FE Mechanical Practice Problems: 18 Free Questions with Solutions

A right circular conical hopper stands apex down, $8$ ft deep with an $8$ ft top diameter. Granular material is fed in at a steady $12$ ft$^3$/min. When the material depth is $6$ ft, the rate at which the surface level rises is most nearly:

1. (A)0.106 ft/min
2. (B)0.141 ft/min
3. (C)0.424 ft/min
4. (D)1.273 ft/min

A bearing assembly line draws 65 percent of its bearings from supplier A and 35 percent from supplier B. Supplier A ships 2.0 percent defective units; supplier B ships 5.0 percent defective units. A bearing drawn at random from the line is found to be defective. The probability that it came from supplier B is most nearly:

1. (A)0.350
2. (B)0.426
3. (C)0.574
4. (D)0.714

A licensed professional engineer is asked to apply a seal to a structural connection design package prepared by an unlicensed designer employed at a different firm. The engineer did not direct or control the preparation of the design but has since reviewed the calculations and found them technically acceptable. Under the NCEES Model Rules, applying the seal is:

1. (A)Permissible, because the calculations were reviewed and found acceptable
2. (B)Permissible, provided the originating designer is credited on the drawings
3. (C)Permissible, provided the engineer accepts liability for the design in writing
4. (D)Not permissible, because the work was not performed under responsible charge

A municipal pumping station rated at $0.85 \text{ m}^3/\text{s}$ has a first cost of USD 480{,}000, annual maintenance of USD 18{,}000, and a major overhaul costing USD 60{,}000 at the end of every eighth year of service. The station is to be maintained in service indefinitely. At an interest rate of 6% per year, the capitalized cost is most nearly:

1. (A)USD 780,000
2. (B)USD 881,000
3. (C)USD 905,000
4. (D)USD 941,000

A 48 V ideal DC source feeds node A through a 6 $\Omega$ series resistor, and a 12 $\Omega$ resistor connects node A to the source return. A variable resistive load is then connected between node A and the return. The maximum power the load can absorb is most nearly:

1. (A)64 W
2. (B)144 W
3. (C)256 W
4. (D)576 W

A vertical mast is fixed at the origin with its top at point A, 12 m above the base. Two guy cables run from A to ground anchors: cable AB to anchor B, located 9 m from the base along the positive $x$ axis, and cable AC to anchor C, located 5 m from the base along the negative $y$ axis. The tension is 3.0 kN in AB and 2.6 kN in AC. The magnitude of the resultant of the two cable forces acting at A is most nearly:

1. (A)2.06 kN
2. (B)3.97 kN
3. (C)4.80 kN
4. (D)5.22 kN

Gravel leaves the end of a horizontal conveyor at 24 ft/s. The discharge point is 18 ft above the surface of the stockpile, and air resistance is negligible. The horizontal distance from the discharge point to the point of impact is most nearly:

1. (A)17.9 ft
2. (B)25.4 ft
3. (C)26.8 ft
4. (D)46.0 ft

A stepped tie rod of high-strength alloy steel with a 690 MPa yield strength hangs from a rigid ceiling and carries a 40 kN axial tensile load at its lower end. The upper segment is 900 mm long with a 20 mm diameter; the lower segment is 600 mm long with a 14 mm diameter. The modulus of elasticity is 200 GPa. The total elongation of the rod is most nearly:

1. (A)0.21 mm
2. (B)0.95 mm
3. (C)1.35 mm
4. (D)1.95 mm

The engineering stress-strain response of a hot-rolled structural steel is idealized by two straight segments: a linear elastic rise from the origin to yield at $350$ MPa and $0.0018$ strain, followed by a straight line to fracture at $520$ MPa and $0.160$ strain. The modulus of toughness is most nearly:

1. (A)$0.32\ \text{MJ/m}^3$
2. (B)$41.4\ \text{MJ/m}^3$
3. (C)$69.1\ \text{MJ/m}^3$
4. (D)$83.2\ \text{MJ/m}^3$

A horizontal venturi meter in a chilled-water line has an inlet diameter of $150$ mm and a throat diameter of $75$ mm. The measured pressure drop from inlet to throat is $28$ kPa, the meter coefficient is $0.98$, and the water density is $1{,}000$ kg/m$^3$. The volumetric flow rate is most nearly:

1. (A)32.4 L/s
2. (B)33.5 L/s
3. (C)34.1 L/s
4. (D)37.4 L/s

A rigid vessel of volume $0.30$ m$^3$ contains 2.0 kg of water at 1.0 MPa. At 1.0 MPa the saturation properties are $v_f = 0.001127$ m$^3$/kg, $v_g = 0.19444$ m$^3$/kg, $u_f = 761.7$ kJ/kg, and $u_{fg} = 1{,}822.0$ kJ/kg. The total internal energy of the contents is most nearly:

1. (A)1,520 kJ
2. (B)2,810 kJ
3. (C)4,330 kJ
4. (D)5,170 kJ

A composite panel consists of a 12 mm thick stainless steel plate ($k = 15$ W/(m·K)) bonded to an 8 mm thick aluminum plate ($k = 180$ W/(m·K)). The bond has a thermal contact resistance of $2.5 \times 10^{-4}\ \text{m}^2\cdot\text{K/W}$. Under steady one-dimensional conduction the exposed steel face is held at 210 °C and the exposed aluminum face at 90 °C. The heat flux through the panel is most nearly:

1. (A)76 kW/m²
2. (B)110 kW/m²
3. (C)142 kW/m²
4. (D)150 kW/m²

A single active foil gauge of gauge factor 2.10 is bonded along the axis of a steel tie rod ($E = 200$ GPa) and wired as one arm of a quarter-bridge excited at 10.0 V DC. The bridge is balanced at no load; under load the bridge output is 1.05 mV. The axial stress in the rod is most nearly:

1. (A)20 MPa
2. (B)40 MPa
3. (C)84 MPa
4. (D)176 MPa

A ductile steel bracket has a yield strength of 46 ksi. At the critical point the plane stress state is $\sigma_x = 18$ ksi, $\sigma_y = -6$ ksi, and $\tau_{xy} = 8$ ksi. Using the maximum distortion energy theory, the factor of safety against yielding is most nearly:

1. (A)1.79
2. (B)1.99
3. (C)2.18
4. (D)2.56