Morning Section — Full Practice Exam 2

Questions in this quiz (55)

1. A sample of size $$16$$ is randomly selected from a normally distributed population. The sample has a mean of $$20$$ and a standard deviation of $$4$$.Construct a $$90\%$$ confidence interval for the population mean.

   • $$[16.247,\ 23.753]$$
   • $$[18.247,\ 21.753]$$
   • $$[18.720,\ 21.280]$$
   • $$[19.000,\ 21.000]$$

2. The slopes of four lines are given:Slope of $$AB=\frac{3}{2}$$Slope of $$CD=-\frac{2}{3}$$Slope of $$XY=\frac{3}{2}$$Slope of $$ZW=2$$Which statement is correct?

   • $$AB$$ is perpendicular to $$XY$$.
   • $$CD$$ is perpendicular to $$AB$$.
   • $$CD$$ is parallel to $$AB$$.
   • $$ZW$$ is perpendicular to $$AB$$.

3. What does the following equation represent?$$5x^2+6xy-2y^2-1=0$$

   • Hyperbola
   • Ellipse
   • Circle
   • Line

4. The integral$$\int_1^3\frac{2}{x^2}\,dx$$equals:

   • $$\frac{2}{3}$$
   • $$1$$
   • $$\frac{4}{3}$$
   • $$2$$

5. If$$y=5x^4+2x^3z+4xz^2+7z^3+9,$$then $$\frac{\partial^2y}{\partial x^2}$$ equals:

   • $$20x^3+6x^2z+4z^2$$
   • $$60x^2+12xz$$
   • $$60x^2+6xz$$
   • $$20x^3+12xz$$

6. Which of the following is a unit vector perpendicular to the plane determined by the vectors$$\mathbf{A}=\mathbf{i}+\mathbf{j}$$and$$\mathbf{B}=\mathbf{i}+\mathbf{k}?$$

   • $$\frac{1}{\sqrt{2}}(\mathbf{i}+\mathbf{j})$$
   • $$\frac{1}{\sqrt{3}}(\mathbf{i}-\mathbf{j}-\mathbf{k})$$
   • $$\frac{1}{\sqrt{3}}(\mathbf{i}+\mathbf{j}+\mathbf{k})$$
   • $$\mathbf{i}-\mathbf{j}-\mathbf{k}$$

7. Two fair $$8$$-sided dice are rolled. Each die is numbered from $$1$$ through $$8$$.The probability that the sum of the two dice will be less than $$16$$ is most nearly:

   • $$0.016$$
   • $$0.125$$
   • $$0.875$$
   • $$0.984$$

8. Which of the following measures the strength and direction of the linear relationship between two quantitative variables?

   • Sample correlation coefficient
   • Standard error
   • Y-intercept
   • Residual value

9. Two engineering firms submit sealed bids for a municipal drainage improvement project. After the bids are received, a city employee privately tells one of the engineers that a competing firm submitted a lower bid and suggests that the engineer revise her bid to beat the competitor's price.What should the engineer do?

   • Submit a revised lower bid because the project has not yet been awarded.
   • Withdraw from the bidding process immediately.
   • Do not revise the bid and remain under consideration based on the original submitted bid.
   • Ask the city employee for the exact amount of the competing bid before deciding.

10. An engineering consultant prepares plans and specifications for a public water distribution project. During the bidding period, one contractor requests additional design details that would help prepare a more accurate bid.Which of the following is the most appropriate action?

    • Provide the additional information only to the contractor that requested it.
    • Provide the information only to contractors the consultant considers qualified.
    • Obtain the client's approval and make the additional information available equally to all prospective bidders.
    • Refuse to provide any additional information once bidding has begun.

11. A professional engineer is asked to sign and seal structural drawings that were prepared by another engineer.Under which circumstance may the professional engineer appropriately sign and seal the drawings?

    • Whenever the engineer holds an active professional engineering license.
    • Only if the engineer is competent in the relevant engineering discipline and exercised responsible charge over the preparation of the documents.
    • Whenever the original engineer gives verbal permission.
    • Only when the original engineer is unavailable to sign the documents.

12. Which of the following are commonly required steps on the traditional path toward professional engineering licensure?Select all that apply.

    • Pass the Fundamentals of Engineering (FE) exam.
    • Obtain qualifying engineering experience.
    • Become a member of the National Society of Professional Engineers.
    • Pass the Principles and Practice of Engineering (PE) exam.

13. A licensed engineer is retained as an expert witness in a lawsuit involving the failure of a retaining wall.When providing professional testimony, the engineer should:

    • Provide opinions that support the attorney who hired the engineer, even if other interpretations are possible.
    • Evaluate the personal character of the engineer who designed the wall.
    • Provide a complete, truthful, and objective technical analysis within the engineer's area of competence.
    • Avoid discussing technical findings that could weaken the client's legal position.

14. You deposit an arithmetic gradient of $$\$500$$ per month. The deposits are $$\$500$$ at the end of month $$2$$, $$\$1,000$$ at the end of month $$3$$, $$\$1,500$$ at the end of month $$4$$, $$\$2,000$$ at the end of month $$5$$, and $$\$2,500$$ at the end of month $$6$$.If the interest rate is $$1.5\%$$ per month, determine the present value of the gradient at $$t=0$$.

    • $$\$985.10$$
    • $$\$1,228.30$$
    • $$\$4,711.45$$
    • $$\$6,997.80$$

15. You want to have $$\$15,000$$ in an investment account $$9$$ years from now. The account earns $$8\%$$ interest compounded annually.How much should you invest today?

    • $$\$6,250$$
    • $$\$7,504$$
    • $$\$8,750$$
    • $$\$9,612$$

16. A dealership offers a vehicle for $$\$24,000$$ with no payment required for $$3$$ years and no interest charged during that period. At the time of purchase, you place money into a savings account earning $$5\%$$ interest compounded annually.How much money should you deposit today so that the account will contain $$\$24,000$$ at the end of $$3$$ years?

    • $$\$18,500$$
    • $$\$19,860$$
    • $$\$20,732$$
    • $$\$22,857$$

17. You will make annual payments of $$\$400$$ at the end of each year for the next $$8$$ years. If the interest rate is $$5\%$$ compounded annually, what is the present worth of these payments?

    • $$\$2,145$$
    • $$\$2,585$$
    • $$\$3,200$$
    • $$\$3,619$$

18. An engineering firm must choose between four pieces of comparable equipment. Each piece of equipment has a useful life of $$7$$ years.Equipment A: First cost $$=\$28,000$$, annual cost $$=\$7,200$$, salvage value $$=\$3,000$$Equipment B: First cost $$=\$34,000$$, annual cost $$=\$5,800$$, salvage value $$=\$4,000$$Equipment C: First cost $$=\$24,000$$, annual cost $$=\$8,000$$, salvage value $$=\$2,500$$Equipment D: First cost $$=\$39,000$$, annual cost $$=\$4,800$$, salvage value $$=\$4,500$$The discount rate is $$10\%$$. Ignore taxes.The two most preferable equipment alternatives based on least present cost, and the approximate difference between their present worth values, are:

    • Equipment A and Equipment C, $$\$151$$
    • Equipment B and Equipment D, $$\$125$$
    • Equipment A and Equipment B, $$\$1,329$$
    • Equipment C and Equipment D, $$\$1,605$$

19. In the figure, three forces are acting on a fixed ring. Find the magnitude and direction of the reaction force of the ring.$$F_1=400\text{ N},\quad F_2=200\text{ N},\quad F_3=350\text{ N},\quad \alpha=20^\circ,\quad \beta=45^\circ$$

    • $$261\text{ N},\ 80.0^\circ$$
    • $$246\text{ N},\ 29.4^\circ$$
    • $$261\text{ N},\ 10.0^\circ$$
    • $$246\text{ N},\ 60.6^\circ$$

20. Determine the $$x$$-coordinate of the centroid $$\bar{x}$$ for the shaded area bounded by the parabolic curve $$y=0.25x^2$$, the $$x$$-axis, and the vertical line $$x=4\text{ m}$$.

    • $$2.00\text{ m}$$
    • $$2.67\text{ m}$$
    • $$3.00\text{ m}$$
    • $$3.33\text{ m}$$

21. Determine the most nearly correct radius of gyration with respect to the centroidal $$y$$-axis, $$r_y$$, for the symmetric I-section shown.

    • $$1.48\text{ in}$$
    • $$2.19\text{ in}$$
    • $$2.89\text{ in}$$
    • $$4.78\text{ in}$$

22. A concrete block is placed on a wooden plank. The coefficient of static friction between the block and plank is $$0.35$$. The angle between the wooden plank and the horizontal surface was originally zero. Gradually, the plank is lifted. Determine the angle at which the block begins to slide.

    • $$19.3^\circ$$
    • $$19.7^\circ$$
    • $$20.3^\circ$$
    • $$20.8^\circ$$

23. Determine the force in member $$BC$$ in the plane truss shown below. Joint $$A$$ is pinned, and joint $$C$$ can slide vertically. A downward force of $$1\text{ kN}$$ is applied at joint $$B$$.

    • $$1\text{ kN}$$ (tension)
    • $$1\text{ kN}$$ (compression)
    • $$2\text{ kN}$$ (tension)
    • $$2\text{ kN}$$ (compression)

24. A planar roof truss is subjected to a horizontal wind load $$P=20\text{ kN}$$ at the top apex joint $$D$$. It is supported by a pin at joint $$A$$ and a roller at joint $$C$$. The horizontal bottom chord consists of members $$AB$$ and $$BC$$, each $$4\text{ m}$$ long. Joint $$D$$ is located $$3\text{ m}$$ vertically above joint $$B$$.Determine the internal axial force in bottom chord member $$AB$$.

    • $$10.0\text{ kN}$$ (tension)
    • $$10.0\text{ kN}$$ (compression)
    • $$12.5\text{ kN}$$ (tension)
    • $$20.0\text{ kN}$$ (compression)

25. A cube-shaped block with dimensions of $$1\text{ m}\times1\text{ m}\times1\text{ m}$$ is placed on a flat horizontal surface. The block has a density of $$2,500\text{ kg/m}^3$$. A horizontal force of $$10\text{ kN}$$ is applied to the centroid of the block. If the coefficient of static friction between the block and the surface is $$\mu_s=0.25$$, which of the following statements is most nearly correct regarding the block's impending motion?

    • The block will not move; the maximum static friction force is $$6.13\text{ kN}$$.
    • The block will move; the maximum static friction force is $$6.13\text{ kN}$$.
    • The block will not move; the maximum static friction force is $$24.5\text{ kN}$$.
    • The block will move; the maximum static friction force is $$2.50\text{ kN}$$.

26. Determine the resulting moment about the base $$A$$ of the structure shown due to the forces applied at point $$C$$. Point $$C$$ is located $$28$$ ft to the left and $$17$$ ft above the base. A horizontal $$50$$ lb force acts to the right at $$C$$, and a vertical $$120$$ lb force acts downward at $$C$$.

    • $$610\text{ ft}\cdot\text{lb}$$
    • $$1,400\text{ ft}\cdot\text{lb}$$
    • $$2,150\text{ ft}\cdot\text{lb}$$
    • $$2,510\text{ ft}\cdot\text{lb}$$

27. A simply supported beam with a $$10$$ ft span is subjected to a triangular distributed load that increases from $$0\text{ kips/ft}$$ at support $$A$$ on the left to $$20\text{ kips/ft}$$ at support $$B$$ on the right. The vertical reaction forces $$R_A$$ and $$R_B$$ are most nearly:

    • $$R_A=33.3\text{ kips},\quad R_B=66.7\text{ kips}$$
    • $$R_A=50.0\text{ kips},\quad R_B=50.0\text{ kips}$$
    • $$R_A=66.7\text{ kips},\quad R_B=33.3\text{ kips}$$
    • $$R_A=100.0\text{ kips},\quad R_B=100.0\text{ kips}$$

28. A square-thread screw jack is used to lower a heavy mechanical component. The axial load on the jack is $$P=15,000\text{ N}$$. The mean thread radius is $$r=0.030\text{ m}$$, and the pitch angle of the thread is $$\alpha=5^\circ$$.If the coefficient of static friction is $$\mu=0.12$$, what is the magnitude of the external moment $$M$$ required for screw loosening?

    • $$11.6\text{ N}\cdot\text{m}$$
    • $$14.5\text{ N}\cdot\text{m}$$
    • $$27.0\text{ N}\cdot\text{m}$$
    • $$54.0\text{ N}\cdot\text{m}$$

29. A car is traveling at $$54\text{ mph}$$ when the driver sees a traffic light turn yellow. The yellow phase lasts for $$4.0\text{ s}$$, and the intersection ahead is $$180\text{ ft}$$ wide. What constant acceleration is required for the car to just clear the intersection at the exact moment the light turns red?

    • $$-17.1\text{ ft/s}^2$$
    • $$-8.6\text{ ft/s}^2$$
    • $$4.5\text{ ft/s}^2$$
    • $$17.1\text{ ft/s}^2$$

30. A pilot accelerates an airplane uniformly from rest for $$20$$ seconds before takeoff. If the acceleration of the airplane is $$8\text{ m/s}^2$$, how far does the airplane travel along the runway before taking off?

    • $$800\text{ m}$$
    • $$1,200\text{ m}$$
    • $$1,600\text{ m}$$
    • $$3,200\text{ m}$$

31. A car is traveling at $$90\text{ km/hr}$$ when the driver sees an obstruction in the roadway. The brakes are immediately applied, producing a constant deceleration of $$5\text{ m/s}^2$$. How far does the car travel before coming to a complete stop?

    • $$31.3\text{ m}$$
    • $$50.0\text{ m}$$
    • $$62.5\text{ m}$$
    • $$125\text{ m}$$

32. A train is traveling at $$72\text{ km/hr}$$ when the engineer applies the emergency brakes. The train experiences a constant deceleration of $$4\text{ m/s}^2$$. How far will the train travel before stopping?

    • $$25\text{ m}$$
    • $$40\text{ m}$$
    • $$50\text{ m}$$
    • $$100\text{ m}$$

33. An astronaut weighs $$784.8\text{ N}$$ on Earth. On another planet, the astronaut weighs $$960\text{ N}$$. What is the gravitational acceleration on the other planet?

    • $$8.00\text{ m/s}^2$$
    • $$9.81\text{ m/s}^2$$
    • $$12.0\text{ m/s}^2$$
    • $$15.3\text{ m/s}^2$$

34. A cantilevered structural member carries a constant distributed load over its entire span. Which statement best describes its elastic deformation?

    • Rotation is greatest at the fixed support.
    • Vertical displacement is greatest at the fixed support.
    • Rotation reaches its greatest magnitude at the unsupported end.
    • Rotation is zero at the unsupported end.

35. At a point in a structural component, the two principal stresses are $$420\text{ kPa}$$ in tension and $$180\text{ kPa}$$ in compression. What is the maximum in-plane shear stress at that point?

    • $$120\text{ kPa}$$
    • $$210\text{ kPa}$$
    • $$300\text{ kPa}$$
    • $$600\text{ kPa}$$

36. A plane-stress condition has principal stresses of $$140\text{ MPa}$$ and $$-20\text{ MPa}$$. For the corresponding Mohr's circle, what are the center $$C$$ and radius $$R$$?

    • $$C=60\text{ MPa},\quad R=80\text{ MPa}$$
    • $$C=80\text{ MPa},\quad R=60\text{ MPa}$$
    • $$C=60\text{ MPa},\quad R=160\text{ MPa}$$
    • $$C=-60\text{ MPa},\quad R=80\text{ MPa}$$

37. A metal tension member has an original length of $$8.00$$ ft. After an axial load is applied, its measured length becomes $$8.032$$ ft. What is the engineering normal strain?

    • $$0.002$$
    • $$0.004$$
    • $$0.032$$
    • $$0.040$$

38. During a tensile test, a rod experiences an axial strain of $$0.0025$$ and increases in length by $$15\text{ mm}$$. What was the rod's original length?

    • $$0.60\text{ m}$$
    • $$3.0\text{ m}$$
    • $$6.0\text{ m}$$
    • $$37.5\text{ m}$$

39. A brass tie rod is heated while remaining free to expand. Its temperature rises by $$30^\circ\text{C}$$, producing an increase in length of $$0.36\text{ mm}$$. If the coefficient of thermal expansion of brass is $$19\times10^{-6}/^\circ\text{C}$$, what was the rod's original length?

    • $$0.316\text{ m}$$
    • $$0.474\text{ m}$$
    • $$0.632\text{ m}$$
    • $$1.263\text{ m}$$

40. An isotropic elastic material has a modulus of elasticity of $$200\text{ GPa}$$ and a shear modulus of $$76.9\text{ GPa}$$. What is the material's Poisson's ratio?

    • $$0.20$$
    • $$0.25$$
    • $$0.30$$
    • $$0.40$$

41. A small element in a steel connection is subjected to a tensile normal stress of $$50\text{ ksi}$$ in the $$x$$-direction, a compressive normal stress of $$10\text{ ksi}$$ in the $$y$$-direction, and an in-plane shear stress of $$12\text{ ksi}$$. The maximum in-plane shear stress in the element is most nearly:

    • $$12.0\text{ ksi}$$
    • $$20.0\text{ ksi}$$
    • $$32.3\text{ ksi}$$
    • $$60.0\text{ ksi}$$

42. A heat-treated steel component is found to have significantly greater hardness than the same steel in its annealed condition. Which material property would most likely also increase?

    • Ductility
    • Yield strength
    • Formability
    • Electrical conductivity

43. A lubricating fluid has a specific gravity of $$1.18$$ and an absolute dynamic viscosity of $$0.84\text{ kg/(m}\cdot\text{s)}$$. If the density of water is $$1,000\text{ kg/m}^3$$, the kinematic viscosity of the fluid is most nearly:

    • $$5.93\times10^{-4}\text{ m}^2/\text{s}$$
    • $$7.12\times10^{-4}\text{ m}^2/\text{s}$$
    • $$8.40\times10^{-4}\text{ m}^2/\text{s}$$
    • $$9.91\times10^{-4}\text{ m}^2/\text{s}$$

44. A rectangular gate is $$3\text{ m}$$ long and $$2\text{ m}$$ wide and is installed on a surface inclined $$30^\circ$$ from the horizontal. The upper edge of the gate is located $$1.5\text{ m}$$ vertically below the water surface.Determine the magnitude of the resultant hydrostatic force and the vertical depth of its line of action below the water surface.

    • $$88\text{ kN},\ 1.83\text{ m}$$
    • $$132\text{ kN},\ 2.33\text{ m}$$
    • $$176\text{ kN},\ 2.25\text{ m}$$
    • $$265\text{ kN},\ 3.17\text{ m}$$

45. Water flows through a $$0.30$$-m-diameter pipe at a flow rate of $$0.09\text{ m}^3/\text{s}$$. At a particular section, the gauge pressure is $$150\text{ kPa}$$ and the pipe centerline is $$8.0\text{ m}$$ above the reference datum.Neglecting energy losses, what is the total energy head at this section?

    • $$15.4\text{ m}$$
    • $$18.1\text{ m}$$
    • $$23.4\text{ m}$$
    • $$31.7\text{ m}$$

46. A U-tube manometer containing water and mercury is connected to a pipe as shown. Determine the pressure in the pipe in pounds per square foot.

    • $$1,305\text{ psf}$$
    • $$1,716\text{ psf}$$
    • $$1,088\text{ psf}$$
    • $$817\text{ psf}$$

47. Water flows steadily through a pipe from section $$1$$ to section $$2$$ with negligible energy loss. Find the diameter of the pipe at section $$2$$.

    • $$0.12\text{ m}$$
    • $$0.17\text{ m}$$
    • $$0.24\text{ m}$$
    • $$0.34\text{ m}$$

48. Water flows steadily from a large open reservoir at a rate of $$10\text{ ft}^3/\text{s}$$ through a $$10$$-in-diameter pipe. The pipe outlet is $$36$$ ft below the reservoir water surface. Both the reservoir surface and the pipe outlet are exposed to atmospheric pressure.Determine the total head loss between the reservoir and the pipe outlet.

    • $$25.6\text{ ft}$$
    • $$30.8\text{ ft}$$
    • $$36.0\text{ ft}$$
    • $$41.2\text{ ft}$$

49. A metal coupon used in a tensile test has an initial gauge length of $$180\text{ mm}$$. At fracture, the distance between the gauge marks is $$216\text{ mm}$$. Based on percent elongation, the ductility of the material is:

    • $$10\%$$
    • $$15\%$$
    • $$20\%$$
    • $$25\%$$

50. An engineer compares two plain-carbon steels that are otherwise similar. One steel has a higher carbon content. Which of the following changes would generally be expected in the higher-carbon steel?I. Greater yield strengthII. Lower ductilityIII. Substantially greater modulus of elasticityIV. Greater tensile strength

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

51. During a tensile test, a steel specimen first begins to undergo permanent deformation and later reaches its highest engineering stress. Which statement correctly identifies these two material properties?

    • Yield strength marks the onset of permanent deformation, while ultimate tensile strength is the maximum engineering stress reached during the test.
    • Ultimate tensile strength marks the onset of permanent deformation, while yield strength is the stress at fracture.
    • Yield strength is the maximum stress reached before fracture, while ultimate tensile strength marks the end of elastic behavior.
    • Yield strength and ultimate tensile strength represent the same point on the stress-strain curve.

52. Groundwater moves through a sandy soil layer with a hydraulic conductivity of $$6.0\times10^{-5}\text{ m/s}$$. The hydraulic head decreases by $$3.0\text{ m}$$ over a horizontal distance of $$10\text{ m}$$.What is the magnitude of the Darcy velocity through the soil?

    • $$1.2\times10^{-5}\text{ m/s}$$
    • $$1.8\times10^{-5}\text{ m/s}$$
    • $$3.0\times10^{-5}\text{ m/s}$$
    • $$6.0\times10^{-5}\text{ m/s}$$

53. A vertical tube is open to the atmosphere at the top. The bottom $$20\text{ cm}$$ of the tube contains water, the next $$12\text{ cm}$$ contains oil with a specific gravity of $$0.75$$, and the upper $$8\text{ cm}$$ contains air. What is the gauge pressure at the bottom of the tube?

    • $$1,960\text{ Pa}$$
    • $$2,550\text{ Pa}$$
    • $$2,845\text{ Pa}$$
    • $$3,630\text{ Pa}$$

54. A vertical rectangular flood-control gate is $$2.40\text{ m}$$ high and $$1.20\text{ m}$$ wide. The gate is hinged along its bottom edge and retains a liquid with a density of $$1,200\text{ kg/m}^3$$. The liquid surface is level with the top of the gate. A horizontal force $$F$$ is applied at the top edge of the gate to keep it from rotating about the hinge.What is the magnitude of $$F$$ most nearly?

    • $$6.8\text{ kN}$$
    • $$13.6\text{ kN}$$
    • $$27.1\text{ kN}$$
    • $$40.7\text{ kN}$$

55. Four materials are tested in tension. Their approximate strain at yielding and strain at fracture are shown below:Which material undergoes the greatest amount of plastic deformation before fracture?

    • Material P
    • Material Q
    • Material R
    • Material S