Transcript Math design template - DigitalElectronics

POE FINAL EXAM REVIEW
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Spool-White
Fall 2013
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STATICS
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1. A see-saw at the park is in static equilibrium with two
children. The child on the left provides 35lbs of
resistance force and the child on the right provides 70lb
effort force. The lever’s effort force (child on the right) is
located 4 ft from the fulcrum.
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1. What is the actual mechanical advantage of the
system?
2. Using static equilibrium calculations, calculate the
length from the fulcrum to the resistance force.
STATICS
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2. An industrial water shutoff valve is designed to operate
with 14 lb of effort force. The valve will encounter 144 lb
of resistance force applied to a 3 ½ in. diameter axle.
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1. What is the required actual mechanical advantage of
the system?
2. What is the required wheel diameter to overcome the
resistance force?
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STATICS
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3. A worker on a zip line crew lifts participants weighing
approximately 240 lb several times during a day from the
ground 42 feet below. A block and tackle system with 30
lb of effort force is designed to lift the materials.
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1. What is the required actual mechanical advantage?
2. How many supporting strands will be needed in the
pulley system?
STATICS
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4. A civil engineer must design a skateboard ramp for a new
skate park. The height from the ground to the top of the
drop in is 12 ft. For safety reasons, the slope must be 1:6
or less.
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1. Using the safety requirements, what is the allowable
minimum length of the ramp base?
2. Using the known height and calculated base length,
what is the length of the slope of the ramp?
STATICS
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5. A 7/16 nut driver with a 6 inch diameter handle is used to
install a ¼ 18 UNC bolt into a robotic arm.
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1. Determine the circumference where the effort is
applied.
2. Determine the pitch of the screw.
3. What is the mechanical advantage gained in the
system?
4. How much force can be overcome if 12 lb of force is
exerted?
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STATICS
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6. A simple gear train is composed of three gears. Gear A is
the driver and has 22 teeth, gear B has 15 teeth, and gear
C has 84 teeth.
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1. If the output is at C, what is the gear ratio?
2. If gear A rotates at 60 rpm, how fast is gear C
rotating?
3. If the output of torque at gear C is 125 ft·lb, what is
the input torque at gear A?
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STATICS
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7. Three students set up a mechanical winch with
FischerTechniks parts and lift a 225 g weight 25 cm in 8
seconds. The students use a multimeter to measure 8.0
volts in the system and the winch needs 165mA to lift the
weight.
1. How many Newtons did it take to lift the weight?
2. How many meters did the weight travel?
3. How much work (J) was done by the system?
4. Calculate the output power of the system.
5. Calculate the input power of the system.
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THERMODYNAMICS
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8. A 3kg piece of aluminum metal at 112°C is placed in 6
liters (=6 kg) of water at 22°C. The specific heat of water
is 4148 J/kg°C and the specific heat of aluminum is 900
J/kg°C. Determine the final temperature (Tf).
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List all known values.
List all unknown values.
Select equations.
Apply known values.
Solve.
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THERMODYNAMICS
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9. A 3/16 in. thick acrylic testing box with dimensions of 12
in. x 6 in. is covered with an unknown ¾ in. insulation
material. Determine the thermal conductivity for the
insulating material if a 65W bulb is used to heat the box.
The bulb maintains the inside temperature at 32ºC higher
than the outside temperature. (1in = 0.0254m)
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List all known values.
List all unknown values.
Select equations.
Apply known values.
Solve.
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BEAM ANALYSIS
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10. Calculate
cross-sectional
area, Moment of Inertia, and
beam deflection, given a load of 265 lbf, Modulus of
Elasticity of 1,700,000 psi, and a span of 12 ft.
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1. Determine the cross-sectional area for this orientation
(1.5 x 5.75) (in.2)
2. Determine the Moment of Inertia (in.4)
3. Determine the Beam Deflection (in.)
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TRUSSES
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11. Using the equilibrium formula about point E, calculate
the reaction force at joints E and D. Note: Joint E is a pin
and Joint D is a roller. Clue: Calculate reaction force at
roller first, followed by reaction forces at pin.
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TRUSSES
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12. Using the equilibrium formula about point E, calculate
the reaction force at joints E and D. Note: Joint E is a pin
and Joint D is a roller. Clue: Calculate reaction force at
roller first, followed by reaction forces at pin.
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1200 lbf
45
150 lbf
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750 lbf
STRESS/STRAIN
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13. A 2.5 in. by 5 in. rectangular steel bar is used as a
diagonal tension member in a bridge truss. The diagonal
member is 30 ft long, and its modulus of elasticity is
30,000,000 psi. If the strain in the diagonal member is
measured as 0.0015, determine:
1. The axial stress
2. The tension force in the bar
3. The elongation of the member
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STRESS/STRAIN
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14. The center of a rod must be machined on a lathe to a
smaller diameter for use as a specimen in a tension test.
The rod material is expected to break at a normal stress of
65,800 psi. If the tension testing machine can apply no
more than 850lb of force to the specimen, what is the
maximum rod diameter that should be used for the
specimen?
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FLUID POWER
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15. A pneumatic system is producing 215 lb/in.2 of gauge
pressure. A cylinder is needed to press an adhesive label
onto a product. It has been determined that 16 lb of force
is optimal to complete this task.
1. What is the required area of the pneumatic cylinder?
2. What is the required diameter of the pneumatic
cylinder?
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FLUID POWER
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16. A hydraulic lift system utilizes (four) 3 in. diameter
cylinders. Workers must determine how much the system
is capable of lifting before deciding how much weight can
be lifted safely. The system runs at a gauge pressure of
3150 lb/in.2.
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1. What is the area of each piston?
2. How much is each piston capable of lifting?
3. How much is the system capable of lifting?
FLUID POWER
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17. The gauge pressure of a pneumatic cylinder reads 61
lb/in.2 when the volume is 12 in.3. The cylinder is
compressed until the gauge reads 12 lb/in.2. Assume
standard atmospheric pressure (14.7 psi).
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1. What is the absolute pressure before and after the
cylinder gas is compressed?
2. What is the volume in the cylinder after the gas is
compressed?
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FLUID POWER
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18. The air temperature in a 55 in.3 container with a free
sliding piston is initially measured at 62 °F. The
temperature is raised to 132°F.
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1. What are the absolute temperature readings initially
and after the temperature is raised?
2. What is the new volume of the container?
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FLUID POWER
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19. A 86 ft3 compressor tank
container has a gauge pressure
of 130 lb/in.2 and a temperature of 89 °F. The temperature
after some time decreases to 44 °F.
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1. What are the absolute temperature readings initially
and after the temperature decreases?
2. What is the absolute pressure of the system before the
temperature decreases?
3. What is the final pressure in the tank? Assume
standard atmospheric pressure (14.7 psi)
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FLUID POWER
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20. A flow meter is attached in a hydraulic line that measures
79 gal/min. The line has an inside diameter of 2.75
in. (1gal = 231 in3/gal)
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1. What is the flow rate measured as in.3 /min at the
meter?
2. What is the area of inside diameter of the line?
3. What is the flow velocity where the fluid passes the
meter?
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PROBABILITY
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21. An experiment is performed 22 times, in which each trial
has probability of success 43%. What is the probability of
getting exactly 12 successes?
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PROBABILITY
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22. What is the probability that I will get at least 1 Heads and
1 Tails 8 times if I flip 3 coins 22 Times?
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STATISTICS
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23. Consider the following three data sets A, B and C.
A = {9,12,11,7,7,13}
B = {10,10,11,10,10,10}
C = {1,1,10,19,22,19}
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Calculate the Mean of each data set.
What is the Median of each data set.
What is the Mode of each data set.
Calculate the Standard Deviation of each data set.
Which set has the largest standard deviation?
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