Engineering

Scalars and Vectors

  • Scalars: Physical quantities with magnitude but no direction.

    • Examples: Mass, length, time, temperature.

  • Vectors: Physical quantities with both magnitude and direction.

    • Examples: Displacement, velocity, acceleration, force.

  • Vector Components:

    • Resultant vector ( R ) can be calculated using:

      • ( R_x = |E| \cos \theta )

      • ( R_y = |E| \sin \theta )

      • Magnitude of vector ( R = \sqrt{R_x^2 + R_y^2} )

      • Direction: ( \tan \phi = \frac{R_y}{R_x} )

      • Example: ( A = A_x i + A_y j ) where ( i, j ) are unit vectors.

Static Equilibrium and Moments

  • Static Equilibrium: A system in static equilibrium has:

    • The sum of all forces acting on it equals zero ( \sum F = 0 )

    • The sum of all moments (torques) about any point is zero ( \sum M = 0 )

  • Force:

    • A vector quantity defined by magnitude and direction.

    • Measured in newtons (N).

    • Components in 2D: Resolved into X and Y components.

  • Moment (Torque):

    • The turning effect of a force about a point.

    • Formula: ( M = F \cdot d )

      • ( F ): Force, ( d ): Perpendicular distance from the pivot to the line of action of the force.

    • Measured in newton-meters (N·m).

    • Moments are directionally defined: Clockwise (CW) = negative; Counterclockwise (CCW) = positive.

  • Moment: A force applied at a distance will affect equilibrium.

    • Equations: ( \sum M = 0 )

    • Example: Given weight scenarios of Frank (50 lbs) and Sally, or Triple Beam Balance example to solve for variables.

  1. Calculate the forces acting on a ring in equilibrium: Given forces T_A and T_B.

  2. Determine the moment caused by a 5kN force at a distance about point O.

Statistics Frequency Distribution

  • Frequency Distribution: Systematic collection of data representing occurrences of values.

    • Graphical representations: Data curves, bar graphs, histograms, etc.

  • Steps to Create Frequency Distribution:

    1. Select classes for data grouping.

    2. Distribute data into classes.

    3. Count items in each class.

  • Mean/Average: Measure of central tendency, calculated as:

    • ( M = \frac{\sum X}{N} )

  • Correlation Coefficient:

    • Quantifies the strength of the relationship between two variables.

    • Examples for calculating correlation from two datasets (e.g., ice cream sales vs. temperature).

Working with Data Points

  1. Find sample means for datasets.

  2. Calculate the distance of each data point from the mean.

  3. Complete the top part of the correlation coefficient equation:

  • Step calculations to determine final correlation value.

Graphing and Function Types

  • Linear Function:

    • Formula: ( y = mx + b )

      • ( m ): Slope, ( b ): y-intercept.

  • Exponential Function:

    • Formula: ( y = b e^{mx} )

  • Power Function:

    • Formula: ( y = b x^h )

Electricity and Circuits

  • Electricity: Energy used in conductive circuits.

  • Electrical Circuit: Facilitates transmission of electric charge.

    • Essential components:

      • Power source, resistors or loads, and wires.

  • Ohm's Law:

    • ( V = IR ) (Voltage = Current x Resistance).

  • Resistors:

    • Series: Add resistances.

      • ( R_{eq} = R_1 + R_2 + R_3 )

    • Parallel: Multiple paths for current.

      • ( \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} )

Professional Ethics

  • Professional Ethics: Standards defined by the community for expected behavior.

  • NSPE Code of Ethics:

    1. Prioritize public safety and welfare.

    2. Perform services only in areas of competence.

    3. Issue truthful public statements.

    4. Act as faithful agents for clients/employers.

    5. Avoid deceptive acts.

    6. Conduct responsibly and ethically.

Dimensions, Units, and Conversions

  • Independent of Units: Base units are fundamental and cannot be broken down.

    • Examples of SI Base Units:

      • Length: meter (m)

      • Mass: kilogram (kg)

      • Time: second (s)

      • Electric Current: ampere (A)

  • Derived Units: Created by combining base units.

Significant Figures

  • Represent precision in measurements.

    • Preceding zeros are not significant (e.g., 0.0415).

    • Trailing zeros are significant if after decimal (e.g., 3300.0).

Decision Matrix Steps

  1. Identify the problem.

  2. List desired attributes.

  3. Rate/score attributes.

  4. Calculate weighted score.

  5. Score candidate solutions based on attributes.