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POE FINAL EXAM REVIEW

Spool-White

Fall 2013

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STATICS

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.

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.

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STATICS

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.

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

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.

1. What is the required actual mechanical advantage?

2. How many supporting strands will be needed in the pulley system?

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STATICS

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.

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?

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STATICS

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.

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

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.

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

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

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).

1. List all known values.

2. List all unknown values.

3. Select equations.

4. Apply known values.

5. Solve.

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THERMODYNAMICS9. 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)

1. List all known values.

2. List all unknown values.

3. Select equations.

4. Apply known values.

5. Solve.

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BEAM ANALYSIS10. Calculate the 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.

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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TRUSSES11. 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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TRUSSES12. 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.

1200 lbf750 lbf

150 lbf

45

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STRESS/STRAIN

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

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

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

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. 

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?

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FLUID POWER

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).

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

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. 

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

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.  

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

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)

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

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

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

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}

1. Calculate the Mean of each data set.

2. What is the Median of each data set.

3. What is the Mode of each data set.

4. Calculate the Standard Deviation of each data set.

5. Which set has the largest standard deviation?