Chapter 1: Physics & The Life Sciences

What is Physics?

Physics is the study of the fundamental laws that govern the structure and behavior of the universe, focusing on matter and energy and their interactions. Unlike chemistry, which is concerned with chemical changes, physics emphasizes the forces between objects and the relationships between matter and energy.

• Definition: Physics is a quantitative science that uses mathematical models to describe cause and effect relationships between physical quantities.

• Key Focus: Understanding the laws of nature, such as Newton's laws, conservation of energy, and momentum.

• Role in Life Sciences: Physics is increasingly important in biological contexts, especially at the biomolecular level, where physical principles help explain complex biological phenomena.

• Example: The physics of the human ear involves concepts like wave mechanics, resonance, and electricity.

Science & Innovation (Technology)

Physics underpins technological innovation by providing models and mathematical descriptions that lead to new devices and applications. The scientific methodology involves making observations, performing experiments, and developing theories based on cause and effect.

• Hierarchy: Scientists (various disciplines) → Scientific Methodology → Physics (models) → Innovation (technology).

• Example: Studying a new species (e.g., cylindra petroconsuma) to develop technology for oil spill cleanup by understanding its physical structure and function.

Physical Quantities, Dimensions, and Units

Base Quantities and SI Units

All measurable physical quantities can be expressed as combinations of a small set of base quantities, each with defined units and dimensions. The SI (International System of Units) is the standard system used in physics.

• Base Quantities:

  • Length [L]: meter (m)

  • Mass [M]: kilogram (kg)

  • Time [T]: second (s)

  • Others: electric current (ampere, A), temperature (kelvin, K), amount of substance (mole, mol), luminous intensity (candela, cd)

• Derived Quantities: Formed by combining base quantities (e.g., velocity, acceleration, force).

• Dimensional Analysis: Ensures equations are dimensionally correct. For example, acceleration has dimensions and units m/s2.

• Example: Force is defined as mass times acceleration: with dimensions and units kg·m/s2 (Newton).

Dimensional Analysis and Correctness

All physical equations must be dimensionally consistent. This means the dimensions on both sides of an equation must match.

• Example: For , dimensions are .

• Exercise: Check if equations are dimensionally correct by substituting dimensions for each quantity.

Unit Conversion Factors

Unit conversion is essential when working with different systems (e.g., Imperial to SI). Conversion factors relate units from one system to another.

• Example 1: Convert 50 mph to SI units:

• Example 2: Find the radius of a sphere with volume 23 cm3 in feet, knowing 1 ft = 30.48 cm.

Measurements and Uncertainties

Uncertainty in Measurement

All measurements have an associated uncertainty, which reflects the limitations of the measuring instrument and the estimation process.

• Measurement Result: Expressed as units, where is the best estimate and is the uncertainty.

• Significant Figures: The uncertainty is quoted to one significant figure, and the least significant figure in the measurement should match the uncertainty.

• Example: Measuring the length of a rectangle: cm, cm.

Propagation of Uncertainties

When calculating derived quantities from measured values, uncertainties must be propagated according to specific rules.

• Addition/Subtraction: for or

• Multiplication/Division: for or

• Powers: for

• Example: Calculating the perimeter of a rectangle: Best estimate: Uncertainty: Final result:

Calculating Area and Density with Uncertainties

When calculating area or density, uncertainties in the measurements must be included in the final result.

• Area of Rectangle:

  • Best estimate:

  • Uncertainty:

  • Final result:

• Density of a Cylinder:

  • For , :

  • Best estimate:

  • Uncertainty:

  • Final result:

Significant Figures, Precision, and Accuracy

Significant figures indicate the precision of a measurement, while accuracy refers to how close a measurement is to the true value.

• Significant Figures: The number of meaningful digits in a measurement.

• Precision: The degree to which repeated measurements yield the same result (smaller least significant figure = higher precision).

• Accuracy: How close a measured value is to the true value (more significant figures = higher accuracy, assuming no systematic error).

• Scientific Notation: Proper way to express numbers for clarity and to indicate significant figures (e.g., ).

Discovering the Physics: Graphs and Linearization

Visualizing Data with Graphs

Graphs are essential tools in physics for visualizing relationships between variables and discovering underlying physical laws.

• Types of Graphs: Linear, log-log, and semi-log graphs can reveal different types of relationships.

• Linearization: Transforming data (e.g., using logarithms) to produce a straight-line graph, which simplifies analysis and interpretation.

• Example: For a power law relationship , taking logarithms yields , which is linear in .

Additional info: These notes provide foundational concepts for later chapters, including motion, force, energy, and other core topics in college physics.