Physics for Scientists and Engineers

Study Notes

Standards must be readily accessible, measurable reliably, yield consistent results, and remain unchanged over time.

Length: Defined as the distance between two points.
- Meter: Distance traveled by light in a vacuum in 1/299,792,458 seconds.
Mass: Represents the quantity of matter in an object.
- Kilogram: Mass of a specific platinum-iridium alloy cylinder at the International Bureau of Weights and Measures, Sèvres, France.
Time: The interval for measuring duration.
- Second: Defined as 9,192,631,770 times the period of vibration of cesium-133 atom radiation.

Density is calculated using the formula: ρ = m/V, where ρ represents density, m is mass, and V is volume.

A model simplifies the real problem to allow easier analysis and solution.
- Conditions for Particle Model:
  - Size is negligible in motion analysis.
  - Internal processes in an object do not affect motion analysis.

Finding the Height of a Tree:
- Position: 50.0 m from the tree, angle of elevation: 25.0°.
- Height calculated using: h = 50.0 m * tan(25.0°) = 23.3 m.

Geometric Model, Simplification Model, Analysis Model, Structural Model.
A representation is a specific method to present information related to the problem.

Used to relate physical quantities and determine the correct units for quantities.
- Example: If the expression x = at, where x is displacement, a is acceleration, and t is time, it must satisfy dimensional consistency.

Dimensional analysis does not provide numerical values for constants of proportionality; it only confirms dimensional correctness.

v = at: Speed (v) equals acceleration (a) multiplied by time (t) confirmed dimensionally correct (L/T).
Power Law Equation: Acceleration (a) is proportional to certain powers of radius (r) and speed (v): a = kr^n * v^m.