1.5 Orderof Operations

Mathematics requires “rules of the road;” without them we would all be getting difference answers. It’s called Order of Operations.

PEMDAS?GEMDAS?

Until you have mastered this, I strongly recommend that you NOT bend the rules. You need to be able to do problems like these by hand and correctly enter them in the calculator.

1)(-10)2)(-3)3) (3)

4) (-16)5)(-1)6) (30)

7)(-16)8) (24)9) (18)

10) (2)11)(59)12) (-46)

13) (4)14) (-16)15) (-10)

15) (-31)16) (-36)17) (82)

18) (29)19)(0)20) (25)

21) (2)22) (-74)23) (-18)

24) (0)25. (-2)

Example 1

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

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 measured in inches

P = weight on the beam measured in pounds

L = length of the beam measured in inches

E = elasticity of the beam measured in pounds per square inch (PSI)

I = moment of inertia of the beam measured in inches4

(Moment of inertia - The beams ability to resist bending. The larger the Moment of Inertia the less the beam will bend.)

Find the deflection of a beam rounded to one decimal place if:

P = 3960 lbs.

L = 184 inNote: Your work on tests and homework must be as demonstrated in class.

E = 1,700,000 psi

I = 432 in4

Example 2

What determines the length of a rafter in a house?

The length of a rafter (R) can be calculated using the formula: .

R = length of the rafter measured in inches

W = width of the building measured in inches

S = slope of the roof.

Notice how R is show in the figure to the right.

Find the length of a rafter for a building that is 268” wide and has a slope of 5/12, rounded to the nearest 16th of an inch.

Example 3

Wha

t 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 centimeters

b = bore (diameter of the cylinder) measured in centimeters

s = stroke (distance that the piston travels) measured in centimeters

c = number of cylinders.

Find the displacement of an 8-cylinder engine with a 3.4-cm bore and a 5.2-cm stroke, rounded to one decimal place.

Why is pi in the equation?

Homework: You are assigned all of the even numbered problems from 1-30, except for #28 (do not do #28) (14 problems). Extra Credit for the two Challenge Problems (2 points each). The first line in your problem should be the formula, the second line pure substitution. Any work you show should be in a top down manner (each line underneath the preceding line). Be careful with your units and don’t forget to include them on your final answer.

Section 1.5:

  1. 3.6 yd3
  1. 7.75 yd3
  1. 128.3 cm
  1. 6.2 CFM
  1. 1,918.1
  1. 648 watts
  1. 2,814.9 in3
  1. 695.2 in2
  1. 800.3 in4
  1. 75 MPH
  1. 22.105 ohms
  1. #12 = 17.6 volts

#10 = 11.1 volts

  1. 1.2 in
  1. 1.9 in
  1. 24
  1. 26.7 in
  1. 180
  1. 280.7 PSI
  1. 4.4 g’s
  1. 216.7 cm3
  1. 34 in
  1. 24,000 watts or 24 Kilowatts
  1. 25 squares
  1. 255 horsepower
  1. 280.7 ohms
  1. 162 MPH
  1. 5.9 kΩ
  1. 232 Ω
  1. 96.8o F
  1. V1 = 3V

V2 = 17V

  1. I1 = .07A

I2 = .04A

  1. 74.7 in4
  1. .284 in