# Overview

The is the Mechanical Engineering PM Mechanics and Materials Session. Questions are ordered from Q 081 through Q 120. Problems are in either S.I. or U.S. Customary Units.

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#### Question to Topic Map

 Q 081–Q 086 Statics Q 087–Q 089 Kinematics Q 090–Q 093 Dynamics Q 094–Q 097 Material Properties Q 098–Q 104 Strength of Materials Q 105–Q 108 Mechanical Components Q 109–Q 112 Joints and Fasteners Q 113–Q 116 Vibration and Dynamic Analysis Q 117–Q 120 Materials and Process

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## Q 081

An initial analysis must be performed on the design of a proposed linear positioning system. All components are aluminum alloy unless otherwise noted. The screw diameter is 0.84 inches.

The critical speed (rpm) of the lead screw prior to the installation of the table can be approximated from:

``critical speed = (215 / L^2) * sqrt(g * E * I / (rho * A))``

where:

 L = lead screw length (inch) = 48 E = modulus of elasticity (psi) = TBD I = moment of inertia (inch^4) = TBD ρ = density (lb/inch^4) = TBD A = cross sectional area (inch^2) = TBD

## Q 082

A signal arm carries two traffic signals and a sign, as shown. They are rigidly attached to the arm. Each traffic signal is 0.2 m^2 in area and weighs 240 N. The sign weighs 60 N/m^2. The design wind pressure is 120 N/m^2 The maximum moment that the connection between the arm and pole can withstand due to the wind is 7000 N x m, and the maximum permitted moment due to the loads is 5000 N x m. As limited by moment on the connection, the maximum allowable area of the sign in m^2 is most nearly.

## Q 083

In the structure shown, the beam is pinned at point B. Point E is a roller support. The beam is loaded with a distributed load from point A to point B of 600 N/m, a 200 N∙m couple at point C, and a vertical 700 N force at point D. If the distributed load and the vertical load are removed and replaced with a vertically upward force of 1500 N at point F (not shown, located 4.5 m to the left of B). What moment at point F would be necessary to keep the reaction at point E the same?

• [A] -7000 N∙m (ccw)
• [B] -4500 N∙m (ccw)
• [C] 3200 N∙m (cw)
• [D] 9400 N∙m (cw)

## Q 084

Consider the figure. The x and y coordinates of the centroid of the area (in cm) are most nearly. • [A] (4.87, 6.03)
• [B] (3.70, 4.50)
• [C] (3.53, 5.79)
• [D] (4.20, 5.10)

## Q 085

A 350 kg square plate (10 m x 10 m) is suspended horizontally by four wires of equal length at each corner. The tension in the four wires is equal. If one of the wires snaps, determine the tension (in N) in each remaining wire. • [A] (Ta, Tb, Tc) = (655, 1715, 655)
• [B] (Ta, Tb, Tc) = (1400, 0, 1400)
• [C] (Ta, Tb, Tc) = (1715, 0, 1715)
• [D] (Ta, Tb, Tc) = (1715, 1715, 0)

## Q 086

A cord is wrapped 1/4th around a 3 inch OD pipe as shown. The coefficient of friction (dynamic and static) between the cord and pipe is u = 0.25.

A dingus with a weight of 100 lb is suspended from one end of the cord and a force P applied to the other end. The minimum force P (lb) required to just support the 100 lb dingus in the position shown is most nearly. ## Q 087

A 100 lbm frozen turkey is launched with initial velocity of 1000 ft/sec. It has a launch angle of 45 degrees from the horizontal, and impact elevation of 5000 ft below the launch elevation. Neglecting air resistance, what is most nearly the horizontal travel distance?

## Q 088

Rigid link AB is 20 m long. It rotates counterclockwise about point A at 30 rpm. A thin disk with a radius of 3 m is pinned at its center to the link at point B. The disk rotates counterclockwise at 100 rpm with respect to point B. The maximum tangential velocity seen by any point on the disk (in m/s) is most nearly ## Q 089

A car traveling at 100 mph must be able to stop within a distance of 700 ft. The wheel diameter is 25 inches. Assume no brakes lock up during this braking; all brakes are on for total time duration. Neglect rolling resistance and aerodynamic drag.

The angular deceleration (rad/s^2) of the wheel as the car brakes uniformly from 100 mph to a stop over a distance of 700 ft is most nearly.

## Q 090

An industrial electromagnet weighing 400 pounds unloaded holds 150 pounds of scrap metal. The current is suddenly removed. If the total equivalent stiffness of the cable and the crane is 2000 pounds/inch, what will be the minimum cable tension (lbf) and frequency (Hz) of oscillation is most nearly.

## Q 091

A 5 kg disk with a diameter of 0.1 m is rigidly attached at point B to a rod 2 m in length. The rod has a mass of 1 kg. The rod-disk combination rotates around point A. The mass moment of inertia about point A for the assembly in kg∙m^2 is most nearly: ## Q 092

A 10 ton train car, traveling at 25 feet per second, passes point A, rolls down an incline, and is stopped by a spring bumper that compresses 3 feet. A constant frictional force of 65 lbf acts on the car. The required spring modulus in lbf / ft is most nearly. ## Q 093

A wheel with a radius of 0.55 m has a mass of 150 kg. The wheel is pinned at its center and has a radius of gyration of 0.25 m. A rope is wrapped around the wheel and supports a hanging 200 kg cube.

When the wheel is allowed to spin, the rope begins to unwind. The angular acceleration of the wheel in rad/sec^2 is most nearly.

## Q 094

An aluminum bar with E = 10 x 10^6 psi that is 2 feet long has a cross sectional area of 0.25 in^2 is mounted against a spring as shown. The spring has a spring constant of 5,000 lb/in. If the nominal coefficient of thermal expansion is 5 x 10^-6 in / in ∙ °F, the increase in force produced in the bar by a temperature increase of 300 °F is most nearly.

## Q 095

The engineering stress and strain for an aluminum sample (Poisson's ratio of 0.2) were 15,000 psi and .0400 inch/inch. The true stress (psi) and true strain (in/in) is most nearly.

• [A] 14,900; .035
• [B] 15,000; .040
• [C] 15,242; .039
• [D] 15,456; .042

## Q 096

Zinc is commonly plated on steel machine screws and fasteners to prevent corrosion. What is the name of this type of corrosion protection?

• [A] passivation
• [B] anodic protection
• [C] cathodic protection
• [D] galvanization

## Q 097

Aluminum is more resistant to rusting than steel. Why?

• [A] Iron can be attracted through a magnetic field
• [B] Iron has a different cubic structure than aluminum resulting in a more corrosive surface
• [C] The reaction rate between aluminum and oxygen is higher
• [D] The reaction rate between iron and aluminum is higher

## Q 098

The Goodman Relation / Failure Criterion is used to relate what two stresses to fatigue life:

• [A] axial and torsional stress
• [B] temperature induced and axial stress
• [C] torsional and bending stress
• [D] alternating and mean stress

##Q 099

A 30 inch long cantilever beam carries a uniformly distributed load of 12 lb/inch extending 10 inches from its free end. The shear force (lb) in the beam at a distance of 6 inch from the free end is most nearly. ## Q 100

A cantilevered flat steel spring supports a tip load that periodically varies between 0 lbf and 2 lbf. The spring is 0.75 in wide and 4.0 in. long. Tensile yield strength is 60,000 psi, tensile ultimate strength is 120,000 psi, and endurance strength after accounting for various derating factors is 50,000 psi. The design factor of safety is 2. The minimum required spring thickness for ultimate life is most nearly.

## Q 101

A 25 ft length of 5 in nominal diameter schedule-40 steel pipe full of water is simply supported. The maximum pipe deflection in inches is most nearly.

## Q 102

Bolt test specimens made of an experimental low carbon steel are subjected to completely reversed loading. At a stress amplitude of 70 ksi, the life is 1,000 cycles. At 30 ksi, the life cycle is 1,000,000 cycles. The number of cycles of life expected at a stress amplitude of 50 ksi is most nearly.

## Q 103

An inner steel cylinder (where its diameter = 5 inch) is surrounded by an aluminum tube (where its diameter = 10 inch) as shown in the cross section. The aluminum and the steel are well bonded. A uniform compressive load of 50 kips is applied axially. Use E_steel = 3.00 x10^7 psi and E_aluminum = 1.00 x 10^7 psi. The stress in the steel inner cylinder in psi is most nearly ## Q 104

The figure shows a flattening device for clay blanks. The device consists of a slider at A. The slider moves in a vertical guide. Joints connect Links ABC, BD, and the slider at A. All links and pins at ABD are made with materials having the following physical properties: Modulus of Elasticity 30 x 10^6 psi Yield Strength, S-y 60,000 psi Ultimate Strength, S-u 100,000 psi Shear Strength 20,000 psi

Link BD, of length 7.07 inch, is made out of a solid bar of circular cross section and is designed to carry an axial load of 500 lb. A safety factor of 2 against yield and 1.5 against buckling is desired for safety reasons. The diameter (in.) of the bar used for Link BD is most nearly.

## Q 105

A ball bearing is subjected to a radial load of 100 lb (with no axial load), has a rated life of 200,000 min, and a rated speed of 500 rpm.

The allowable radial load (lb) of the bearing when rotating at 5 rad/sec with a design life of 350,000 min is most nearly.

## Q 106

An 10 in diameter schedule 40 seamless steel pipe carries steam at 800 F. The maximum allowed tensile stress is 12.8 x 10^3 psi. The double butt flange welds are not radiographed. The manufacturing allowance is 20%, and corrosion allowance is 0.12 in. The maximum allowable pressure in psi is most nearly.

## Q 107

A hydraulic cylinder with an inside diameter of 10 inch is subjected to an internal pressure of 2,500 psi. Ignore end effects. Assuming allowable stress of 10,000 psi and a safety factor of 3, the required thickness (in.) is most nearly.

## Q 108

A gear drive is used to lift a garage door to a factory, as shown in the figure. The coefficient of friction for all mating surfaces of the vertical screw is 0.15, and the friction in the gearbox is negligible. The vertical screw shown in the figure has a mean diameter of 2 inch and a pitch of 0.50 inch. The gearbox ratio is 4:1 When the total vertical force to lift the garage door is 2,000 lb, the output torque (lb-in) from the motor is most nearly.

## Q 109

The end of a circular steel tube is welded to a steel plate. The full-perimeter external fillet weld has a 3/16 in leg, and allowable load is 8,400 lbf/in of leg. The tube outside diameter is 2 in. The tube and plate thickness is 1 in. A load is applied 4 in. from the plate surface, parallel to the plate, perpendicular to the tube axis, and at the centroid of the tube section. What is most nearly the maximum supported load?

## Q 110

A cantilevered beam 40 m long is supported at its left end (Point A) and 8 m from its right end (Point B). The beam bears a uniform load of 25 N/m and a concentrated load of 600 N applied 10 m from its right end. The vertical shear acting on the beam at point C, in N, which is 12 m from the left end, is most nearly. ## Q 111

A 1/4 inch steel plate is attached to a steel beam with three 1/4-inch UNC bolts, as shown. The load (lb) that the highest loaded bolt will carry is most nearly.

## Q 112

The blind pressure vessel flange is restrained by eight equally spaced 7/16-14 inch UNC steel bolts. The internal diameter of the pressure vessel is 12 inches. To maintain an adequate seal, each bolt is preloaded to 7,000 lb. The bolt stiffness (k_bolt) and the material stiffness (k_parts) are numerically equal. The bolt stress (psi) for an internal pressure of 300 psi is most nearly:

## Q 113

An experimental widget can be modeled as a mass/spring mechanism. The spring constant of 50 lbf/in and a mass of 7 lbm undergoes free vibration.

The linear frequency (cycles/sec) of this vibration is most nearly.

## Q 114

A 100 lbm motor turns at 2000 rpm and is supported on a resilient pad having a stiffness of 2000 pounds per inch. Due to an imbalance condition, a periodic force of 30 pounds is applied in the vertical direction once each revolution. If the motor is constrained to move vertically, the amplitude of vibration in inches is most nearly.

## Q 115

A rotating mechanisms comprises a vertical axis, three steel balls spinning around that axis, and an ideal torsional spring resisting the motion.

Arms supporting the balls are rigid and massless, the distance from the vertical axis to ball centers is 0.5 inch. The torsional spring constant is 3.5 x 10^-3 inch-lbf / rad. The steel ball diameter and density are 1.5 inch and 0.125 lbm/inch^3, respectively. The natural torsional frequency (in Hz) of the pendulum is most nearly.

## Q 116

The block spring system shown oscillates once every 6 seconds. There is no friction between the block and the surface. If the spring constant is 2 N/m the approximate mass of the block in kg is nearly. ## Q 117

You manage a toy production department and you are new to the job. You must make a decisions about equipment selection and production costs. Part material cost is \$7 for each part scrapped, not including sunk labor costs.

 Machine Labor Cost (per hour) Production Rate (units/hr) Part Scrap Rate Part Setup Cost Manual \$40 10 1 of 32 \$9 CNC w/ manual load \$22 11 1 of 80 \$4 CNC w/ auto load \$17 16 1 of 60 \$16 3d printing \$10 7 1 of 300 \$250

The % increase of good parts per 80-hr work week that can be made on the CNC with auto loading vs manual loading is most nearly.

## Q 118

Bean counters must select a structural polymer from the following list of materials. Based on the following requirements and info, they are going to attempt to make a design selection. One critical dimension, fabricated to 10.000 inches at 25 degrees C, must not exceed 10.055 inches at the operating temperature of 100 degrees C. Material weight must be less than half that of aluminum, which has a specific gravity of 2.71.

 Material Yield Strength [psi] Specific Gravity Coefficient of Thermal Expansion [in / (in∙°C)] Maximum Operating Temperature [°F] A 4,500 1.05 90 x 10^-6 190 B 10,000 1.5 70 x 10^-6 220 C 8,000 1.1 80 x 10^-6 165 D 9,300 1.20 70 x 10^-6 260

Which is the best material for the application?

• [A] Material A
• [B] Material B
• [C] Material C
• [D] Material D

## Q 119

Table I shows subgroup data from a measurement process over a 12-hour period. Each subgroup is made up of a sample size of 6.

#### Table 1

 Subgroup 6:00 9:00 12:00 15:00 18:00 1 7.2 7.5 8.3 8.3 6.8 2 7.1 7.1 7.6 8.1 7.3 3 6.9 7.6 7.9 7.2 7.0 4 7.4 7.8 8.1 8.4 7.2 5 7.2 7.8 8.9 8.4 6.9

#### Table 2

 Sample Size A2 D4 D3 2 1.88 3.27 0.00 3 1.02 2.57 0.00 4 0.73 2.28 0.00 5 0.58 2.11 0.00 6 0.48 2.00 0.00

From the data provided in Tables 1 and 2, the upper control limit (UCL) and the lower control limit (LCL) of an R chart are most nearly.

• [A] UCL = 3.41; LCL = 0
• [B] UCL = 1.39; LCL = -1.39
• [C] UCL = 2.42; LCL = -2.42
• [D] UCL = 2.68; LCL = 0

## Q 120

A 0.500 inch diameter hole and pin are to be combined during assembly. Drawings indicate tolerances as listed. The basic hole system is used.

 Feature High Tolerance Low Tolerance Hole Diameter +4.6 x 10^-3 inch -0 x 10^-3 inch Pin Diameter -6.0 x 10^-3 inch -7.0 x 10^-3 inch

This fit is most nearly designated as:

• [A] RC7 free running fit
• [B] RC9 free running fit
• [C] LT3 locational-transitional fit
• [D] FN2 medium drive fit