Models & Experiments

Scientific Method

ControlledExperiments

AnalysisHypotheses

Model BuildingData Good

Models

PrinciplesTheories

Laws

CuriosityObservationImaginationQuestions Unanswered Questions

Model Modifications

Models in Science• In science we develop models (mental

images) that represent physical phenomena– Models show relationships between things– Models can predict what will happen (What if?)– A good model is accurate and has broad utility– Examples:

• Theory of Evolution• Atomic Theory• Theory of Chemical Bonding• Kinetic Molecular Theory

• Models can be:– Equations (E=mc2, F=ma, V=IR)– Diagrams (pictures, drawings, schematics, maps)– Replicas (small-scale model, molecular model set)

• Models show relationships between:– physical objects (block spring wall)– physical quantities (force = mass × accel)

• Models can make predictions– How far will the ball go?– How much time will it take?

• Models are not perfect– Models are based on simplifying assumptions

• Examples: frictionless tableconstant acceleration

– Models focus only on the system of interest – Things that have a very small effect are left out

• Example: When analyzing the motion of a car we ignore the gravitational pull of the Moon

Controlled Experiments• Models are determined by

controlled experiments– Only one thing is changed at

a time, called the independent variable

– Another quantity is measured, called the dependent variable

– The data are graphed and analyzed

– Often an equation can be found that is a good model of the system

• Example: Mass-on-a-spring experiment– Mass is the independent variable (we change it)– Stretch is the dependent variable (we measure it)– Temperature is a control variable (we keep the same)– Experimental Result:

stretch = mass × constantx = mk

stre

tch

mass

(m1,x1)

(m2,x2)m1

m2

x0 = 0

x1

x2

x

Experimental Error

• Our models of reality are base on experiments which in turn are base on measurements

• Measurements are never perfect regardless of how carefully we make them

• Measurements are vulnerable to errors of accuracy and precision due to problems with instruments and how humans use them

• All measurements have a some randomness built into them which adds uncertainty

Minimizing Error

• When doing experiments we must do our best to minimize measurement error by– anticipating sources of error– using good experimental practices

• When reporting on experiments we must– be able to identify primary sources of error– know the precision of our instruments– be able to estimate the accuracy of our

measurements

Good Practices• A few ways to minimize error:

– Avoid parallax error– Record the units being used– Measure as precisely as possible by estimating the

last digit (and never round a measurement)– Have one person measure while another performs

quality control– Repeat measurements (when possible) and

average the results– Throw out obviously bad values and re-measure

Summary• In physics we create and use models of reality• Models consist of equations, diagrams, and ideas• We use models to show relationships between

physical quantities and make predictions• Models have simplifying assumptions that make

them useable (no model is perfect)• Physical models are based on the results of

controlled experiments• Controlled experiments change one thing at a

time (indep. var.) and measure what happens• When doing experiments we try to minimize

measurement error by using good practices