Physics for Scientists and Engineers

Questions and Answers

Which standard of measurement must yield the same result?

Readily accessible

Possess some property that can be measured reliably

Not change with time

All of the above (correct)

What is the definition of 'Length' in physics?

Distance between two points in space

What is a meter defined as?

Distance traveled by light in vacuum during a time interval of 1/299,792,458 second

What is the mass of a kilogram defined as?

Mass of a specific platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures Signup and view all the answers

How is a second defined?

9,192,631,770 times the period of vibration of radiation from the cesium-133 atom Signup and view all the answers

In a machine shop, if two cams have the same mass, which can you infer?

Nothing can be determined. Signup and view all the answers

A model is a simplified substitute for the real problem.

True Signup and view all the answers

How is the height of a tree measured indirectly according to the example?

Using the tangent of the angle of elevation and the distance from the tree. Signup and view all the answers

What is the formula for calculating height using tangent?

h = (50.0 m) tan(25.0°) Signup and view all the answers

Dimensional analysis can give you the numerical value of constants of proportionality.

False Signup and view all the answers

What is the expression for speed in relation to acceleration and time?

v = at Signup and view all the answers

What does the variable 'a' represent in the expression v = at?

Acceleration Signup and view all the answers

If acceleration 'a' is proportional to some power of radius 'r' and some power of speed 'v', what is the form of the equation?

a = kr^n v^m Signup and view all the answers

Study Notes

Standards of Measurement

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

Measurement Units

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

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

Modeling in Physics

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.

Examples of Modeling

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.

Types of Models

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

Dimensions in Physics

Speed dimension: [v] = L/T; Area dimension: [A] = L².

Dimensional Analysis

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.

Quick Quiz Insights

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

Examples of Equations Analysis

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.