Physics Toolkit Mathematics and Measurements. Physics Toolkit Objectives Use the metric system Evaluate answers using dimensional analysis Perform.

Physics Toolkit

Mathematics and Measurements

Physics Toolkit Objectives

Use the metric system

Evaluate answers using dimensional analysis

Perform arithmetic operations using scientific notation

Distinguish between accuracy and precision

Determine the precision of measured quantities

Physics Toolkit What is Physics?

Physics is a branch of science that involves the study of the physical world: energy, matter, and how they are related

Physicists investigate the motions of electrons and rockets, the energy in sound waves and electrical circuits, the structure of a proton and of the universe

Physics uses mathematical equations for modeling observations and for making predictions

Physics Toolkit Fields in Physics

Acoustics AstronomyAstrophysicsAtomic PhysicsBiophysics ChaosChemical PhysicsComputational PhysicsCosmologyCryophysicsCrystallographyElectromagnetismElectronicsFluid Dynamics / Fluid MechanicsGeophysicsHigh Energy PhysicsHigh Pressure PhysicsLaser Physics

Mathematical PhysicsMechanicsWeather PhysicsMolecular Physics NanotechnologyNuclear PhysicsLight PhysicsParticle PhysicsPlasma PhysicsQuantum ElectrodynamicsQuantum Mechanics / Quantum PhysicsQuantum OpticsQuantum Field TheoryQuantum GravityRelativityStatistical MechanicsString Theory / Superstring TheoryThermodynamics

Physics Toolkit Solving Physics Problems

Step 1: Analyze the Problem

Rewrite the equation Substitute values

Step 2: Solve for the Unknown

Rewrite the equation so the unknown is alone on the left

Step 3: Evaluate the Answer

Physics Toolkit Solving Physics Problems

A light bulb with a resistance of 50.0 ohms is used in a circuit with a 9.0 volt battery. What is the current (amperes) through the bulb? (V = IR)

An object with uniform acceleration (a), starting from rest, will reach a velocity (v) in time (t) according to the formula v = at. What is the acceleration of a bicyclist who accelerates from rest to 7.00 m/s in 4.00 s?

The pressure on a surface is equal to the force divided by the area, P = F/A. A 53 kg woman exerts a force (weight) of 520 newtons (N). If the pressure exerted on the floor is 32,500 N/m2, what is the area of the soles of her shoes?

Physics Toolkit Standard Units

The Système International d’Unités, or SI, uses seven base quantities

Physics Toolkit Standard Units

Base quantities are defined in terms of direct measurements. Derived units created by combining base units

SI system is regulated by the International Bureau of Weights and Measures in Sèvres, France

National Institute of Science and Technology

(NIST) in Gaithersburg, Maryland, also

keeps standards of length, time, and mass

against which our meter sticks, clocks,

and balances are calibrated

Physics Toolkit Standard Units

Prefixes used to change units by powers of 10

Physics Toolkit Dimensional Analysis

You will often need to use different versions of a formula, or use a string of formulas, to solve a physics problem

To check that you have set up a problem correctly, write the equation or set of equations you plan to use with the appropriate units

Method of treating the units as algebraic quantities, which can be cancelled. Also used in choosing conversion factors

Dimensional Analysis

Conversion factor – multiplier equal to 1

Since 1 kg = 1000 g, it has these conversion factors

Choose conversion factor that makes units cancel, leaving answer in correct units

To convert 1.34 kg of iron ore to grams

Physics Toolkit

Dimensional Analysis

Physics Toolkit

Physics Toolkit Dimensional Analysis

How many seconds are there in a leap year?

Covert the speed 5.300 m/s to km/hr.

Convert 5021 centimeters to kilometers.

Physics Toolkit Significant Digits

A pen is measured using a meter stick and recorded as 14.3 cm

Three valid digits: two you are sure of, and one estimated

Valid digits in measurement are significant digits

Last digit given is uncertain but significant

Physics Toolkit Significant Digits

All nonzero digits in a measurement are significant, but not all zeros are significant

Example: 0.0860 m. First two zeros only locate decimal point and are not significant

The last zero is estimated digit and significant

Physics Toolkit Significant Digits

When you perform any arithmetic operation, result can never be more precise than the least-precise measurement

To add or subtract measurements, first perform the operation, then round to correspond to the least-precise value involved

To multiply or divide, perform the calculation and then round to the same number of significant digits as the least-precise measurement

Note that significant digits are considered only when calculating with measurements

Physics Toolkit Scientific Models

Scientific model - idea, equation, structure, or system to model phenomenon explained

Based on experimentation

If the new data does not fit, then

both new data and model

re-examined

Physics Toolkit Scientific Law

Scientific law – rule of nature that sums up related observations to describe a pattern in nature

Physics Toolkit Scientific Theory

Scientific theory – explanation based on many observations supported by experimental results

Best available explanation of why things work as they do May serve as explanations for laws

In scientific use, only a very well-supported explanation is called a theory

Laws and theories may be revised or discarded over time

Physics Toolkit Measurement

Measurement – comparison between unknown quantity and standard

Quantify observations Enable you to derive relationship between any two quantities

Physics Toolkit Measurement Results

When a measurement is made, the results are often reported with uncertainty

Therefore, before fully accepting new data, other scientists examine the experiment, looking for possible sources of errors, and try to reproduce the results

A new measurement that is within the margin of uncertainty confirms the old measurement

Physics Toolkit Precision Versus Accuracy

Physics Toolkit Precision Versus Accuracy

Physics Toolkit Techniques of Measurement

To assure precision and accuracy, measuring instruments need to be used correctly

One common source of error comes from angle at which an instrument is read (parallax error)

Difference in readings caused by parallax, the apparent shift in position of an object when viewed from different angles

Physics Toolkit Techniques of Measurement

Scales should be read with one’s eye straight in front of the measure

If read from an angle you will get a different, and less accurate, value

(a)

(b)