A 4 ¼-in diameter carbon steel shaft is machined on a lathe with HSS tool. What is the RPM?

CS = RPM * π * (D) / 12
CS = Cutting speed (in feet per minute)
D = Diameter of the shaft (in inches)
cutting speed for carbon steel using HSS tools = around 100 feet per minute
RPM= 100×12/ π×4.25 = 94 RPM

- A four part bridle sling has a total lifting capacity of 90 000lb and is hoisting at a 45deg angle.
What is the working strength of this configuration?
90000/2 * sin(45)= 45000*0.85=31815lb

- What is the maximum load in pounds that can be moved when set to 1500psi, and a cylinder
bore of 3.00”?
Force=1500× 𝜋𝑟 =1500×(𝜋 1.5 ) = 10,600 lbs

A battery consisting of 9 lead acid cells is arranged in 3 parallel banks of 3. Each cell is rated at
2V and 20Ah. What is the total ampere hour rating of the battery?
(Parallel = ampere, series= volt )
- 60 Ah

Which of the following is the net blank cut size for a 90° 14-in. diameter seven-piece elbow,
used in a material handling system?
π×14×(360 / 90)×7 = 48.44 in. × 44 in.

Which of the following is the pitch of a ¾ - 9 UNC screw thread?

P= 1 / Number of Threads Per Inch = 1 / 9 = 0.1111

How long of a strap is required to wrap around a 24" drum having a 1.5'' overlap?
π×24+1.5 ≈76.86in

- Calculate the speed that a cylinder will retract lift has a 6" bore? A l" rod and a fluid supply of
15 gpm?
Retraction Speed= 231* Flow Rate / Area of the Cylinder = (231*15) / π * (9 - 0.25)
= 126.4 in/min

If a roller chain has a 16T driver sprocket, a 24T driven sprocket, and a centre to centre distance
(N+n) /2 + (N-n) / C + 2C
C= c / p = 42/0.75
if the cross sectional area of a pipe increases from 3 sq in to 12 sq in through a transition piece,
then the l.D. has increased by?
100%

Calculate the speed of a chain that has an 8" drive pulley, a 12" driven pulley, a centre to centre
distance of 36" and a drive of 350 rpm.
V=π * N * (D drive+D driven) / 12
= Speed (ft/min)= π * 350 * (8+12) / 12

if you have a 24v dc power supply and a 5 amp fuse in the line, how much power can the circuit
draw without blowing a fuse?
Ohm's Law : V=I×R
The power : P=V×I =120 WP=120W

What is the cutting speed in F .P .M. for a high speed steel drill of 5/16" diameter, cutting into a
2" thick block of stainless steel?
Cutting Speed (FPM)= RPM*π*(Drill Diameter / 12)
stainless steel, the recommended cutting speed for high-speed steel drills is typically around 100
FPM

A ½" diameter drill is rotating in a drilling MIC@ 400 rpm. What is the cutting speed in ft. per
min.?
Cutting Speed (FPM)= RPM*π*(Drill Diameter / 12) = π*(1/ 24 ft)*400rpm

A shaft is 30 ft. long. How much expansion will take place with a temperature increase of 20
deg. F and a co-efficient of expansion of 0.0000032?
Expansion = Original Length × Temperature Change × Coefficient of Linear Expansion
Expansion=30ft×20°F×0.0000032 =0.00192ft

What force is needed for a cylinder to punch a hole ½ in. dia. through a sheet of material 1/8 in.
thick with a material sheer strength of 60,000 psi?
Shear Force=Shear Strength × Shear Area
Shear Area=π*d*t =3.14159×0.5×0.125≈ 0.19635 in^2
Shear Force=Shear Strength × Shear Area =60,000 psi × 0.19635 in^2≈11,781 lbs

A pump is out of balance and has a vibration of 2.mm. @ 32 hz? This is the same as?
cpm=Hz×60
Vibration in mm = 2 mm @ 32 Hz.
Convert 2 mm to inches: 2mm * 0.03937 ≈ 0.07874in (1 inch = 25.4 mm)
Convert frequency from Hz to cpm: 32 Hz×60=1920 cpm
0.078 in. movement @ 1,920 cpm
Calculate the amount of material required to make a steel tank 13 ft. diameter, 19 ft. long and
closed at one end.
Lateral Surface Area (cylinder): Alateral=2πrh =2π(6.5 ft)(19 ft)
Area of Closed End (half of a circle, since one end is closed): π𝑟 = π(6.5 ft) ^2
Total Surface Area: =Alateral + Aend

A wire rope has an ultimate Tensile Strength of 8,000 lbs. What is its approximate diameter
likely to be?
4 ton =D*D*8=1 1/2

A load is being lifted with two 3.7-m (12-ft.) slings. Using the working angle of 60 at the apex.
What is the distance between the lift points?

METRIC IMPERIAL
3.7m 12 ft.

How much torque would you need to set the torque where to tighten bolt to 200 in lbs if the
hands are 18 inch long and wrench has a 6-inch extension?
T=(TA*L) / (L+A) = (200*18) / (18+6)= 150 Ibs

Steel plates are 1.27 cm x 1.22 m x 2.44 m (1/2 in. x 4 ft. x 8 ft.). What is the weight of 35
plates?
METRIC
C. 10 370 kg

Length = 1.27 cm = 0.0127 m

Volume of one plate = Length x Width x Height = 0.0127 m * 1.22 m * 2.44 m = 0.0371 cubic
meters
Total volume = Volume of one plate * 35 = 0.0371 cubic meters/plate * 35 plates = 1.2985 cubic
meters
The density of steel varies around 7850 kg/m³. (The density of steel is approximately 490 lbs/ft³)
Weight = Volume * Density = 1.2985 cubic meters* 7850 kg/m³ = 10196.725 kg
What is the weight of a 4 in. diameter steel shaft that is 6 ft. long?

D=4 in=4/12 ft ≈ 0.3333 ft , r = 0.1667

V= π(r) ^ 2 * L ≈ π * (0.1667) ^ 2 * 6 ≈ 0.5236ft^3
Weight= V × Density ≈ 0.5236 * 490lbs/ft^3 ≈ 256.6lbs

Using the average weight of 500 lbs per cubic foot for steel, Calculate the approximate weight of
a plate you want to lift that is 6' long, 5'8" wide, and 1 ¼" thick.

Length: 6 ft
Width: 5 ft 8 in = 5+8/12=5.6667 ft
Thickness: 1 ¼ in = 1.25 in=1.25/12 ft= 0.1042 ft
V≈ 6*5.6667*0.1042≈3.537ft^3
Weight=3.537ft^3 * 500lbs/ft^3≈1768.5 lbs

You are using an 18" level and the machine is 6' long. After placing the level on the machine,
you must shim the level .05" to make the bubble center on the level. What is the shim
requirement for the machine to be level?
6' *12=72" , 72" / 18" = 4
0.05"*4 = 0.200"

When the downward force at C2 is 100 lb and D2 = 2.5 inches, the upward force at C1 will
be ________lb if D1 = 4 inches.

x/12.56 sq in = 100 lbs/7.85 sq in

x = (100lbs/7.85 sq in)12.56
x = 160 lbsc

Determine the taper per foot of a 9" dia. shaft tapered down to 3" dia. over an 8" span.
(9"-3") / 8" = 6"/8" = 0.75" * 12" = 9 ft

What is the cutting speed in ft/min for ½" drill at 600 rpm?
RPM = Cutting speed (CS) * 4 / Diameter of cutter (D)
600 RPM = (CS*4) / 0.5
CS = (600 RPM * 0.5) / 4 = 75

A steel plate measuring 48" x 96" x ½" weighs roughly how much?
48" * 96" * 0.5" x 1/12*1/12*12 *490 = 663.552 lbs
Calculate the volume of a tank with inside dimensions of 32" x 45" x 21"?
32" x 45" x 21" = 2.666...x 3.75 x 1.75 = 17.4999

Calculate the accurate belt length for the following: Large diameter pulley is 11.25" and the
small diameter pulley is 6.125". Shaft centers are 17.5" apart.
L=2C+1.57(D1+d2)+[(D1-d2)²/4C]
L=2(17.5)+1.57(11.25+6.125)+[(11.25-6.125)²/4(17.5)]
L=35+27.27875+(26.265625/70)
L=62.65

A belt is wrapped around a 6.25" pulley and has 220 degrees of contact. How much of the belt is
contacting the pulley? (Use 3.14159 for pi)
Circumference = 6.25 x 3.14 = 19.634 / 360º
= 0.05454"/º * 220º = 11.999"

If you have a shaft with a diameter of 3.125", and it tapers down to 1.250" over a length of
7.525", what is the taper per foot?
3.125" - 1.250" = 1.875" difference

Taper per inch = Change in Diameter / Length =1.875 in / 7.525 in ≈ 0.2494 in/in
Taper per foot = Taper per inch×12 ≈ 0.2494 in/in × 12≈2.9928 in

You have a 46 cubic inch container holding 23 PSI. You transfer the air into a 17 cubic inch
container. What is the new pressure?
P1/P2 = V2/V1 , 23/ P2=17/46 = 62.23 PSI

With a pressure of 950 psi and a load of 7.5 tons, what must the bore of the cylinder be if we add
a 10% safety factor?

F=PA
F = 7.5 Tons x 2200 = 16500 lbs
16500x1.1 = 18150lbs
P = 950psi

A = 18150lbs/950 psi
A = 19.105 inches squared

A = d(squared) x 0.7854
19.105/0.7854 = d (squared)
24.3255 = d (squared)
d = 4.93" round up
d = 5"

Calculate the retract speed of a cylinder with a 2.5" bore, and a rod diameter of 1", with a supply
of 15gpm.

Speed = Flow rate / Area

Speed = 15 gpm * 231 / (π(1.25) ^2) - (π(0.5) ^2)
Speed = (3465 in/min) / 4.12 in sq
Speed = 841 in/min

A cylinder of gas under a pressure of 1,800 psig at 70 °F heats up to a temperature of 130 °F.
What is the new pressure within the cylinder? (Charles Law questions)

P1/P2 = T1/T2
First convert psig to psia = 1,800 + 14.7 = 1814.7
Convert F to Rankine = 70 + 460 = 530
= 130 + 460 = 590
1,814.7/ n = 530/590
n = 2020.138 psia

What is the formula for the area of a cylinder?

- Area = 2 πr*h + 2 πr^2

A tank has following measurements. Find the capacity of the tank in imperial gallons.
Length: 45 inches
width: 20 inches
height: 55 inches

Volume = l x w x h
Volume = 45” x 20” x 55”
Volume = 49,500 cubic inches
Convert cubic inches to imperial gallons divide by 277
49, 500 / 277 = 178.7 imperial gallons

An angle of 27 degrees is required. Using a 5" sine bar, the gauge block build up is:
Gauge Block Height = 5inches × sin (27) = 5 ×0.4540 ≈ 2.2700 inches

A 5" sine bar has a gauge block build-up of 2.1919". What angle is obtained?
sin(θ)=Length of sine bar / Height of gauge blocks = 2.1919 / 5 = 0.43838 ,
θ = arc sin (0.43838) ≈ 25.8 = 26 degrees

When checking vertical angular alignment the gap size difference is .018” the distance between
the hold down bolts on the side of the motor is 6” and the coupling diameter is 4”. By much must
the motor be shimmed?
.027 “(bolts/coupling) × gap

Calculate the reduction ratio of the following gear train. {Gear A;;; 24; Gear B ;;; 120; Gear C;;;
18; Gear D = 72)

Reduction Ratio = Number of teeth on driven gears / Number of teeth on driving gears
Ratio A to B=120 / 24=5,
Ratio C to D=72 / 18=4,
Overall Reduction Ratio = 5×4=20

The inner gear in the illustration has 45 teeth. The large gear has 75 teeth. The small gear is
rotating at 300 R.P.M. What is the speed of the large gear.
(45*300) / 75 = 180 rpm

The gears in the illustration have the following number of teeth: A-20 teeth, C-65 teeth, D-90
teeth, E-24 teeth, B-68 teeth. Gear A is rotating at 6 R.P.M., At what R.P.M is gear B
rotating?

RPM1×Teeth1=RPM2×Teeth2 = RPMB=RPMA× Teeth A / Teeth B, 6×20/ 68 = 1.76

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