After 3 seconds, runner achieved 1.2 m/s (2.7 mph) so acceleration is reasonable

EX. Watermelon Drop A annual tradition at a university campus involves dropping a watermelon from the 7th floor of one of the campus buildings. The watermelon hits the ground 2.20 second after being released from rest. Assume that air resistance is negligible. (a) Calculate the height from which the watermelon was dropped.

g = -9.80 m/s2 t = 2.20 s

(b) Calculate the velocity of the watermelon when it strikes the ground. 0.0 + (-9.80 m/s2)2.20 s -21.6 m/s

EX. Total Toss Up A carnival game requires a player to toss a ball straight up so that it reaches an exact height, but no higher. Assume that air resistance is negligible. If a player releases the ball upwards at a chest level of 1.20 meters above the ground, then what initial velocity must the ball have to reach a maximum height of exactly 3.00 meters from the ground?

g = -9.80 m/s2

5.94 m/s

Chapter 4: 2D Kinematics on a Surface

Thursday, September 5, 2019 12:30 PM

I.

Introduction: HOW THINGS MOVE a. b.

2D Motion: objects moving horizontally and vertically Independence in Perpendicular Directions: horizontal and vertical motion are independent and do not affect each other c. 2D Vectors: description with magnitude and direction in 2D plane d. Vector Components: decompose vector into vertical and horizontal portion e. Projectile Motion: kinematics in 2D motion by applying independence of x and y

II.

2D Motion: Walking in a City a.

No direct path in diagonal (as the crow flies); must move in horizontal and vertical direction b. Shortest/most direct path = displacement i. Calculate hypotenuse by trigonometry

EX. Calculating final displacement

I.

Significant Figures for Counted Quantities a. Discrete numbers: infinite number of sig figs since it is an exact/counted value b. Ignoring possibility of counting error

I.

Vectors in 2D a. b. c. d.

II.

Magnitude and direction Magnitude of vector = absolute value Denote vector = arrow on top Direction with respect to positive x-axis i. Negative = clockwise ii. Positive = counter-clockwise

Vector Addition: Head-to-Tail Method a. Head-to-tail graph: place tail of one vector to head of another STEP 1: DRAW arrow to represent 1st vector STEP 2: DRAW arrow to represent 2nd vector; tail to head STEP 3: CONTINUE if more vectors STEP 4: DRAW arrow from tail of 1st vector to head of last vector Result...