Engineering g Problem Solving Process

Transcription

1 Engineering g Problem Solving Process GIVEN State briefly and concisely (in your own words) the information given. FIND State the information that you have to find. DIAGRAM A drawing showing the physical situation with all quantities involved should be included. BASIC LAWS Give appropriate mathematical formulation of the basic laws that you consider necessary to solve the problem. ASSUMPTIONS List the simplifying assumptions that you feel are appropriate in the problem. ANALYSIS Carry through the analysis to the point where it is appropriate to substitute numerical values. NUMBERS Substitute numerical values (using a consistent set of units) to obtain a numerical answer. The significant figures in the answer should be consistent with the given data. CHECK Check the answer and the assumptions made in the solution to make sure they are reasonable. Estimate the answer. Check the units, if appropriate. LABEL Label the answer (e.g., underline it or enclose it in a bo). Engineering Discovery Fall 009 K. Craig 1

2 IMPORTANT: This solution procedure is required. Include name and section number on each page. Indicate problem title / number at the top of each page. Staple pages together. Always use engineering computation paper. Always start a problem solution on a new page. Always use pencil. Always use a straight edge and a compass. Never write on the back of a page. Handwriting and diagrams must be legible and work should not be crowded. Keep all assigned work in a binder for reference when studying for eams. Professional Presentation! Take Pride in Your Work! Engineering Discovery Fall 009 K. Craig

3 The Three Main Challenges for an Automotive Engineer are: Economy, Emissions, and Performance Engineering Discovery Fall 009 K. Craig 3

4 Electromagnet Infrared LED Phototransistor ( ) f,i i C = Levitated Ball Magnetic Levitation System Electromagnetic Valve Actuator For a Camless Automotive ti Engine Engineering Discovery Fall 009 K. Craig 4

5 Engineering Discovery Fall 009 K. Craig 5

6 Engineering Problem A steel ball of mass m is connected to ground by a linear spring with a spring constant K and an unstretched position given by 0. An electromagnet eerts a force f e on the ball. This attractive force is proportional to the square of the current in the electromagnet and inversely proportional to the square of the distance between the ball and the electromagnet. i fe (,i) = C For a constant current in the electromagnet, the ball will come to an equilibrium i position. Find the equilibrium position or positions, and assess the stability of each one. Engineering Discovery Fall 009 K. Craig 6

7 Problem Solution Given: Ball has mass m. Ball is connected to ground by a linear spring. Spring has constant K and an unstretched position given by 0. An electromagnet eerts a force f e on the ball. This force is proportional to the square of the current in the electromagnet and inversely proportional to the square of the distance between the ball and the electromagnet. Find: For the ball in static equilibrium, find the position(s) of the ball, i.e., the distance(s) from the electromagnet, and comment on the stability of the system(s) in static equilibrium. Engineering Discovery Fall 009 K. Craig 7

8 Diagram: i f,i C e ( ) = Engineering Discovery Fall 009 K. Craig 8

9 Basic Laws: Newton s nd Law of Motion Assumptions: F = F = ma Ball is magnetic. Gravity constant g = 9.81 m/s and is directed downwards. Spring is linear with a spring constant K (N/m). The electromagnetic force is proportional to the square of the current in the electromagnet and inversely proportional to the square of the distance between the ball and the electromagnet. Electromagnetic force does not change with time or temperature. ma Current in the electromagnet is constant i 0. Electromagnetic force proportionality constant C is known. There are no forces other than the forces in the direction. Engineering Discovery Fall 009 K. Craig 9

10 Analysis: F = 0 static equilibrium f + mg+ K( ) = 0 e 0 f = K( ) + mg e 0 i f (,i) e = C i fe (,i ) = C f g = mg ( ) f = K k 0 Free Body Diagram Engineering Discovery Fall 009 K. Craig 10

11 Numbers: SI Units Ci = 1 (assume for simplicity) m= 3.06 K = 5 = i = 0 + C K( ) mg = + Engineering Discovery Fall 009 K. Craig 11

12 Unstable Equilibrium K(0 ) + mg f e Stable Equilibrium Stability f = K( ) + mg e 0 UNSTABLE MARGINALLY STABLE STABLE Engineering Discovery Fall 009 K. Craig 1