Engineering Solutions Mathematical Models Engineering Solutions n n

Engineering Solutions Mathematical Models

Engineering Solutions n n n 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 knowhow 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.

Engineering Solutions Engineers use a specific problem organization to document solutions to problems. Standard Problem Organization: n n 1. 2. 3. 4. 5. 6. 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

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

Engineering Solutions Problems: n 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 40 kg of mass is placed on the right end. n ? kg 12 meters 4 m 40 kg

Engineering Solutions Problems n 2. Given the basic quadratic equation ax 2 + bx + c = 0 and the coefficients a=2, b = -5, c = 1. n Find the discriminant = b 2 – 4 ac). n Provide a graph of this equation. n

Engineering Solutions Problems n 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? n Specify the dimensions that will result. n

Engineering Solutions Problem 4: n Convert scalar quantities to vector quantities. n

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

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

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

Engineering Solutions n n n Problem 5: 4. A weight of 100 kg 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/s 2 and b) 1. 63 m/s 2 (approximate value for the surface of the moon. ) Theory: F=ma 100 kg n Assumptions: neglect the mass of the rope.