College Physics I: BIIG problem-solving method

Created Feb. 7, 2024 by C N Hiremath

Universe

  • Galaxies are big. Atoms are small. The same laws of physics describe both. An indication of the underlying unity in the universe.
  • The laws of physics are surprisingly few in number, implying an underlying simplicity of nature’s apparent complexity.

 

Role of Physics

  • The study of physics can improve problem-solving skills. It makes other sciences easier to understand.
  • Physics has retained the most basic aspects of science. It is used by all of the sciences.

 

Model, Theory, and Law

  • A model is a representation of something that is too difficult (or impossible) to display directly.
  • A theory is an explanation for patterns in nature that is supported by scientific evidence and verified multiple times by various groups of researchers. It is much more complex and dynamic. It explains an entire group of related phenomena. It is the end result of a process.
  • A law uses concise language to describe a generalized pattern in nature that is supported by scientific evidence and repeated experiments. It describes a single action. It is a postulate that forms the foundation of the scientific method.

 

The Scientific Method

  • Scientific method is the process followed by scientists as they inquire and gather information about the world. It can be applied to many situations that are not limited to science.
  • The process begins with an observation and question that the scientist will research. Next, they perform some research. Then, devices a hypothesis. Test the hypothesis by performing an experiment.  Then analyzes the results of the experiment and draws a conclusion.

 

Classical Physics

  • Classical physics is not an exact description of the universe, but it is an excellent approximation.
  • For the laws of classical physics to apply, the following criteria must be met:

           Matter must be moving at speeds less than about 1% of the speed of light,

           The objects dealt with must be large enough to be seen with a microscope, and

           Only weak gravitational fields can be involved.

 

Modern Physics

  • Modern physics consists of two revolutionary theories: Relativity (very fast) and Quantum mechanics (very small)
  • Relativity must be used whenever an object is traveling at greater than about 1% of the speed of light or experiences a strong gravitational field.  Example, near the sun.
  • Quantum mechanics must be used for objects smaller than can be seen with a microscope.

 

Physical Quantities

  • We define a physical quantity either by specifying how it is measured or by stating how it is calculated from other measurements.
  • Measurements of physical quantities are expressed in terms of units, which are standardized values.
  • There are two major system of units in the world.

            SI units – also known as metric system (widely used)

            English units – also known as the imperial system

 

SI Units

  • The acronym “SI” is derived from the French Systeme International.
  • The metric system is the standard agreed upon by scientists and mathematicians.
  • Fundamental SI Units:      Length – meter (m)        Mass – kilogram (kg)         Time – second (s)

 

The Derived Units

  • Derived units are units that can be expressed as algebraic combination of fundamental units.
  • Example,  speed  =  length / time

 

The Second

  • The SI units for time the second (s) is defined as 1/86,400 of a mean solar day.
  • It is the time required for 9,192,631,770 vibrations of cesium atoms.
  • An atomic clock uses the vibrations of cesium atoms to keep time to a precision of better than a microsecond per year.

 

The Meter

  • The SI unit for length. The meter (m) is defined as 1/10,000,000 of the distance from the equator to the North Pole.
  • It is defined as the distance the light travels in vacuum in 1/299,792,458 of a second.

 

Kilogram

  • The SI unit for mass, the kilogram (kg), is defined to be the mass of a platinum-iridium cylinder kept at the International Bereau of Weights and Measures near Paris.

 

Unit Factor

  • A conversion factor is a ratio expressing how many of one unit are equal to another unit.
  • For example, there are 12 inches in 1 foot, 100 centimeters in 1 meter, 60 seconds in 1 minute, and

            1,000 meters in 1 kilometer.

  • It is often necessary to convert from one type of unit to another.

 

Accuracy and Precision

  • Science is based on observation and experiment on measurements.
  • Accuracy is how close a measurement is to the correct value for that measurement.
  • Precision of the measurement system refers to how close the agreement is between measurements which are repeated under the same conditions.

 

Uncertainty

  • Uncertainty is a quantitative measure of how much the measured values deviate from a standard or expected value.
  • If the measurements are not very accurate or precise, then the uncertainty of the values will be very high.
  • The factors contributing to uncertainty in a measurement include: Limitations of the measuring device - The skill of the person making the measurement - Irregularities in the object being measured - Any other factors that affect the outcome (highly dependent on the situation).

 

Percent Uncertainty

  • Uncertainty is often expressed as a percent of the measured value.
  • If a measurement A is expressed with uncertainty, δA, the percent uncertainty is defined as

             up   =  δA / A × 100%

  • Problem (E1.2):  A grocery store sells 5 lb bags of apples. You purchase four bags over the course of a month and weight the apples each time. You determine that the weight of the 5 lb has an uncertainty of ± 0.4 lb.  What is the percent uncertainty of the bag’s weight?                                  ( 8% )
  • There is an uncertainty in anything calculated from measured quantities.
  • The percent uncertainty in a quantity calculated by multiplication or division is the sum of percent uncertainties in the terms used to make the calculation.

 

Precision of Measuring Tools

  • An important factor in the accuracy and precision of measurements involves the precision of the measuring tool.  A precise measuring tool is one that can measure values in very small increments.

            Ruler:              1 mm               Caliper:  0.01 mm

  • The more precise the measuring tool, the more precise and accurate the measurements can be.

 

Significant Figures

  • Significant figures indicate the precision of a measuring tool that was used to measure a value.
  • For example, the measured valve 36.7 cm has three significant figures.
  • Calculations with measured numbers follow the “weakest link” rule.
  • When multiplying or dividing measured values, the final answer can contain only as many significant figures as the least precise value.
  • When adding or subtracting measured values, the final answer cannot contain more decimal places than the least precise value.

 

Exact Numbers

  • If a number is exact, such as the two in the formula for the circumference of a circle, c  =  2 π r

            it does not affect the number of significant figures in a calculation.

 

Scientific Notation

  • A value in scientific notation is a number with one digit to the left of the decimal point and zero or more to the right of it, multiplied by a power of ten.
  • Solves the problem of all the zeros. Makes the number of significant digits immediately apparent.
  • Example, the distance to the sun:

            1.50 x 1011 m   (3 digits are significant)          1.5 x 1011 m     (2 digits are significant)


BIIG: Problems & Solutions


Download: OER_Hiremath_ch01_The_Nature_of_Science_and_Physics.pdf


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