Models & Experiments

Scientific Method Controlled Experiments Analysis Hypotheses Model Building Data Good Models Principles Theories Laws Curiosity Observation Imagination Questions 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=mc 2, 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 table constant 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 × constant x = m  k stretch mass (m 1,x 1 ) (m 2,x 2 ) m1m1 m2m2 x 0 = 0 x1x1 x2x2 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