Morning Section — Full Practice Exam 1

Questions in this quiz (55)

1. If $$y=5x^3+2x^2z+4xz^2+7z^3+10$$, then $$\frac{\partial^2 y}{\partial x^2}=$$?

   • $$30x+8z$$
   • $$30x+4z$$
   • $$10x^2+4z$$
   • $$30x+2z$$

2. Evaluate the definite integral $$\int_1^3(2x^2+3x-1)\,dx$$.

   • $$26$$
   • $$\frac{82}{3}$$
   • $$20$$
   • $$32$$

3. What is most nearly the area bounded by $$y=0$$, $$y=e^x$$, $$x=0$$, and $$x=1$$?

   • $$1.4$$
   • $$1.7$$
   • $$2.7$$
   • $$3.4$$

4. Five fair coins are each flipped once. What is the probability that at least two of the coins will show heads?

   • $$0.19$$
   • $$0.80$$
   • $$0.81$$
   • $$0.84$$

5. Ten samples of a concrete cube were tested for compressive strength. The resulting data presented below is in psi: $$2995,3005,3001,2991,2984,3004,3009,3015,2998,3002$$ Find the mean and the variance of the sample data.

   • $$3000.4;\;79.6$$
   • $$3000.4;\;71.6$$
   • $$2997.8;\;87.1$$
   • $$2997.8;\;78.4$$

6. When faced with a potential conflict of interest, what is the most ethical course of action for a licensed civil engineer?

   • Conceal the conflict to avoid delays
   • Consult a colleague only
   • Disclose the conflict and address it
   • Proceed without acknowledgment

7. Under legal and professional requirements, which document best outlines an engineer's duties regarding public safety?

   • Professional Engineer License
   • Construction Standards Manual
   • Building Code
   • Engineer Code of Ethics

8. Which of the following is the best description of plan stamping?

   • Signing off on a project you won on tender
   • Signing off after being paid
   • Signing off after checking only
   • Signing off on work you did not design or review

9. You are aware that a registered engineer intentionally violates a state's rule of professional conduct. What should you do?

   • Do nothing
   • Report to employer
   • Report to affected parties
   • Report to state engineering board

10. An engineer-architect works for a big design firm. During the night after working hours, he uses some of the office's equipment and materials to make an architectural model for his side job. He receives overtime salary because he is considered as working overtime. Why is this action considered unethical?

    • His contract prohibits misuse and misappropriation of the office's equipment
    • He may wear out the office's materials
    • He may encourage other employees to do side jobs in the office
    • He can undercut his fee because he has a lower overhead

11. A municipality must choose between four comparable pumping systems for a water facility. Each system will provide the required service for $$10$$ years. The interest rate is $$10\%$$ per year, and taxes may be ignored. System $$A$$: first cost $$42{,}000$$ dollars, annual operating cost $$9{,}500$$ dollars, major overhaul at end of year $$5$$ of $$6{,}000$$ dollars, salvage value at end of year $$10$$ of $$4{,}000$$ dollars. System $$B$$: first cost $$55{,}000$$ dollars, annual operating cost $$7{,}200$$ dollars, major overhaul at end of year $$5$$ of $$4{,}500$$ dollars, salvage value at end of year $$10$$ of $$6{,}000$$ dollars. System $$C$$: first cost $$48{,}000$$ dollars, annual operating cost $$8{,}400$$ dollars, major overhaul at end of year $$5$$ of $$5{,}500$$ dollars, salvage value at end of year $$10$$ of $$5{,}000$$ dollars. System $$D$$: first cost $$60{,}000$$ dollars, annual operating cost $$6{,}800$$ dollars, major overhaul at end of year $$5$$ of $$3{,}500$$ dollars, salvage value at end of year $$10$$ of $$7{,}500$$ dollars. Based on present worth of cost, which two alternatives are the most economical, and what is the approximate difference between their present worth values?

    • B and D, $$1{,}343$$ dollars
    • C and B, $$2{,}400$$ dollars
    • D and B, $$1{,}900$$ dollars
    • B and C, $$1{,}100$$ dollars

12. What is the annual effective interest rate of money that is invested at $$2.5\%$$ per year and compounded quarterly?

    • $$2.50\%$$
    • $$2.51\%$$
    • $$2.53\%$$
    • $$2.55\%$$

13. A manufacturer is considering replacing a semi-automated packaging line with a fully automated system. The semi-automated line has a current market value of $$12{,}000$$ dollars, annual operating and labor costs of $$48{,}000$$ dollars, and no salvage value at the end of its remaining $$6$$-year life. The fully automated system will cost $$95{,}000$$ dollars, require $$18{,}000$$ dollars per year in operating and labor costs, and have a salvage value of $$11{,}000$$ dollars at the end of $$6$$ years. Assume the company can sell the existing semi-automated line now, and neglect interest. The payback period for investing in the fully automated system is most nearly:

    • $$2.0\text{ years}$$
    • $$2.8\text{ years}$$
    • $$3.1\text{ years}$$
    • $$4.0\text{ years}$$

14. A contractor is evaluating whether to purchase extended insurance for a fleet vehicle. The vehicle has a value of $$120{,}000$$ dollars. The annual insurance premium is $$3{,}200$$ dollars, with a deductible of $$2{,}500$$ dollars per incident. The following outcomes are possible over one year: $$0.80$$ probability of no accident $$0.15$$ probability of a minor accident costing $$4{,}000$$ dollars in repairs $$0.04$$ probability of a major accident costing $$25{,}000$$ dollars in repairs $$0.01$$ probability of a total loss of the vehicle If insurance is purchased, the contractor pays the premium and any deductible per incident. If insurance is not purchased, the contractor pays all repair or replacement costs. Based on expected cost, what is the best decision and the approximate expected savings?

    • Purchase insurance and save $$1{,}150$$ dollars
    • Purchase insurance and save $$2{,}300$$ dollars
    • Do not purchase insurance and save $$900$$ dollars
    • Do not purchase insurance and save $$2{,}300$$ dollars

15. Mrs. Smith deposits $$2{,}000$$ dollars in a bank that gives $$5\%$$ interest compounded annually. The money she will receive in her account after $$15$$ years is most nearly:

    • $$2{,}100$$ dollars
    • $$3{,}950$$ dollars
    • $$4{,}200$$ dollars
    • $$31{,}500$$ dollars

16. What is most nearly the reaction at $$A$$ for a simply supported beam $$10$$ m long with a triangular distributed load extending from $$A$$ to $$4$$ m, varying from $$0$$ to $$100$$ N/m?

    • $$50\text{ N}$$
    • $$100\text{ N}$$
    • $$130\text{ N}$$
    • $$150\text{ N}$$

17. Three ropes are connected and hold a box that weighs $$2500$$ lb. Rope $$T_1$$ has direction ratios corresponding to a triangle with horizontal side $$6$$ and vertical side $$8$$. Rope $$T_2$$ is horizontal. What are the tensions in ropes $$T_1$$ and $$T_2$$ if the system is in equilibrium?

    • $$T_1=3125\text{ lb},\;T_2=1875\text{ lb}$$
    • $$T_1=2500\text{ lb},\;T_2=2500\text{ lb}$$
    • $$T_1=2725\text{ lb},\;T_2=2225\text{ lb}$$
    • $$T_1=2925\text{ lb},\;T_2=1725\text{ lb}$$

18. A steel I-beam has flanges $$180$$ mm by $$20$$ mm and a web $$20$$ mm by $$260$$ mm. The total depth is $$300$$ mm. Calculate the moment of inertia about the horizontal centroidal axis.

    • $$29.3\times10^6\text{ mm}^4$$
    • $$171\times10^6\text{ mm}^4$$
    • $$405\times10^6\text{ mm}^4$$
    • $$119\times10^6\text{ mm}^4$$

19. What is most nearly the frictional force between an $$80$$ kg block and a $$40^\circ$$ ramp? The coefficient of static friction is $$0.2$$ and the coefficient of dynamic friction is $$0.15$$.

    • $$60\text{ N}$$
    • $$80\text{ N}$$
    • $$90\text{ N}$$
    • $$120\text{ N}$$

20. Find the axial forces in members $$CD$$ and $$EG$$ for the truss shown, with a downward load of $$1200$$ lb applied at joint $$C$$.

    • $$T_{CD}=600\text{ lb tension},\;T_{EG}=600\text{ lb compression}$$
    • $$T_{CD}=1200\text{ lb compression},\;T_{EG}=900\text{ lb tension}$$
    • $$T_{CD}=0,\;T_{EG}=950\text{ lb compression}$$
    • $$T_{CD}=0,\;T_{EG}=900\text{ lb compression}$$

21. Find the moment of inertia about the centroid x-axis of the shape.

    • $$3.66$$
    • $$9.66$$
    • $$12.5$$
    • $$30.52$$

22. Refer to the composite plane areas shown. What is the polar radius of gyration?

    • $$3.6$$
    • $$4.0$$
    • $$4.2$$
    • $$4.9$$

23. A vehicle traveling at $$25\text{ m/s}$$ applies its brakes and decelerates uniformly at $$5\text{ m/s}^2$$. Determine the distance traveled before coming to a complete stop.

    • $$125\text{ m}$$
    • $$62.5\text{ m}$$
    • $$31.25\text{ m}$$
    • $$50.0\text{ m}$$

24. A spring has a spring constant of $$10\text{ N/cm}$$ and is compressed $$5\text{ cm}$$. It pushes a projectile of mass $$1\text{ kg}$$. What is the velocity after leaving the spring?

    • $$0.32\text{ m/s}$$
    • $$1.6\text{ m/s}$$
    • $$32\text{ m/s}$$
    • $$50\text{ m/s}$$

25. A girl rolls a ball up an incline with initial speed $$4\text{ m/s}$$. The acceleration along the incline is constant at $$0.25g$$ downward. Determine the distance traveled before stopping and the total time to return to the starting point.

    • $$s=2.45\text{ m},\;t=2.90\text{ s}$$
    • $$s=3.26\text{ m},\;t=3.26\text{ s}$$
    • $$s=4.10\text{ m},\;t=3.80\text{ s}$$
    • $$s=3.26\text{ m},\;t=2.60\text{ s}$$

26. A passenger elevator in a $$20$$-story residential building has a mass of $$1800\text{ kg}$$. The elevator can accelerate at a maximum rate of $$1.4\text{ m/s}^2$$ and move at a top speed of $$2.5\text{ m/s}$$. A person with a mass of $$67\text{ kg}$$ stands on a scale while the elevator is moving upward with its maximum acceleration. What reading will the scale display most nearly?

    • $$67\text{ N}$$
    • $$560\text{ N}$$
    • $$660\text{ N}$$
    • $$750\text{ N}$$

27. A vehicle moves along a flat, unbanked circular roadway of radius $$r$$. The coefficient of static friction between the tires and the pavement is $$0.30$$. If the car is traveling at a speed of $$10\text{ m/s}$$, what is the minimum radius the curve can have before the car begins to skid?

    • $$10\text{ m}$$
    • $$34\text{ m}$$
    • $$50\text{ m}$$
    • $$68\text{ m}$$

28. A material experiences a shear stress of $$\tau_{xy}=35\text{ MPa}$$ and has a shear modulus of $$G=75\text{ GPa}$$. What is the corresponding shear strain most nearly equal to?

    • $$2.5\times10^{-5}\text{ rad}$$
    • $$4.7\times10^{-4}\text{ rad}$$
    • $$5.5\times10^{-4}\text{ rad}$$
    • $$8.3\times10^{-4}\text{ rad}$$

29. A steel bar is subjected to an axial tensile load of $$80\text{ lb}$$. The bar is $$25\text{ ft}$$ long and has a diameter of $$\frac{1}{4}\text{ in}$$. Assuming the modulus of elasticity of steel is $$10{,}900\text{ ksi}$$, determine the elongation of the bar caused by the applied load.

    • $$0.0018\text{ in}$$
    • $$0.1495\text{ in}$$
    • $$0.00015\text{ in}$$
    • $$0.045\text{ in}$$

30. A hollow circular shaft with a length of $$2\text{ m}$$ is subjected to torsion. The allowable shear stress is $$40\text{ MPa}$$, and the maximum permissible angle of twist is $$0.025\text{ rad}$$. The shaft has an outside diameter of $$75\text{ mm}$$ and an inside diameter of $$50\text{ mm}$$. Given that the shear modulus is $$70{,}000\text{ MPa}$$ and the torsional constant is $$250\text{ cm}^4$$, determine the maximum allowable torque $$T$$.

    • $$2\text{ kN}\cdot\text{m}$$
    • $$3\text{ kN}\cdot\text{m}$$
    • $$4\text{ kN}\cdot\text{m}$$
    • $$5\text{ kN}\cdot\text{m}$$

31. An alloy steel pipe measures $$1\text{ m}$$ in length at a temperature of $$25^\circ\text{C}$$. If the coefficient of thermal expansion is $$8\times10^{-6}/^\circ\text{C}$$, determine the pipe length when the temperature increases to $$60^\circ\text{C}$$.

    • $$1.3\text{ m}$$
    • $$1.03\text{ m}$$
    • $$1.003\text{ m}$$
    • $$1.0003\text{ m}$$

32. A thin-walled cylindrical pressure vessel has a radius of $$200\text{ mm}$$ and a wall thickness of $$8\text{ mm}$$. The vessel is subjected to an internal pressure of $$3\text{ MPa}$$ and a torsional moment of $$15\text{ kN}\cdot\text{m}$$. Determine the maximum in-plane shear stress developed in the wall of the vessel.

    • $$7.5\text{ MPa}$$
    • $$18.8\text{ MPa}$$
    • $$20.2\text{ MPa}$$
    • $$26.2\text{ MPa}$$

33. A plane element in a body is subjected to a normal stress of $$120\text{ MPa}$$ and a shear stress of $$50\text{ MPa}$$ as shown. What is most nearly the maximum shear stress?

    • $$50\text{ MPa}$$
    • $$64\text{ MPa}$$
    • $$72\text{ MPa}$$
    • $$78\text{ MPa}$$

34. A simply supported beam supports a triangular distributed load over its full $$10\text{ m}$$ span. The load varies from $$0$$ at the left support to $$5\text{ N/m}$$ at the right support. What is the approximate bending moment at a point $$7\text{ m}$$ from the left end of the beam?

    • $$15\text{ N}\cdot\text{m}$$
    • $$17\text{ N}\cdot\text{m}$$
    • $$22.75\text{ N}\cdot\text{m}$$
    • $$30\text{ N}\cdot\text{m}$$

35. An aluminum shaft has a shear modulus of $$2.8\times10^{10}\text{ Pa}$$, a diameter of $$25\text{ mm}$$, and a length of $$50\text{ cm}$$. One end of the shaft is fixed to a rigid support. What torque must be applied at the free end to produce an angular twist of $$4.5^\circ$$ about the longitudinal axis?

    • $$26\text{ N}\cdot\text{m}$$
    • $$84\text{ N}\cdot\text{m}$$
    • $$110\text{ N}\cdot\text{m}$$
    • $$170\text{ N}\cdot\text{m}$$

36. A laboratory gas cylinder contains compressed gas at an internal gage pressure of $$8\text{ MPa}$$. The cylinder has an outside diameter of $$25\text{ cm}$$. If the allowable stress for the steel is $$90\text{ MPa}$$, determine the minimum wall thickness required for the cylinder.

    • $$0.69\text{ cm}$$
    • $$0.95\text{ cm}$$
    • $$1.1\text{ cm}$$
    • $$1.9\text{ cm}$$

37. Consider a cantilever beam made of steel with a modulus of elasticity of $$210\text{ GPa}$$. Its cross-sectional area is $$37.9\text{ cm}^2$$, and its moment of inertia is $$2880\text{ cm}^4$$. The beam weighs $$45.9\text{ kg/m}$$. A $$6000\text{ N}$$ compressive load is applied at the free end at an angle of $$30^\circ$$ relative to the horizontal. Neglect buckling effects. What is the maximum shear force developed in the beam?

    • $$3000\text{ N}$$
    • $$3900\text{ N}$$
    • $$5200\text{ N}$$
    • $$6100\text{ N}$$

38. ASTM provides many standard testing methods for materials. Which of the following testing methods is included for aggregates?

    • Sieve analysis
    • Relative density
    • Absorption
    • All of the above

39. A composite material specimen is subjected to a tensile test. During the test, the material experiences a strain of $$4.5\%$$ while a stress of $$270\text{ MPa}$$ is applied. Based on these results, determine the modulus of elasticity of the material.

    • $$12\text{ MPa}$$
    • $$60\text{ MPa}$$
    • $$6000\text{ MPa}$$
    • $$600\text{ MPa}$$

40. Which of the following tests is commonly used to evaluate the bearing capacity of soil for pavement and highway design?

    • Tensile test
    • CBR test
    • Charpy impact test
    • Rockwell hardness test

41. Which of the following quantities are used in determining the Reynolds number for fluid flow? I. Fluid density II. Flow velocity III. Surface tension IV. Dynamic viscosity

    • I and III
    • II and III
    • I, II, and IV
    • III and IV

42. Which of the following does affect the kinematic viscosity of a fluid? I. Density II. Surface tension III. Stress IV. Absolute viscosity

    • I and II
    • II and III
    • III and IV
    • I and IV

43. A cylindrical oil tank is completely filled with oil having a density of $$850\text{ kg/m}^3$$. The height of the oil column is $$8\text{ m}$$. Determine the gage pressure at a point located $$2\text{ m}$$ above the bottom of the tank. Use $$g=9.81\text{ m/s}^2$$.

    • $$16.7\text{ kPa}$$
    • $$25.0\text{ kPa}$$
    • $$50.0\text{ kPa}$$
    • $$66.7\text{ kPa}$$

44. A glass capillary tube with a diameter of $$2.5\text{ mm}$$ is inserted into water at $$25^\circ\text{C}$$. The surface tension of water is $$0.072\text{ N/m}$$, the contact angle is zero, and the specific weight of water is $$9.81\text{ kN/m}^3$$. Determine the approximate height the water will rise in the tube.

    • $$3.0\text{ mm}$$
    • $$5.9\text{ mm}$$
    • $$7.2\text{ mm}$$
    • $$11.7\text{ mm}$$

45. A pressure vessel is connected to a simple U-tube open to the atmosphere. A $$10\text{ cm}$$ deflection of mercury is observed. The density of mercury is $$13600\text{ kg/m}^3$$. The atmospheric pressure is $$101\text{ kPa}$$. The vacuum within the vessel is most nearly:

    • $$1.0\text{ kPa}$$
    • $$13\text{ kPa}$$
    • $$39\text{ kPa}$$
    • $$78\text{ kPa}$$

46. A Pitot-static tube is used to measure the velocity of water flowing in a pipe. The fluid density is $$1000\text{ kg/m}^3$$, and the flow velocity is $$3\text{ m/s}$$. If the stagnation pressure is $$18.5\text{ kPa}$$, determine the static pressure of the fluid at the measurement location.

    • $$9.0\text{ kPa}$$
    • $$12.5\text{ kPa}$$
    • $$14.0\text{ kPa}$$
    • $$18.0\text{ kPa}$$

47. At a section in a pipeline, the elevation is $$15\text{ m}$$, the gage pressure is $$180\text{ kPa}$$, and the velocity is $$6\text{ m/s}$$. Assuming $$\rho=1000\text{ kg/m}^3$$ and $$g=9.81\text{ m/s}^2$$, determine the total head at this section.

    • $$33.3\text{ m}$$
    • $$35.2\text{ m}$$
    • $$20.2\text{ m}$$
    • $$40.5\text{ m}$$

48. Which of the flows has a cross section that does not vary with time at any location along an open channel?

    • Uniform flow
    • Non-uniform flow
    • Steady flow
    • Critical flow

49. Oil flows through a pipe at a velocity of $$1.5\text{ m/s}$$. The kinematic viscosity of the oil is $$9.0\times10^{-7}\text{ m}^2/\text{s}$$. If the inside diameter of the pipe is $$40\text{ mm}$$, determine the Reynolds number and identify the type of flow.

    • $$1.67\times10^3$$, laminar
    • $$3.25\times10^3$$, transitional
    • $$6.67\times10^4$$, turbulent
    • $$1.50\times10^5$$, turbulent

50. A two-dimensional function $$f(x,y)$$ is defined as $$f(x,y)=2x^2-y^2+3x-y$$. What is the direction of the line passing through the point $$(1,-2)$$ that has the maximum slope?

    • $$4\mathbf{i}+2\mathbf{j}$$
    • $$7\mathbf{i}+3\mathbf{j}$$
    • $$7\mathbf{i}+4\mathbf{j}$$
    • $$9\mathbf{i}-7\mathbf{j}$$

51. A simulation model for a transportation system is run for $$30$$ replications, and the mean percentage utilization of the transporter is recorded for each replication. Those $$30$$ data points are used to form a confidence interval on mean transporter utilization. At a $$95\%$$ confidence level, the confidence interval is found to be $$37.2\%\pm3.4\%$$. Which statement can be definitively stated about the system?

    • At $$95\%$$ confidence, the sample mean lies in the range $$37.2\%\pm3.4\%$$.
    • At $$95\%$$ confidence, the population mean lies in the range $$37.2\%\pm3.4\%$$.
    • At $$95\%$$ confidence, the population mean lies outside the range $$37.2\%\pm3.4\%$$.
    • At $$5\%$$ confidence, the population mean lies inside the range $$37.2\%\pm3.4\%$$.

52. If one is aware that a registered engineer willfully violates a state's rule of professional conduct, what should one do?

    • Do nothing
    • Report the violation to the state engineering registration board
    • Report the violation to the employer
    • Report the violation to the parties it affects

53. Complete the sentence: A professional engineer who took the licensing examination in mechanical engineering...

    • May not design in electrical engineering
    • May design in electrical engineering if she feels competent
    • May design in electrical engineering only if the electrical portion is insignificant and incidental
    • May design in electrical engineering if another engineer checks the work

54. A new $$200\text{ mm}$$ diameter pipeline is installed over a distance of $$1000\text{ m}$$. Annual maintenance and pumping costs are paid at the end of the years in which their costs are incurred. The pipe has an initial cost of $$\$1350$$, annual interest rate of $$6\%$$, service life of $$6$$ years, salvage value of $$\$120$$, annual maintenance of $$\$500$$, pump cost of $$\$2.75$$ per hour, and pump operation of $$2000$$ hours per year. What is most nearly the equivalent uniform annual cost of the pipe?

    • $$\$5700$$
    • $$\$5980$$
    • $$\$6150$$
    • $$\$6260$$

55. A piece of equipment has an initial cost of $$\$5000$$ in year $$1$$. The maintenance cost is $$\$300$$ per year for the total lifetime of $$7$$ years. During years $$1$$ through $$3$$, the rate of inflation is $$5\%$$, and the effective annual interest rate is $$9\%$$. The uninflated present worth of the equipment during year $$1$$ is most nearly:

    • $$\$3200$$
    • $$\$3300$$
    • $$\$3400$$
    • $$\$3500$$