2.1 Solving Simple Equations

This Section pertains to taking an equation and “solving” for a variable in that equation.

This process can be VERY easy or more complicated.

Solve for x: Solve for s if :

When working the type of problems addressed in this section, you will be expected to:1) Start by writing down the correct formula.2) Substituting in the correct values (no calculation).3) Solve in a top down manner.4) Always attach units (if applicable) to the final answer.

Example 1:

What is involved in determining the size of a car’s engine?

An engine’s volume or Displacement (D) is D = engine displacement measured in cubic centimetersb = bore (diameter of the cylinder) measured in centimeterss = stroke (distance that the piston travels) measured in centimetersc = number of cylinders.

Find the stroke necessary for a 6-cylinder enginewith a 4.8-cm bore with 542 cubic centimeters ofdisplacement, rounded to one decimal place.

You really need to know the “order of operations” well, because we will be using them

in reverse. Following is a demonstration of each.

Example 2:

What determines how much a beam will flex and bend when it is used in a house or a bridge?

Answer: Moment of Inertia.

Note: Deflection is simply a measurement of the amount of bend in a beam.

The point load deflection (D) of a beam is .

D = deflection is measured in inchesP = weight on the beam measured in poundsL = length of the beam measured in inchesE = elasticity of the beam measured in pounds per square inch (PSI)I = moment of inertia of the beam measured in inches4

Find the moment of inertia (I) for a beam rounded to the nearest whole number:D = 1 inP = 3250 lbs.L = 156 inE = 1,950,000 psi

Example 3:

The voltage drop in an electrical wire is

AWG R16 4.88414 3.07212 1.93210 1.2158 .7646 .4814 .302

.

V = voltage drop measured in voltsL = length of the wire measured in feetI = current measured in amps R = resistance in the wire measured in ohms

Use the table to determine the length of electric cord that will have a voltage drop of 9 volts in a #12 AWG electrical cord attached to a heater drawing 18 amps of current. Round the answer to the nearest foot.

Example 4:

A conical pile of gravel is to be hauled away in a dump truck bed that measures 4’ x 7’ x 10’.

Calculate how many loads it will take if the bed is full to the top and how deep the last load will be.

The following two pieces of information were taken from the appendix. We are interested in volume (the last column).

Homework: Problems 2, 3, 7, 8, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21 (15 problems).

Section 2.1:1. 36 in2. 232 gallons3. E = .54. 24 holes5. 6,800 gallons6. 978 miles7. C = 35.6o Celsius8. 31 hours9. 16.64 mm

10. 2 1”8

11. 331 horsepower12. gear ratio = 2.513. length = 34.6 feet14. 4.6 in15. 2,674 lbs16. 6,156 RPM’s17. 2,634 RPM’s18. 123.9%19. 7,244 RPM’s20. .000072 farads21. L = .017 H