DC Theory, Lvl III Lesson 3: Working with Ratios and Proportion
The ratio of the speeds of pulleys is inversely proportional to the ratio of their diameters. The speed reduction required on a pulley and belt drive is 4 to 1. If the drive is 4 inches in diameter, what size would be required for the driven pulley?
16 Inches D^1/D^2=S^2/S^1 4/X=1/4 X=16
The weight of outlet boxes is proportional to the volume of boxes involved. If 400 boxes weigh 120 pounds, how much would 500 boxes weigh?
400/120 = 500/X 150 Pounds 400X=60,000 60,000/400=150 lbs.
If 50 feet of number 12 copper wire has a resistance of 1.2 ohms, what length of number 12 copper would have a resistance of 12 ohms?
500 Feet R^1/R^2=L^1/L^2 1.2/12=50/L^2 1.2L^2=600 600/1.2 L^2=500
Which of the two pulleys of Question 8 has the higher RPM?Question 8 stated: A certain belt drive has a 10-inch pulley driving a 4-inch pulley. a. 4" pulley b. 10" pulley
A. 4" Pulley
Which of the following is NOT one of the three rules that are to be applied when solving problems involving direct or inverse proportions? a. Solve by subtraction b. Solve by cross-multiplication c. Set up the proportion d. Substitute the values
A. Solve by subtraction
In a proportion, the ? of the equivalent fractions are always equal. a. fraction b. cross products c. direct proportion d. inverse proportion
B. Cross Products
? is/are two quantities related and dependent in such a way that as one increases or decreases the other varies the same way. a. A fraction b. Cross products c. Direct proportion d. Inverse proportion
C. Direct Proportion
In final form, how would a ratio of 3/2 be properly stated? I. 1.5 II. 2/3 III. 3 to 2 IV. 3:2
C. III and IV
What is the compression ratio for an engine if each cylinder has a maximum volume of 500 cubic centimeters and a minimum volume of 50 cubic centimeters? a. 1:1 b. 1:2 c. 5:1 d. 10:1
D. 10:1 500/50=10/1=10:1
A certain belt drive has a 10-inch pulley driving a 4-inch pulley. What is the ratio of the pulley diameter? a. 2.5:1 b. 2.5 to 1 c. 2.5/1 d. All of the above
D. All of the above
A number 10 AWG copper wire has a resistance of 0.9989 ohms per 1,000 feet and a cross sectional area of 10,380 CM. If the resistance of copper wire is inversely proportional to its cross-sectional area, what would be the resistance of 1,000 feet of Copper wire with a cross section of 5,178 CM? (Round the FINAL answer to four decimal places.)
D1/D2 = R2/R1 10380/5178 = R2/.9989 2.0024Ohm
An apprentice productively working a 40-hour week earns more wages and is worth considerably more to the local union and the industry than one who works only 30 hours per week. Consider two apprentices, A and B, working the same job at the same scale. Apprentice A works 40 hours and is paid $160.00 from which $4.80 is paid to the local union. Apprentice B only works 30 hours. How much will the local union receive in dues for the 30 hours work?
Da/Db = Ha/Hb 4.8/Db = 40/30 40Db=144.0 Db=3.60 $3.60 Dues
Direct proportion is two quantities related and dependent in such a way that as one increases the other decreases, and conversely, as one decreases the other increases. T/f
False
If the 10-inch pulley of Question 8 were turned at 1,000 RPM, what would be the speed of the 4-inch pulley?
RPM = 2500 10/4=X/1,000 4X=10,000 X=2,500 RPM
The rotational speed of a driven gear is inversely proportional to the number of teeth on a gear. You are replacing a gear having 200 teeth with one that has 50 teeth and turns 2,000 RPM. What was the RPM of the gear having 200 teeth?
RPM = 500 G^1/G^2=S^2/S^1 200/50=2,000/X 100,000=200X X=500 RPM
The following ratios are true for transformers. (T = number of turns)
Tp/Ts = Ep/Es 250/900 = 240V/Es =(240 x 900)/250 Es = 864V
The following ratios are true for transformers. (T = number of turns)
Tp/Ts = Is=Ip 250/900 = 6A/I =(6 x 900)/250= Ip=21.6A
By definition, a ratio initially takes on the form of a fraction.
True
An apprentice productively working a 40-hour week earns more wages and is worth considerably more to the local union and the industry than one who works only 30 hours per week. Consider two apprentices, A and B, working the same job at the same scale. Apprentice A works 40 hours and is paid $160.00 from which $4.80 is paid to the local union. Apprentice B only works 30 hours. How much money does Apprentice B get paid prior to any deductions?
Wa/Wb = Ha/Hb 160/Wb = 40/30 40Wb=4,800 Wb=120 $120