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 Astronomy Astrophysics Atomic Physics Biophysics Chaos Chemical Physics Computational Physics Cosmology Cryophysics Crystallography Electromagnetism Electronics Fluid Dynamics / Fluid Mechanics Geophysics High Energy Physics High Pressure Physics Laser Physics Mathematical Physics Mechanics Weather Physics Molecular Physics Nanotechnology Nuclear Physics Light Physics Particle Physics Plasma Physics Quantum Electrodynamics Quantum Mechanics / Quantum Physics Quantum Optics Quantum Field Theory Quantum Gravity Relativity Statistical Mechanics String Theory / Superstring Theory Thermodynamics

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/m 2, 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

 Dimensional Analysis  How many seconds are there in a leap year?  Covert the speed 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: 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)