Engineering Solutions Mathematical Models

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Engineering SolutionsMathematical Models
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Engineering Solutions

• Engineers are problem solvers mastering art and
  science.
• Science is the knowledge and principles of math,
  chemistry, physics, mechanics, and other
  technical subjects.
• Art is proper judgment, common sense, and
  know-how that must be used to reduce a real-life
  problem to such a form that science can be
  applied to its solution.
• Decisions must be substantiated by data.
• Engineers are excellent at generating data to
  verify and support design decisions.

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Engineering Solutions

• Engineers use a specific problem organization to
  document solutions to problems.
• Standard Problem Organization
• Problem statement restate the problem trying to
  be solved.
• Diagram Sketch a diagram showing the physical
  setup.
• Theory statement State the scientific theory or
  mathematical equation that will be used in the
  analysis.
• Assumptions Explicitly list in sufficient detail
  any and all pertinent assumptions that must be
  made to obtain a solution. (i.e., givens in
  physical science such as acceleration due to
  gravity, etc.)
• Solution steps Math equation, show all work,
  variables, units. May include a graph to
  extrapolate relationships in variables (i.e.,
  what happens to momentum as mass increases.)
  Useful in making predicitons.
• Verify and identify results

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Engineering Solutions

• Open Engineering Solutions Layout in Excel
• This is the format in which mathematical
  solutions should be presented

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Engineering Solutions

• Problems
• 1. Calculate the mass necessary to balance a 12
  meter see-saw type beam when the fulcrum is
  placed 4 meters from the left end and 40kg of
  mass is placed on the right end.

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Engineering Solutions

• Problems
• 2. Given the basic quadratic equation ax2 bx
  c 0 and the coefficients a2, b -5, c 1.
• Find the discriminant b2 4ac).
• Provide a graph of this equation.

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Engineering Solutions

• Problems
• 3. A tank is to be constructed to hold 500,000
  gallons when filled. The shape is to be a
  cylindrical with a flat top. Costs to construct
  the cylindrical portion will be 300/ft in
  height. The radius of the structure will be 20
  feet. What will be the cost of the structure?
• Specify the dimensions that will result.

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Engineering Solutions

• Problem 4
• Convert scalar quantities to vector quantities.

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Engineering Solutions

• Units of Measure
• Base Units SI and EES (English Eng. System)
• Quantity SI EES
• Length meter foot
• Mass kilogram lb.
• Time second second
• Electric current ampere
• Thermd temp Kelvin Fahrenheit
• Amount of Substance mole
• Luminous intensity candela

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Engineering Solutions

• Units of Measure
• Supplemental Units SI and EES (English Eng.
  System)
• Quantity SI EES
• Plane Angle radian
• Solid Angle steradian

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Engineering Solutions

• Units of Measure
• Derived Units and Common Derived Units
• Unit Conversions
• Several should be committed to memory.
• Fahrenheit to Celsius
• Millimeters to inches
• Kilograms to pounds
• Gallons to liters
• Online Conversion Sources

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Engineering Solutions

• Problem 5
• 4. A weight of 100kg is suspended by a rope that
  is attached to a winch and loops around a pulley.
  Calculate the tension on the rope in newtons when
  the mass is lifted vertically at constant
  velocity and the local gravitational acceleration
  is a) 9.807 m/s2 and b) 1.63m/s2 (approximate
  value for the surface of the moon.)
• Theory Fma
• Assumptions neglect the mass of the rope.

100kg