ME102-FinalExam-Answers

The idealized schematic below could be thought of as an umbrella stand or a fishing rod holder. In the schematic, a narrow dowel is placed in a receptacle. The dowel is subject to a downward load F_L at the outer end. F_L= 50 N. We may neglect the force due to gravity acting on the dowel. The angle α = 28 degrees. The dowel is 1 meter long, and the distance d is 40 cm. The dowel is not moving. The force acting at point A is normal to the axis of the dowel (friction is negligible there). What is the net force acting at the end of the dowel from the multiple contact points near B?

Choose one answer.

	a. 70.26 N
	b. 66.22 N
	c. 23.47 N
	d. 50 N
	e. 93.47 N

Question 2

Choose one answer.

	a. 70.26 N
	b. 110.37 N
	c. 23.47 N
	d. 50.00 N
	e. 66.22 N

Question 3

The idealized schematic below could be thought of as an umbrella stand or a fishing rod holder. In the schematic, a narrow dowel is placed in a receptacle. The dowel is subject to a downward load F_L at the outer end. F_L= 50 N. We may neglect the force due to gravity acting on the dowel. The angle α = 38 degrees. The dowel is 1 meter long, and the distance d is 40 cm. The dowel is not moving. The force acting at point A is normal to the axis of the dowel (friction is negligible there). What is the net force acting at the end of the dowel from the multiple contact points near B?

Choose one answer.

	a. 50.00 N
	b. 110.367 N
	c. 70.26 N
	d. 66.22 N
	e. 66.64 N

Question 4

Which of the following units are appropriate for expressing pressure?

Choose one answer.

	a. N/m²
	b. N/m
	c. lb_m
	d. N/s
	e. lb_f/s

Question 5

Convert a pressure of 2 atmospheres to units of millimeters of water (at the earth’s surface). Which of the following best corresponds to that result?

Choose one answer.

	a. 67.8
	b. 32.4
	c. 20664
	d. 101325
	e. 202650

Question 6

Which of the following best corresponds to a speed of 50,000 furlongs/fortnight in terms of miles per hour?
1 furlong = 1/8 mile
1 fortnight = 2 weeks

Choose one answer.

	a. 50
	b. 38
	c. 72
	d. 19
	e. 12

Question 7

Which of the following is true for two vectors for which the dot product is zero?

Choose one answer.

	a. They are perpendicular (orthogonal).
	b. They are parallel.
	c. They are coplanar.
	d. They form a 45 degree angle with respect to one another.
	e. They are antiparallel.

Question 8

Calculate the dot product of y = 2 i + 4 j + 8 k and z = 6 i + 4 j + 2 k. Which of the following matches the result?

Choose one answer.

	a. 12
	b. 16
	c. 72
	d. 38
	e. 44

Question 9

Calculate the cross product of y = 2 i + 4 j + 8 k and z = 6 i + 4 j + 2 k.Which of the following best matches the result?

Choose one answer.

	a. 28 i + 12 j + 8 k
	b. 8 i + 48 j + 8 k
	c. -32 i + -4 j -24 k
	d. 2 i -12 j + 8 k
	e. -24 i + 44 j -16 k

Question 10

Find the angle between the two vectors y = 2 i + 4 j + 8 k and z = 6 i + 4 j + 2 k in degrees. Which of the following best matches the result?

Choose one answer.

	a. 55 degrees
	b. 50 degrees
	c. 70 degrees
	d. 32 degrees
	e. 5 degrees

Question 11

A projectile is launched at an angle of 60 degrees from the horizontal at a speed of 1275 feet per second. What is the horizontal component of the projectile velocity in feet per second?

Choose one answer.

	a. 425 ft/sec
	b. 638 ft/sec
	c. 736 ft/sec
	d. 1275 ft/sec
	e. 901 ft/sec

Question 12

Two forces acting at an angle of 60 degrees with respect to one another result in a force of 14 N. If they act at right angles, they result in a force of 11.662 N. What are the magnitudes of the two forces?

Choose one answer.

	a. 12 N and 7 N
	b. 10 N and 6 N
	c. 9 N and 14 N
	d. 15 N and 12 N
	e. 7 N and 8 N

Question 13

Two forces of magnitude 9 N and 12 N act on a point. The angle between the two forces is 30 degrees. Estimate the resultant force.

Choose one answer.

	a. 5 N
	b. 10 N
	c. 20 N
	d. 25 N
	e. 30 N

Question 14

A horizontal force is applied to a block of weight of 1500 N to hold it in position on an inclined plane which makes a 30 degree with the horizontal. Assuming no friction, calculate the horizontal force.

Choose one answer.

	a. 866 N
	b. 423 N
	c. 978 N
	d. 1232 N
	e. 823 N

Question 15

In the figure below, the angle alpha is 18 degrees. The block B has a mass of 10 kg and is subject to a gravitational acceleration of 9.8 m²/s straight down. Block A is being held in place by external forces.

If the coefficient of static friction is 0.05, then what is the horizontal force required to start block B moving to the left?

Choose one answer.

	a. 34.9 N
	b. 4.7 N
	c. 30.3 N
	d. 37.3 N
	e. 42.8 N

Question 16

In the figure below, the angle alpha is 33 degrees. The block B has a mass of 10 kg and is subject to a gravitational acceleration of 9.8 m²/s straight down. Block A is being held in place by external forces.

If the coefficient of static friction is 0.05, then what is the horizontal force required to start block B moving to the left?

Choose one answer.

	a. 70.8 N
	b. 30.7 N
	c. 37.4 N
	d. 0.57 N
	e. 98 N

Question 17

If the coefficient of static friction is 0.07, then what is the horizontal force required to start block B moving to the left?

Choose one answer.

	a. 70.8 N
	b. 73.9 N
	c. 75.8 N
	d. 33.7 N
	e. 98 N

Question 18

As illustrated in the figure below, block B resides on an incline. The static coefficient of friction between the block and the incline is 0.343. At what value of the inclination (in degrees) will the block begin to slide under the influence of vertical gravitational acceleration?

Choose one answer.

	a. 21 degrees
	b. 2 degrees
	c. 19 degees
	d. 32 degrees
	e. 26 degrees

Question 19

As illustrated in the figure below, block B resides on an incline. The static coefficient of friction between the block and the incline is 0.38. At what value of the inclination (in degrees) will the block begin to slide under the influence of vertical gravitational acceleration?

Choose one answer.

	a. 21 degrees
	b. 2 degrees
	c. 7 degees
	d. 32 degrees
	e. 26 degrees

Question 20

In the schematic below, the block B has a mass of 25 kg. The coefficient of static friction between the block and the ramp is 0.42. The angle alpha is 0.19 radians. What is the magnitude of the force F_Rrequired to keep the block from sliding under the influence of a vertical gravitational acceleration of 9.8 m²/s?

Choose one answer.

	a. 42 N
	b. 12 N
	c. 245 N
	d. 246 N
	e. 46 N

Question 21

In the schematic below, the block B has a mass of 18 kg. The coefficient of static friction between the block and the ramp is 0.42. The angle alpha is 0.25 radians. What is the magnitude of the force F_Rrequired to keep the block from sliding under the influence of a vertical gravitational acceleration of 9.8 m²/s?

Choose one answer.

	a. 61 N
	b. 44 N
	c. 245 N
	d. 246 N
	e. 46 N

Question 22

In the schematic below, the block B has a mass of 25 kg. The coefficient of static friction between the block and the ramp is 0.42. The angle alpha is 0.25 radians. What is the magnitude of the force F_Rrequired to keep the block from sliding under the influence of a vertical gravitational acceleration of 9.8 m²/s?

Choose one answer.

	a. 61 N
	b. 44 N
	c. 245 N
	d. 246 N
	e. 46 N

Question 23

As illustrated in the figure below, block B resides on an incline. The static coefficient of friction between the block and the incline is 0.488. At what value of the inclination (in degrees) will the block begin to slide under the influence of vertical gravitational acceleration?

Choose one answer.

	a. 21 degrees
	b. 2 degrees
	c. 19 degees
	d. 32 degrees
	e. 26 degrees

Question 24

The coefficient of static friction between a belt and a circular pulley is 0.62. The contact length between the belt and the pulley subtends an angle of 130 degrees. What is the ratio of belt tensions on the tight (pulling) side to the loose side of the pulley that can be accommodated without the belt slipping?

Choose one answer.

	a. 2.2
	b. 0.62
	c. 4.1
	d. 4023
	e. 1x10³⁵

Question 25

The coefficient of static friction between a belt and a circular pulley is 0.57. The contact length between the belt and the pulley subtends an angle of 150 degrees. What is the ratio of belt tensions on the tight (pulling) side to the loose side of the pulley that can be accommodated without the belt slipping?

Choose one answer.

	a. 4.4
	b. 2.6
	c. 1.5 x 10³⁵
	d. 0.57
	e. 7.1

Question 26

Consider three collinear horizontal forces acting on a rigid body. Their magnitudes are 200 N, 100 N, and 300 N. All of the forces are acting in the same direction. Determine the resultant of the forces.

Choose one answer.

	a. 200 N
	b. 300 N
	c. 880 N
	d. 600 N
	e. 500 N

Question 27

Consider three collinear horizontal forces acting on a rigid body. Their magnitudes are 20 N, 10 N, and 30 N. The force 10 N opposes the other two forces. Determine the resultant of the forces.

Choose one answer.

	a. 5 N
	b. 40 N
	c. 50 N
	d. 60 N
	e. 30 N

Question 28

In the diagram below, the angle alpha is 60 degrees and the angle beta is 150 degrees. Which of the following statements must be true in order for the particle at the center to not accelerate under the influence of forces F1, F2, and F3?

Choose one answer.

	a. F1, F2, and F3 must all be of equal magnitude.
	b. All forces must be zero.
	c. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(30 degrees) \|F2\|.
	d. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(60 degrees) \|F2\|.
	e. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 sin(30 degrees) \|F2\|.

Question 29

Consider a rope 5 m long running from points A to B as in the figure below. The two walls are only 3 m apart; therefore, the rope sags. The difference in elevation of points A and B is 1 m. Along the rope, a frictionless pulley suspends a load of 200 N. Calculate the tension in the rope at equilibrium.

Choose one answer.

	a. 125 N
	b. 250 N
	c. 175 N
	d. 75 N
	e. 50 N

Question 30

Consider a rope 5 m long running from points A to B as in the figure below. The two walls are only 3 m apart; therefore, the rope sags. The difference in elevation of points A and B is 1 m. Along the rope, a frictionless pulley suspends a 200 N weight. When the system is at equilibrium, calculate the horizontal distance from the left wall to the weight.

Choose one answer.

	a. 0.55 m
	b. 1.25 m
	c. 1.125 m
	d. 2.25 m
	e. 0.33 m

Question 31

Consider a rope 5 m long running from points A to B as in the figure below. The two walls are only 3 m apart; therefore, the rope sags. The difference in elevation of points A and B is 1 m. Along the rope, a frictionless pulley suspends a 200 N weight. When the system is at equilibrium, calculate the vertical distance from point A to the lowest point on the rope.

Choose one answer.

	a. 0.55 m
	b. 1.25 m
	c. 1.125 m
	d. 2.25 m
	e. 1.5 m

Question 32

In the diagram below, the angle alpha is 50 degrees and the angle beta is 155 degrees. Which of the following statements must be true in order for the particle at the center to not accelerate under the influence of forces F1, F2, and F3?

Choose one answer.

	a. F1, F2, and F3 must all be of equal magnitude.
	b. All forces must be zero.
	c. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(25 degrees) \|F2\|.
	d. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(60 degrees) \|F2\|.
	e. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 sin(30 degrees) \|F2\|.

Question 33

In the diagram below, the angle alpha is 120 degrees and the angle beta is 120 degrees. Which of the following statements must be true in order for the particle at the center to not accelerate under the influence of forces F1, F2, and F3?

Choose one answer.

	a. F1, F2, and F3 must all be of equal magnitude.
	b. All forces must be zero.
	c. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(30 degrees) \|F2\|.
	d. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 sin(30 degrees) \|F2\|.
	e. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 sin(45 degrees) \|F2\|.

Question 34

The coefficient of static friction between a belt and a circular pulley is 0.57. The contact length between the belt and the pulley subtends an angle of 120 degrees. What is the ratio of belt tensions on the tight (pulling) side to the loose side of the pulley that can be accommodated without the belt slipping?

Choose one answer.

	a. 4.4
	b. 2.6
	c. 1.5 x 10³⁵
	d. 0.57
	e. 3.3

Question 35

Consider a wire suspended from a ceiling at points A and D and bearing two loads F1 = 20 kN and F2 = 25 kN at points C and D, respectively. The angles alpha and beta are 30 and 60 degrees, respectively. Calculate the tension in the wire segment AB.

Choose one answer.

	a. 190 kN
	b. 225 kN
	c. 427 kN
	d. 390 kN
	e. 475 kN

Question 36

Choose one answer.

	a. 190 kN
	b. 225 kN
	c. 427 kN
	d. 390 kN
	e. 475 kN

Question 37

Choose one answer.

	a. 190 kN
	b. 225 kN
	c. 238 kN
	d. 390 kN
	e. 475 kN

Question 38

Consider a circular cylinder of diameter 16 cm. The cylinder is open at both ends and placed on a smooth horizontal plane. There are 2 spheres inside the cylinder. The diameters of the spheres are 8 cm and 12 cm. The spheres weigh 10 N and 30 N respectively. Calculate the minimum weight of the cylinder so it will not tip over.

Choose one answer.

	a. 7.5 N
	b. 15 N
	c. 3.5 N
	d. 8.5 N
	e. 12 N

Question 39

Which of the following formulas correctly describes the area moment of inertia for an object with elements a distance r from the axis of interest and with local mass density m?

Choose one answer.

	a. ∫ r ² dA
	b. ∫ r ³ dA
	c. ∫ m r ² dA
	d. ∫ r m² dA
	e. ∫ mr ⁴ dA

Question 40

Which of the following is an appropriate unit for an area moment of inertia?

Choose one answer.

	a. L ⁴
	b. M L ⁴
	c. L ²
	d. M ² L ²
	e. M ² L ³

Question 41

Which of the following correctly relates the polar area moment of inertia (J0) to Ix and Iy?

Choose one answer.

	a. J0 = Ix + Iy
	b. J0 = Ix ² + Iy ²
	c. J0 = sqrt (Ix ² + Iy ²)
	d. J0 = 1/2 Ix ² + 1/2 Iy ²
	e. J0 = 1/2 Ix + 1/2 Iy

Question 42

In the figure below, if a = 1 m, b = 2 m, c = 3 m, and d = 1 m, then what is the area moment inertia of the shape about the x-axis?

Choose one answer.

	a. 26/3 m ⁴
	b. 8/3 m ⁴
	c. 6/3 m ⁴
	d. 6/3 m ²
	e. 4 m ³

Question 43

In the figure below, if a = 1 m, b = 2 m, c = 3 m, and d = 1 m, then what is the area moment inertia of the shape about the y-axis?

Choose one answer.

	a. 63/3 m ⁴
	b. 5 m ⁴
	c. 5 m ³
	d. 4 m ²
	e. 16/3 m²

Question 44

In the figure below, if a = 1 m, b = 2 m, c = 3 m, and d = 1 m, then what is the area moment inertia of the shape about the z-axis?

Choose one answer.

	a. 33 1/3 m ⁴
	b. 7 m ⁴
	c. 3 m ²
	d. 8 m ²
	e. 89/3 m ⁴

Question 45

Which of the following formulas correctly expresses the mass moment of inertia I for a specimen of mass density rho, mass m, and volume V? Here, l is the distance of a volume element dV from the axis of rotation.

Choose one answer.

	a. I = ∫_v l ² ρ dV
	b. I = ∫_v m ρ dV
	c. I = ∫_v m ² ρ dV
	d. I = ∫_v l ² ρ/m dV
	e. I = ∫_v m/V ρ dV

Question 46

Which of the following formulas correctly expresses the relationship between the mass moment of inertia I and the radius of gyration k for an object of mass m?

Choose one answer.

	a. I = m k ²
	b. I = m k ⁰
	c. I = m k ^-2
	d. I = m k ^m
	e. I = m k ¹

Question 47

Which of the following is consistent with the parallel axis theorem for the mass moment of inertia?

I. The mass moment of inertia of an object about an axis through the center of mass is smaller than that about any other axis in the same direction.

II. The mass moments of inertia of an object about any parallel axes are identical.

III. The mass moment of inertia of an object about an axis (a) is equal to the moment about an axis (b) through the center of mass plus the mass times the square of the distance from (a) to (b).

IV. The mass moment inertia about parallel axes is proportional to the square of the separation between axes.

Choose one answer.

	a. II only
	b. I and III only
	c. IV only
	d. III only
	e. III and IV only

Question 48

The box below extends from x= e to x = e + a, from y = f to y=f+c, and from z = d to z = d+b and has a uniform density rho (kg/m3). What is the mass moment inertia of the box about the y axis?

Choose one answer.

	a. ((c+a)³ - a³)/3 ρ bc
	b. ((e+a)³ - a³)/3 ρ ac
	c. ((e+a)³ - a³)/3 ρ bc
	d. ((e+a)³ - a³)/3 ρ bc³
	e. ((e+a)³ - a³)/ ρ bc

Question 49

The box below extends from x= e to x = e + a, from y = f to y=f+c, and from z = d to z = d+b and has a uniform density rho (kg/m3). What is the mass moment inertia of the box about the x axis?

Choose one answer.

	a. ((f+c)³ - f³ )/3 ab ρ
	b. ((f+d)³ - f³ )/3 ab ρ
	c. ((e+c)³ - e³ )/3 ab ρ
	d. abc ρ
	e. bd ρ

Question 50

The box below extends from x= e to x = e + a, from y = f to y=f+c, and from z = d to z = d+b and has a uniform density rho (kg/m3). What is the mass moment inertia of the box about the z axis?

Choose one answer.

	a. ((d+b)² -d²) ac ρ/2
	b. ((d+b)³ -d³) ab ρ
	c. ((d+b)³ -d³) ac ρ
	d. ((d+b)³ -d³) ac ρ/3
	e. ((d+b)³ -d³) ac ρ/9

Question 51

What is the appropriate unit for a mass moment of inertia?

Choose one answer.

	a. M T L
	b. M L ³
	c. M L ²
	d. L ⁴
	e. M/L

Question 52

Which of the following statements best describes an elastic material?

Choose one answer.

	a. An elastic material gradually deforms under load and rebounds instantaneously when the load is removed.
	b. An elastic material deforms instantaneously and reversibly to changes in load.
	c. An elastic material deforms instantaneously under a load and gradually rebounds when the load is removed.
	d. An elastic material absorbs heat when stretched.
	e. An elastic material stretches under load but fractures at some critical load.

Question 53

How is the axial tensile strength of a cylindrical member related to the diameter of the member?

Choose one answer.

	a. It increases linearly with diameter.
	b. It increases in proportion to the cube of the diameter.
	c. It is independent of diameter.
	d. It increases approximately as the square of the diameter.
	e. It increases approximately as the square root of the diameter.

Question 54

Which of the following correctly describes stress in the sense used in mechanics?

Choose one answer.

	a. It is the vector sum of all forces acting on a system.
	b. It is the sum of all torques acting on a system.
	c. It is the square of the magnitude of the total force acting on a system.
	d. It is a loading force per unit area.
	e. It is a force per unit volume.

Question 55

A rod is being used to carry a tensile load of 5000 N. The ultimate tensile stress of the material used in the rod is 1000 MPa. What should be the absolute minimum diameter of the rod to safely carry the load?

Choose one answer.

	a. 5 mm
	b. 10 mm
	c. 2.5 mm
	d. 50 mm
	e. 0.5 mm

Question 56

A rod is used to carry a tensile load of 10000 lbf. The ultimate tensile stress of the material used in the rod is 1000 MPa. What should be the minimum diameter of the rod to safely carry the load?

Choose one answer.

	a. 20 mm
	b. 25 mm
	c. 50 mm
	d. 7.5 mm
	e. 2 mm

Question 57

A cylindrical rod is hung in a gravitational acceleration of 9.8 m/s². The ultimate tensile stress of the rod material is 1800 MPa. The density of the rod material is 4000 kg/m³. How long may we make the rod before it fails under its own weight?

Choose one answer.

	a. 1000 ft
	b. 52 miles
	c. 46 km
	d. 3 km
	e. 1.2 km

Question 58

A cylindrical rod is hung in a gravitational acceleration of 9.8 m/s². The ultimate tensile stress of the rod material is 1800 MPa. The density of the rod material is 1000 kg/m³. How long may we make the rod before it fails under its own weight?

Choose one answer.

	a. 46 km
	b. 12 km
	c. 184 km
	d. 1.8 km
	e. 0.2 km

Question 59

Which of the following is an appropriate unit for stiffness?

Choose one answer.

	a. lb_f
	b. lb_f / ft
	c. kg/m
	d. psi/ft
	e. lb_m/s

Question 60

Which of the following is an appropriate unit for Young’s modulus?

Choose one answer.

	a. kspi
	b. torr/ft
	c. Pa s
	d. N m
	e. N/yard

Question 61

A member of square cross section (10 mm on each side) and of 20 cm in length is subject to atensile load of 1 kN. The Young’s modulus of the material composing the member is 250 GPa.What is the extension of the member under load in mm?

Choose one answer.

	a. 12 mm
	b. 14 mm
	c. 80 mm
	d. 0.2 mm
	e. 8 mm

Question 62

A member of square cross section (15 mm on each side) and of 20 cm in length is subject to a tensile load of 1 kN. The Young’s modulus of the material composing the member is 250 GPa.What is the extension of the member under load?

Choose one answer.

	a. 0.53 inches
	b. 0.35 inches
	c. 3.6 mm
	d. 5 cm
	e. 22 mm

Question 63

Which of the following statements most closely describes Hooke’s law?

Choose one answer.

	a. Extension is proportional to tension.
	b. Extension varies as the square root of tension.
	c. Extension varies as the square of tension.
	d. Extension reaches a maximum after which fracture occurs.
	e. Fracturing is a gradual process that occurs in proportion to extension.

Question 64

Which of the following statements correctly describes the properties of metallic, ionic, and covalently bonded materials?

I. Bonding electrons in covalent materials are localized to specific small sets of atoms.

II. Electrons in ionic materials are localized to one atom.

III. Covalent materials are more brittle than ionic materials.

IV. Metallic materials share a pool of delocalized electrons.

V. Metallic materials do not share electrons between atoms.

Choose one answer.

	a. I and II
	b. I, II, and IV
	c. II, III, and V
	d. III and V
	e. V only

Question 65

The following curve is recorded in a tensile stress test for a rod of length 3 cm and diameter 10 mm. What is the ultimate tensile stress of the material?

Choose one answer.

	a. 28 MPa
	b. 280 MPa
	c. 13000 psi
	d. 12 psi
	e. 55 GPa

Question 66

The following curve is recorded in a tensile stress test for a rod of length 10 cm and diameter 50 mm. What is the modulus of elasticity of the material?

Choose one answer.

	a. 18 GPa
	b. 250 GPa
	c. 12 GPa
	d. 7 GPa
	e. 1.5 GPa

Question 67

The following curve is recorded in a tensile stress test for a rod of length 5 cm and diameter 3 mm. What is the ultimate tensile stress of the material?

Choose one answer.

	a. 9 GPa
	b. 7 GPa
	c. 12 GPa
	d. 1 GPa
	e. 3 GPa

Question 68

The following curve is recorded in a tensile stress test for a rod of length 5 cm and diameter 25 mm. What is the modulus of elasticity of the material?

Choose one answer.

	a. 243 GPa
	b. 142 GPa
	c. 285 GPa
	d. 12 GPa
	e. 1.2 TPa

Question 69

The following curve is recorded in a tensile stress test for a rod of length 5 cm and diameter 5 mm. What is the 0.1%-strain-offset yield stress of the material?

Choose one answer.

	a. 200 MPa
	b. 100 MPa
	c. 50 MPa
	d. 10 MPa
	e. 1 GPa

Question 70

The following curve is recorded in a tensile stress test for a rod of length 5 cm and diameter 1 mm. What is theapproximate yield stress of the material?

Choose one answer.

	a. 5 GPa
	b. 20 GPa
	c. 100 GPa
	d. 100 MPa
	e. 2 MPa

Question 71

Which of the following expressions best describes the rule of mixtures for the modulus of elasticity of a fiber reinforced composite with volume fractions V_{_fiber and V_medium and Young's moduli E_fiber and E_medium for stress in the fiber direction?}

Choose one answer.

	a. E_composite + V_fiber E_fiber + V_medium E_medium
	b. E_composite + V_fiber/ E_fiber + V_medium / E_medium
	c. 1/E_composite + V_fiber E_fiber + V_medium E_medium
	d. 1/E_composite + V_fiber /E_fiber + V_medium /E_medium
	e. E_composite = E_fiber + E_medium

Question 72

Which of the following statements best describes the rule of mixtures for the modulus of elasticity of a fiber reinforced composite for stress transverse to the fiber direction? The volume fractions and moduli of the individual phases are V_fiber and Vmedium and E_fiber and E_medium.

Choose one answer.

	a. 1/E_composite = V_fiber /E_fiber + V_medium/E_medium
	b. 1/E_composite = V_fiber E_fiber + V_mediumE_medium
	c. E_composite = V_fiber /E_fiber + V_mediumE_medium
	d. 1/E_composite = V_fiber E_fiber + V_mediumE_medium
	e. 1/E_composite = V_fiber E_fiber + V_medium/E_medium

Question 73

What is meant by the phrase composite material in engineering mechanics?

Choose one answer.

	a. A material that is improperly mixed
	b. A material consisting of two or more phases or materials at a molecular level
	c. A material that deforms in stages when exposed to stress
	d. A material that fractures unevenly when exposed to stress
	e. A material that is glued together from plates or fibers

Question 74

What would the rule of mixtures predict for the transverse modulus of elasticity for a 60-40% by volume mixture of fiber (E = 120 GPa) and polymer (E = 15 GPa), respectively?

Choose one answer.

	a. 32 GPa
	b. 16 GPa
	c. 8 GPa
	d. 68 GPa
	e. 115 GPa

Question 75

What would the rule of mixtures predict for the parallel modulus of elasticity for a 60-40% by volume mixture of fiber (E = 120 GPa) and polymer (E = 15 GPa)?

Choose one answer.

	a. 38 GPa
	b. 15 GPa
	c. 12 GPa
	d. 55 GPa
	e. 78 GPa

Question 76

Which of the following statements best describes the rule of mixtures as predictive for the behavior of fiber/polymer composite media?

Choose one answer.

	a. It is a good rule to keep in mind, but it may be unreliable for many materials.
	b. It is a well established rule that is applicable to a wide range of materials.
	c. It is a universal law that is applicable to all composites.
	d. It describes behaviors in the limits of small volume fractions of one phase or the other.
	e. It is an idealization that has not proven useful.

Question 77

How do engineering stress and engineering strain differ from actual stress and actual strain in a stress-strain curve measurement?

Choose one answer.

	a. Engineering stresses and strains are always reported in metric units.
	b. Engineering stresses and strains are calculated in terms of the undeformed or original cross-sectional area, but the acutal stresses and strains are calculated from the simultaneous areas.
	c. Engineering stresses and strains are calculated in terms of the simultaneous cross-sectional areas, but the acutal stresses and strains are calculated in terms of the original or undeformed areas.
	d. Engineering measures are always reported in powers of 1000. Actual stresses and strains may be reported in any system.
	e. Actual stresses and strains take into account thermal expansion; engineering calculations do not.

Question 78

How do brittle materials differ from ductile materials?

Choose one answer.

	a. Brittle materials fail more suddenly under stress; ductile materials yield before fracture.
	b. Ductile materials fail more suddenly under stress; brittle materials yield before fracture.
	c. Ductile materials have a lower yield stress than brittle materials.
	d. Brittle materials have a higher ultimate tensile strength than ductile materials.
	e. Brittle materials have a lower modulus of elasticity than ductile materials.

Question 79

Which of the following statements best describes the differences between elastic and plastic deformation?

Choose one answer.

	a. Plastic deformation stores energy; elastic deformation dissipates energy.
	b. Elastic deformation occurs in metals; plastic deformation occurs in polymers.
	c. Elasitc deformation occurs at higher temperatures than plastic deformation.
	d. Elastic deformation automatically reverses upon removal of the stress; plastic deformation does not.
	e. Elastic deformation is not as reproducible as plastic deformation.

Question 80

Which of the following statements best describes the differences between necking and drawing of mechanical specimens?

Choose one answer.

	a. They are synonymous.
	b. Necking refers to the strain hardening upon deformation; drawing refers to reduction in neck diameter.
	c. Drawing refers to the strain hardening upon deformation; necking refers to reduction in neck diameter.
	d. Necking refers to the reduction in cross sectional area under tension; drawing refers to the introduction of new material into a necked region.
	e. Drawing refers to the reduction in cross-sectional area under tension; necking refers to the introduction of new material into a drawn region.

Question 81

Estimate the strain hardening parameter for the material exhibitingthe stress-strain relationship in the figure below?

Choose one answer.

	a. 0.17
	b. 0.57
	c. 0.71
	d. Undefined
	e. 6.03

Question 82

Estimate the strain hardening parameter for the material exhibitingthe stress-strain relationship in the figure below?

Choose one answer.

	a. 0.03
	b. 0.08
	c. 0.005
	d. 0.17
	e. 0.32

Question 83

For a material with a Young’s modulus of 57 GPa, estimate the stored strain energy per unit volume for a linear elastic strain of 1%.

Choose one answer.

	a. 28 GPa
	b. 57 GPa
	c. 2.8 kPa
	d. 2.8 MPa
	e. 5.7 MPa

Question 84

For a material with a Young’s modulus of 112 GPa, estimate the stored strain energy per unit volume for a linear elastic strain of 0.05%.

Choose one answer.

	a. 28 GPa
	b. 14 GPa
	c. 2.8 kPa
	d. 2.8 MPa
	e. 1.4 MPa

Question 85

Which of the following are appropriate units for energy per unit area?

Choose one answer.

	a. Pa m
	b. N m
	c. psi
	d. dynes
	e. lb_f/s

Question 86

Which of the following is true for statically indeterminate trusses?

I. They are inherently unstable.

II. They deflect more than statically determinate trusses.

III. Consideration of deflection is necessary to solve for all internal forces.

IV. They require welded joints rather than pin-connected joints.

Choose one answer.

	a. II and IV only
	b. IV only
	c. II and III only
	d. III and IV
	e. III only

Question 87

A spherical pressure vessel is made of a material with an ultimate tensile strength of about 200 MPa. What pressure can a vessel that is 50 cm in diameter and 0.5 cm in wall thickness withstand?

Choose one answer.

	a. 8 x 10 ⁹ Pa
	b. 125 atm
	c. 78 atm
	d. 14.7 psi
	e. 8 x 10 ⁴ Pa

Question 88

A spherical pressure vessel is made of a material with a yield strength of about 200 MPa. What pressure can a vessel that is 25 cm in diameter and 0.4 cm in wall thickness withstand?

Choose one answer.

	a. 13 x 10 ⁶ Pa
	b. 12 atm
	c. 1300 atm
	d. 14.7 atm
	e. 101325 Pa

Question 89

A four inch inner diameter pipe with wall thickness 0.2 inches is pressurized to 150 psi. What is the percentage expansion in the pipe diameter upon pressurization if the Young’s modulus of the pipe material is 25 GPa?

Choose one answer.

	a. 7
	b. 0.08
	c. 1.5
	d. 0.0008
	e. 0.04

Question 90

A 10 inch inner diameter pipe with wall thickness 0.25 inches is pressurized to 1500 psi. What is the percentage expansion in the pipe diameter upon pressurization if the Young’s modulus of the pipe material is 250 GPa?

Choose one answer.

	a. 0.08
	b. 0.8
	c. 0.04
	d. 0.004
	e. 0.4

Question 91

How do shear stresses and normal stresses differ?

Choose one answer.

	a. They have different units.
	b. Shear stresses act to slide parallel planes of material apart without changing separation, whereas normal stresses act to increase or decrease the separation between parallel planes of material.
	c. Shear stresses are the absolute stresses, whereas normal stresses have been divided by the total stress.
	d. Normal stresses act at the surfaces of materials, whereas shear stresses act within materials.
	e. Normal stresses act within materials, whereas shear stresses act at the surfaces of materials.

Question 92

Asolid shaft of diameter 2 inches, shear modulus of 75 GPa, and length 1 m is subject to a torque of 5 kNm. What is the angular strain of the shaft?

Choose one answer.

	a. 32 degrees
	b. 1.6 radians
	c. 5.8 degrees
	d. 1.6 degrees
	e. 0.004 radians

Question 93

Asolid shaft of diameter 2 inches, shear modulus of 50 GPa, and length 0.5 m is subject to a torque of 5 kNm. What is the angular strain of the shaft?

Choose one answer.

	a. 0.5 radians
	b. 0.44 degrees
	c. 0.88 degrees
	d. 0.09 degrees
	e. 4.4 degrees

Question 94

Drive shafts are often constructed from thin walled cylinders. Consider such a cylinder of length 0.75 m, outer diameter 3 inches, and wall thickness 0.25 inches. The material has a shear modulus of 68 GPa. What is the angular strain for an applied torque of 750 Nm?

Choose one answer.

	a. 0.27 degrees
	b. 0.36 radians
	c. 0.32 degrees
	d. 4 radians
	e. 0.18 degrees

Question 95

Choose one answer.

	a. 0.64 degrees
	b. 0.34 radians
	c. 2.1 degrees
	d. 8 radians
	e. 0.006 degrees

Question 96

In which of the following geometries is stress concentration most pronounced?

Choose one answer.

	a. In the center of a large beam under transverse load
	b. At the middle of a column under a parallel load
	c. Near the corners of a triangular window in a pressure vessel
	d. On the edge of a spherical pressure vessel
	e. At the apex of a free standing column

Question 97

Calculate the volumetric or dilatational strain for a cube subject to normal strains of e_x= 0.001, e_y = 0.003, and e_z = 0.0007, and a shear strain t_xy of 0.0048.

Choose one answer.

	a. 0.0052
	b. 0.0035
	c. 0.001
	d. 0.01
	e. 0.0047

Question 98

Calculate the volumetric or dilatational strain for a cube subject to normal strains of ex= 0.001, ey = 0.02, and ez = 0.0009, and a shear strain tyz of 0.0077.

Choose one answer.

	a. 0.077
	b. 0.097
	c. 0.0219
	d. 0.0438
	e. 0.015

Question 99

How does a normal stress differ from a traction vector?

Choose one answer.

	a. A normal stress is a force per area of unit magnitude; a traction vector is not normalized.
	b. A traction vector is a shearing force per unit area; a normal stress is a force orthogonal to the area on which it is acting.
	c. A traction vector is a force per area of arbitrary direction; a normal stress is orthogonal to the area on which it is acting.
	d. A normal stress is a force per area of arbitrary direction; a traction vector is orthogonal to the area on which it is acting.
	e. Normal stresses and traction vectors act in opposite directions.

Question 100

Which of the following is an appropriate unit for a traction vector?

Choose one answer.

	a. Pa m
	b. Pa s
	c. N m
	d. psi
	e. N

Question 101

Which of the following adequately describes the difference between a first order tensor and a second order tensor?

Choose one answer.

	a. The order of a tensor describes the dimensionality of an array; a first order tensor is like a vector; a second order tensor is like a two-dimensional array.
	b. The order of a tensor describes the dimensionality of an array; a zeroth order tensor is like a vector; a first order tensor is like a two-dimensional array.
	c. The order of a tensor describes the dimensionality of the elements; a first order tensor contains only primary quantities; a second order tensor contains quadratic quantities.
	d. The order of a tensor describes the order of elements; a first order tensor has elements in increasing order; a second order tensor has the largest elements near the center.
	e. The order of a tensor describes the geometry from which it is derived; a first order tensor is applicable to two dimensional (planar) mechanics; second order tensors are required for three-dimensional mechanics.

Question 102

Which of the following best describes the utility of Mohr’s circle?

Choose one answer.

	a. It is a measure of hardness of materials.
	b. It provides a way of visualizing and remembering how tensors rotate.
	c. It allows for the convenient computation of torque from applied forces.
	d. It is a conventient accounting tool for tallying applied torques.
	e. It is a method of computing resultant forces.

Question 103

Which of the following adequately describes the differences between equilibrium relations, kinematic relations, and constitutive relations?

Choose one answer.

	a. Equilibrium relationships describe materials chemistry; kinematic relationships describe velocities as a function of time; constitutive relationships describe compliance with codes for material behavior.
	b. Constitutive relations describe tensor rotations; equilibrium relationships describe bending forces; kinematic relationships describe trajectories.
	c. Equilibrium relations describe static objects; kinematic relations describe moving objects; constitutive relations describe material composition.
	d. Equilibrium relations consider the action of external forces or tractions; kinematic relations consider the geometry of deformation; constitutive relations characterize a the response of a material to deformation.
	e. Constitutive relations characterize the temperature and pressure dependence of density and shear modulus; equilibrium relations are overall force balances; kinematic relations describe the velocities of individual particles at the object surfaces.

Question 104

The stress tensor in a plane contains the following elements sigma_x = 4 psi, sigma_y = 6 psi, and tau_xy = 2.3 psi. In a new coordinate system _x’y’ rotated 15 degrees counter clockwise from the original coordinate system, what is tau_x’y'?

Choose one answer.

	a. 1.2 psi
	b. 2.3 psi
	c. 6.0 psi
	d. 2.5 psi
	e. 0.3 psi

Question 105

The stress tensor in a plane contains the following elements sigma_x = 4 psi, sigma_y = 6 psi, and tau_xy = 2.3 psi. In a new coordinate system _x’y’ rotated 45 degrees counter clockwise from the original coordinate system, what is tau_x’y'?

Choose one answer.

	a. 2.8 psi
	b. 4.3 psi
	c. 6.2 psi
	d. 2.0 psi
	e. 1.0 psi

Question 106

Consider the structure depicted in figure below. There are two forces of 200kN and 100kN acting on point A. What is the tension in the segment AB?

Choose one answer.

	a. -150 kN
	b. 200 kN
	c. -200 kN
	d. 100 kN
	e. -100 kN

Question 107

Consider the structure depicted in figure below. There are two forces of 200kN and 100kN acting on point A. What is the tension in the segment AD?

Choose one answer.

	a. -150 kN
	b. 200 kN
	c. -200 kN
	d. -100 kN
	e. -50 kN

Question 108

Consider the structure depicted in the figure below. There are two forces of 200kN and 100kN acting on point A. What is the tension for the segment BC?

Choose one answer.

	a. 0 kN
	b. 50 kN
	c. 144 kN
	d. -50 kN
	e. -144 kN

Question 109

Consider the structure depicted in figure below. There are two forces of 200kN and 100kN acting on point A. The distances between A and B as well as B and C are 2 m. What is the tension in the segment CF?

Choose one answer.

	a. 0 kN
	b. 50 kN
	c. 144 kN
	d. -50 kN
	e. -100 kN

Question 110

Choose one answer.

	a. 0 kN
	b. 50 kN
	c. 144 kN
	d. -50 kN
	e. -100 kN

Question 111

Consider the structure depicted in the figure below. There are two forces of 200kN and 100kN acting on point A. The distances between A and B as well as B and C are 2 m. What is the tension in segment BF?

Choose one answer.

	a. -144 kN
	b. 50 kN
	c. 144 kN
	d. -50 kN
	e. 100 kN

Question 112

Choose one answer.

	a. -144 kN
	b. 50 kN
	c. 144 kN
	d. -50 kN
	e. -100 kN

Question 113

How many members does a perfect truss with 8 joints have?

Choose one answer.

	a. 16
	b. 8
	c. 12
	d. 13
	e. 6

Question 114

A three-rod assembly forms an equilateral triangle. The mass of each rod is M=1 kg. The length of each rod is L= 1m. Determine the moment of inertia about an axis that is perpendicular to the surface of the triangle passing through the center of the triangle.

Choose one answer.

	a. 1.5 kg m ²
	b. 1 kg m ²
	c. 1.25 kg m ²
	d. 2.0 kg m ²
	e. 3.0 kg m ²

Question 115

The major and minor radii of a thin elliptical disk of uniform density and mass 1 kg are 2 m and 1 m, respectively. Determine the moment of inertia about an axis that is perpendicular with the disk surface and goes through the center of the disk.

Choose one answer.

	a. 2.25 kg m²
	b. 3 kg m²
	c. 2 kg m²
	d. 1.25 kg m²
	e. 0.75 kg m²

Question 116

Fill in the blank. The number of unknowns at a joint should not exceed ________, so the method of joints can be used to solve a planar truss problem.

Choose one answer.

	a. 4
	b. 3
	c. 2
	d. 1
	e. 9

Question 117

Which of the following statements is true for a statically indeterminate beam?

Choose one answer.

	a. The number of reactions is unknown.
	b. The number of reactions is greater than the number of equilibrium equations.
	c. The number of reactions is equal to the number of equilibrium relations.
	d. The number of reactions is less than the number of equilbirium relations.
	e. The number of reactions is equal to the number of equilibrium relations minus 2.

Question 118

A homogeneous cube of weight 100 kN sits on a horizontal plane. Determine the minimum force F acting on the upper top edge (parallel with the surface) that is required for tipping the block over.

Choose one answer.

	a. 100 kN
	b. 75 kN
	c. 50 kN
	d. 200 kN
	e. 25 kN

Question 119

The deflection of a center loaded beam is approximately FL³/48EI. For a beam with square cross section, I = b⁴/12 (where b is the length of a side). If the deflection is 5 cm, b is 4 inches, L = 10 ft, and the load is 5kN, then what is the approximate value of Young’s modulus?

Choose one answer.

	a. 6.6 GPa
	b. 42 GPa
	c. 0.42 GPa
	d. 66 MPa
	e. 33 MPa

Question 120

Choose one answer.

	a. 25 kN
	b. 15 kN
	c. 11 kN
	d. 9kN
	e. 90 kN

Question 121

The deflection of a center loaded beam is approximately FLsup>3/48EI. For a beam with square cross section, I = b⁴/12 (where b is the length of a side). If the load is 50 kN, b is 4 inches, L = 10 ft, and E = 20 GPa, then what is the deflection of the beam?

Choose one answer.

	a. 1 cm
	b. 3 cm
	c. 7 cm
	d. 12 cm
	e. 120 cm

Question 122

The downward deflection of an end loaded cantilevered beam can be written as FL³/3EI, where I is the area moment of inertia of the beam. How does the deflection of the beam increase if the length is tripled and all else remains constant?

Choose one answer.

	a. Increases by 6 fold
	b. Increases by 9 fold
	c. Increases by 3 fold
	d. Increases by 81 fold
	e. Increases by 27 fold

Question 123

Which of the following best represents a simplified beam equation?

Choose one answer.

	a. EI d⁴/dx⁴ = q(x)
	b. EI d²/dx² = q(x)
	c. EI d^{/dx^{= q(x)}}
	d. EIx d³/dx³ = q(x)
	e. EI d³/dx³ = q(x)

Question 124

What form does a beam displacement equation typically take?

Choose one answer.

	a. A constant coefficient second order differential equation
	b. A first order differential equation
	c. A fifth order differential equation
	d. A fourth order differential equation
	e. A second order differential equation

Question 125

To whom is the development of beam theory commonly attributed?

I. Bernoulli

II. Gauss

III. Tesla

IV. Liebnitz

V. Franklin

VI. Euler

Choose one answer.

	a. I and VI
	b. I, II, III, IV, and VI
	c. I, II, and VI
	d. V
	e. IV and I

Question 126

A horizontal beam simply supported at either end and loaded in the middle will exhibit which of the following?

Choose one answer.

	a. Compression in the upper portion of the beam and tension in the lower portion
	b. Compression in the upper portion of the beam and compression in the lower portion
	c. Tension in the upper portion of the beam and compression in the lower portion
	d. Compression in the upper portion of the beam and tension in the lower portion
	e. Deflection or bending without tension or compression

Question 127

How does a cantilever support differ from a simple beam support?

Choose one answer.

	a. They do not differ.
	b. A cantilever support can provide both support force and moment, whereas a simple support can only force at a point.
	c. A simple support can provide both support force and moment, whereas a cantilever support can only force at a point.
	d. A cantilever support can only provide transverse support, whereas a simple support can provide both vertical and horizontal support.
	e. A cantilever support can provide only vertical support, whereas a simple support can only provide transverse support.

Question 128

Which of the following would be the most appropriate description of the beam configuration shown in the figure below?

Choose one answer.

	a. End loaded, cantilevered beam
	b. Simply supported, end loaded beam
	c. Simply supported, cantilevered beam
	d. Center loaded, cantilevered beam
	e. Center loaded, simply supported beam

Question 129

Which of the following would be the most appropriate description of the beam configuration shown in the figure below?

Choose one answer.

	a. End loaded, cantilevered beam
	b. Simply supported beam with a distributed load
	c. Simply supported, cantilevered beam
	d. Center loaded, cantilevered beam
	e. Center loaded, simply supported beam

Question 130

Which of the following would be the most appropriate description of the beam configuration shown in the figure below?

Choose one answer.

	a. End loaded, cantilevered beam
	b. Simply supported beam with a distributed load
	c. Simply supported, cantilevered beam
	d. Center loaded, cantilevered beam
	e. Center loaded, simply supported beam

Question 131

A loaded crane hook is shown in the schematic below. A long which plane is the hook likely to have the largest stress?

I. AB

II. CB

III. DE

IV. EF

V. FG

Choose one answer.

	a. I
	b. II
	c. III
	d. IV
	e. V

Question 132

Consider the following matrix notation equation.

What is the correct expression for tau₁₂?

Choose one answer.

	a. τ₁₂ = -sc σ_x + scσ_y + (c²-s² ) τ_xy
	b. τ₁₂ = -sc σ_x + scσ_y + 2sc τ_xy
	c. τ₁₂ = -sc σ_x + scσ_x + (c²-s² ) τ_xy
	d. τ₁₂ = -sc σ_x + scσ_y + (-2sc) τ_xy
	e. τ₁₂ = -sc σ_x + scσ_y + (c²-s² ) σ_x

Question 133

Consider the following matrix notation equation.

What does the term c²-s² refer to?

Choose one answer.

	a. cos² θ - sin² θ where θ is the angle between coordinate systems
	b. cos θ² - sin θ² where θ is the angle between coordinate systems
	c. cos θ² - sin θ² where θ is the angle between principal axes
	d. cos² θ - sin² θ where θ is the angle between fibers
	e. cos θ² - sin² θ where θ is the angle between coordinate systems

Question 134

Which of the following is the best description of an orthotropic material?

Choose one answer.

	a. Orthotropic materials have material properties which are the same in all directions.
	b. Orthotropic materials have properties which are different along each orthogonal axis.
	c. An orthotropic material has a steep temperature dependence of material properties.
	d. An orthotropic material has material properties that are the same in at least two orthogonal directions.
	e. An orthotropic material has material properties that are independent of temperature.

Question 135

Which of the following are examples of anisotropic materials?

I. Wood

II. Steel

III. Water

IV. Aluminum

Choose one answer.

	a. III
	b. II and III
	c. I
	d. II and IV
	e. I and III

Question 136

Consider the following matrix notation equation.

Which of the following is the equation for the normal strain in the y direction?

Choose one answer.

	a. ε_y = -ν/E σ_x + 1/E σ_y
	b. ε_y = -ν/E σ_x + 1/G σ_y
	c. ε_y = -ν/E σ_x + 1/E γ_xy
	d. ε_y = -ν/E σ_y + 1/E σ_y
	e. ε_y = -ν/E σ_y + 1/E σ_x

Question 137

Consider the following matrix notation equation.

Which of the following is the equation for the shear strain?

Choose one answer.

	a. γ_xy = -ν/E σ_x + 1/E σ_y
	b. γ_xy = -ν/E σ_x + 1/G σ_y
	c. γ_xy = -ν/E σ_x + 1/E γ_xy
	d. γ_xy = -ν/E σ_y + 1/E σ_y
	e. γ_xy = 1/G τ_xy

Question 138

Which of the following best describes the use of moiré interferometry for strain measurements?

Choose one answer.

	a. Display of light fringes that change when light passes through gradients of changing orientation or spacing
	b. Display of diffraction gratings that change with strain
	c. Display of optical birefringence patterns that change with strain
	d. Display of laser induced grid displacement upon strain
	e. Display of grid rotation and alignment upon strain

Question 139

Which of the following defect geometries has found special utility in the analytical or closed-form modeling of crack propagation?

Choose one answer.

	a. Cube
	b. Rhombus
	c. Sphere
	d. Circle
	e. Ellipse

Question 140

Consider a circular hole drilled in a flat plate. The plate is then subjected to uniaxial tension in the plane of the plate from top to bottom. Where would the stress be concentrated the most in the plate?

Choose one answer.

	a. Just above and below the hole
	b. At both lateral edges of the hole
	c. Far from the hole in the bulk of the material
	d. At the top edge of the hole
	e. Near the entire edge of the hole

Question 141

Which of the following best describes the meaning of the compatibility equation in mechanics?

Choose one answer.

	a. All measures of strain are not independent of one another.
	b. There is no slip at boundaries between different materials.
	c. Strain releases energy.
	d. Strains of two touching materials may be different.
	e. Thermal expansion of different materials may cause defects at boundaries.

Question 142

Which of the following properties are exploited to use photoelasticity to monitor strain?

Choose one answer.

	a. Refractive index
	b. Birefringence
	c. Absorbance
	d. Temperature-dependent refraction
	e. Reflection

Question 143

In which of the following ways do common electrical strain gauges work?

Choose one answer.

	a. Changes in inductance upon strain
	b. Changes in radio-frequency penetration upon strain
	c. Changes in electrical resistance upon strain
	d. Creation of short circuits upon strain
	e. Changes in dielectric constant upon strain

Question 144

Which of the following best describes the finite element method?

Choose one answer.

	a. Description of mechanical materials in terms of a finite number of chemical elements
	b. Description of mechanical behavior in terms of a finite number of motions
	c. Method for reducing the mathematical complexity of problems by writing them in terms of a finite number of algebraic relations
	d. Method of approximating mechanical behavior by including only the most important truss elements
	e. Representation of material behavior by a finite number of mechanical rods and springs

Question 145

In wire drawing, the drawing stress can often be represented by σ = σ_Y ln(A₀/A), where A₀ and A are the initial and final areas of the wire. If we constrain σ/σ_Y to be 0.9, then what is the percentage reduction (100*(1-d/d₀)) in wire diameter that can be achieved in a single drawing operation?

Choose one answer.

	a. 24%
	b. 12%
	c. 36%
	d. 48%
	e. 56%

Question 146

In wire drawing, the drawing stress can often be represented by σ = σ_Y ln(A₀/A), where A₀ and A are the initial and final areas of the wire. If we constrain σ/σ_Y to be 0.7, then what is the percentage reduction (100*(1-d/d₀)) in wire diameter that can be achieved in a single drawing operation?

Choose one answer.

	a. 30%
	b. 20%
	c. 10%
	d. 5%
	e. 15%

Question 147

How do yield and fracture processes generally vary with temperature?

Choose one answer.

	a. Fracture becomes more likely at lower temperatures, and yield becomes more likely at higher temperatures.
	b. Both yield and fracture become more likely at higher temperatures.
	c. Both yield and fracture become more likely at lower temperatures.
	d. Yield becomes more likely at lower temperatures, and fracture becomes more likely at higher temperatures.
	e. Both responses have unpredictable variations with temperature.

Question 148

The stress tensor in a test configuration is given (in MPa) by

1024

2123

438

Compute the Von Mises stress according to

σ_M =sqrt( ½ [(σx − σy)²+ (σx − σz)²+ (σy − σz)²+ 6(τxy + τyz + τxz)]).

Choose one answer.

	a. 3 MPa
	b. 6 MPa
	c. 1 MPa
	d. 8 MPa
	e. 12 MPa

Question 149

The stress tensor in a test configuration is given (in MPa) by

1224

263

438

Compute the Von Mises stress according to

σ_M =sqrt( ½ [(σx − σy)²+ (σx − σz)²+ (σy − σz)²+ 6(τxy + τyz + τxz)]).

Choose one answer.

	a. 3.2 MPa
	b. 6.2 MPa
	c. 9.3 MPa
	d. 7.4 MPa
	e. 7.0 MPa

Question 150

What is the value of the von Mises yield stress compared to the Tresca critical stress for yield in a uniaxial tension test?

Choose one answer.

	a. They are equal.
	b. The von Mises stress is twice the Tresca stress.
	c. The von Mises stress is four times the Tresca stress.
	d. The von Mises stress is square root (2) times the Tresca stress.
	e. The von Mises stress is half the Tresca stress.

Question 151

What is the maximum shear stress occurring in a cylindrical pressure vessel of length 1m, diameter 0.3 m, and wall thickness 1 cm when pressurized to12 atm?

Choose one answer.

	a. 3 MPa
	b. 1 MPa
	c. 6 MPa
	d. 9 MPa
	e. 12 MPa

Question 152

What is the maximum shear stress occurring in a cylindrical pressure vessel of length 1m, diameter 0.3 m, and wall thickness 1 cm when pressurized to 100 psi?

Choose one answer.

	a. 1 MPa
	b. 5 MPa
	c. 10 MPa
	d. 15 MPa
	e. 25 MPa

Question 153

In a tensile test, a material is found to yield at a normal stress of 82 MPa. What is the Tresca critical shear stress for yield for that material?

Choose one answer.

	a. 20 Mpa
	b. 11 Mpa
	c. 12 Mpa
	d. 41 MPa
	e. 82 MPa

Question 154

What value of Poisson’s ratio characterizes deformation without change in volume?

Choose one answer.

	a. -0.5
	b. 0.0
	c. 0.33
	d. 0.5
	e. 1.0

Question 155

How do the processes leading to fracture differ from those causing yield?

Choose one answer.

	a. Yield depends more upon shear stresses, and fracture depends more upon normal stresses.
	b. Fracture depends more upon shear stresses, and yield depends more upon normal stresses.
	c. Yield results from steady stress, and fracture results from time-varying stress.
	d. Both phenomena result from the same forces.
	e. Fracture results from steady stress, and yield results from time-varying stress.

Question 156

How does plastic flow differ from elastic deformation?

Choose one answer.

	a. Elastic deformation is instantaneous upon loading and reversible upon removal of load; plastic deformation may be slow and persists after removal of the load.
	b. The phenomena are very similar.
	c. Plastic flow releases more heat than elastic deformation.
	d. Plastic flow is reversible upon removal of the load; elastic deformation is not.
	e. Plastic flow stores the energy of deformation; elastic deformation does not.

Question 157

Which of the following best defines fracture as used in the study of the strength of materials?

Choose one answer.

	a. The process of a piece of material separating into two or more pieces
	b. The growth of defects
	c. The process of the creation of many small fragments from one large piece
	d. The process of crack formation during shear flow
	e. The process of embrittlement at cold temperatures

Question 158

In the linear-elastic regime, how does the stress required for fracture scale with the size of the initiating defect?

Choose one answer.

	a. Inversely with the square root of the size of the defect
	b. Inversely with the first power of the size of the defect
	c. Inversely with the square of the size of the defect
	d. In proportion to the square root of the size of the defect
	e. In proportion to the size of the defect

Question 159

How does the critical loading force for a long column vary with the Young’s modulus of the column material?

Choose one answer.

	a. It is proportional to the Young's modulus of the column.
	b. It is inversely proportional to the Young's modulus of the column.
	c. It is proportional to the square root of the Young's modulus of the column.
	d. It is inversely proportional to the square root of the Young's modulus of the column.
	e. It does not depend upon the Young's modulus of the column.

Question 160

How does the critical loading force for a long column vary with the length of the column?

Choose one answer.

	a. It varies inversely as the square of the length of the column.
	b. It varies in proportion to the column length.
	c. It varies inversely with the first power of the column length.
	d. It varies inversely with the square root of the column length.
	e. It varies inversely with the fourth power of the column length.

Question 161

How does the critical loading force for a long column vary with the diameter of the column?

Choose one answer.

	a. It increases linearly with diameter.
	b. It increases as the square of the diameter.
	c. It increases with the fourth power of the diameter.
	d. It increases in proportion to the square root of the column diameter.
	e. It is independent of column diameter.

Question 162

How does column buckling differ from column fracture?

Choose one answer.

	a. Fracture entails vertical cracks; buckling entails horizontal failure.
	b. Column buckling and column fracture are the same.
	c. Column buckling is the bending of a column under load; fracture is column breakup.
	d. Column fracture is bending under load; buckling is complete collapse.
	e. Buckling occurs when the footing of a column collapses; fracture occurs when the column itself breaks up.

Question 163

How does creep vary with temperature?

Choose one answer.

	a. It increases exponentially with increasing temperature.
	b. It increases linearly with increasing temperature.
	c. It increases with the fourth power of temperature.
	d. It increases with the reciprocal of temperature.
	e. It increases with the square root of temperature.

Question 164

Which of the following best describes behavior during primary creep?

Choose one answer.

	a. Primary creep exhibits a constant strain rate.
	b. Primary creep exhibits a decreasing strain rate.
	c. Primary creep exhibits an increasing strain rate.
	d. Primary creep is an incubation period in which little strain occurs.
	e. Primary creep exhibits an exponentially increasing strain rate with time.

Question 165

Which of the following statements best describes behavior during tertiary creep?

Choose one answer.

	a. Tertiary creep exhibits a constant strain rate.
	b. Tertiary creep exhibits a decreasing strain rate.
	c. Tertiary creep exhibits an increasing strain rate followed by material failure.
	d. Tertiary creep is an incubation period in which little strain occurs.
	e. Tertiary creep exhibits an exponentially increasing strain rate with time.

Question 166

Which of the following best describes behavior during secondary creep?

Choose one answer.

	a. Secondary creep exhibits a constant strain rate.
	b. Secondary creep exhibits a decreasing strain rate.
	c. Secondary creep exhibits an increasing strain rate followed by material failure.
	d. Secondary creep is an incubation period in which little strain occurs.
	e. Secondary creep exhibits an exponentially increasing strain rate with time.

Question 167

The vapor pressure of a material is 2 torr at 1289 degrees Kelvin. The melting temperature of the material is 3098 degrees Kelvin. The boiling point of that material is 12032 degrees Kelvin. What is the homologous temperature at 1089 degrees Kelvin?

Choose one answer.

	a. 0.35
	b. 0.84
	c. 0.42
	d. 0.09
	e. 0.26

Question 168

Choose one answer.

	a. 0.38
	b. 0.84
	c. 0.42
	d. 0.09
	e. 0.26

Question 169

Choose one answer.

	a. 0.38
	b. 0.84
	c. 0.42
	d. 0.09
	e. 0.26

Question 170

Which of the following is the best definition of homologous temperature?

Choose one answer.

	a. It is the ratio of material temperature (absolute) to the melting point temperature (absolute).
	b. It is the ratio of material temperature (degrees centigrade) to the melting point temperature (degrees centigrade).
	c. It is the ratio of boiling point temperature (absolute) to the melting point temperature (absolute).
	d. It is the ratio of the boiling point temperature (degrees centigrade) to the melting point temperature (degrees centigrade).
	e. It is the ratio of the triple point temperature (absolute) to the melting point temperature (absolute).

Question 171

How does creep deformation differ from cyclic fatigue?

Choose one answer.

	a. Creep deformation is slow, plastic flow from a constant stress; cyclic fatigue is weakening from repeated or oscillatory loading.
	b. Cyclic fatigue is slow, plastic flow from a constant stress; creep is weakening from repeated or oscillatory loading.
	c. Creep only occurs at low temperatures, but cyclic fatigue can occur at all temperatures.
	d. Creep occurs on time scales of years; cyclic fatigue occurs on time scales of days.
	e. Cyclic fatigue occurs on time scales of years; creep occurs on time scales of decades.

Question 172

What design considerations can reduce or limit the effects of cyclic fatigue?

I. Keeping the material in compression rather than tension

II. Keeping the material in tension rather than compression

III. Alleviating stress by drilling holes in the part at regions of high stress

Choose one answer.

	a. I and III
	b. II and III
	c. I only
	d. II only
	e. III only

Question 173

Low-cycle fatigue can often be correlated with a relationship resembling S=kN^c.If the strain amplitude S = 0.01 k for a particular piece, and N = 500, then what is c?

Choose one answer.

	a. -0.74
	b. -0.64
	c. -0.68
	d. -0.55
	e. -0.5

Question 174

Low-cycle fatigue can often be correlated with a relationship resembling S=kN^c.If the strain amplitude S = 0.1 k for a particular piece, and c = -0.5, then what is N?

Choose one answer.

	a. 10
	b. 100
	c. 1000
	d. 10000
	e. 100000

Question 175

How do low-cycle and high-cycle fatigue differ?

Choose one answer.

	a. Low-cycle fatigue occurs at higher stresses and fewer repetitions than high-cycle fatigue.
	b. Low-cycle fatigue occurs at higher stresses and more repetitions than high-cycle fatigue.
	c. Low-cycle fatigue occurs at lower stresses and more repetitions than high-cycle fatigue.
	d. Low-cycle fatigue occurs at lower stresses and fewer repetitions than high-cycle fatigue.
	e. They are identical processes.

Question 176

What is the maximum oscillating stress amplitude that can be sustained for the machine part exhibiting the following S-N curve if the part needs to sustain 10000 cycles?

Choose one answer.

	a. 20 MPa
	b. 50 MPa
	c. 100 MPa
	d. 100 kPa
	e. 50 GPa

Question 177

A part exhibits the following S-N curve. What is the maximum number ofcycles at a stress amplitude of 30 MPa that the part is likely to survive without failure?

Choose one answer.

	a. 80000
	b. 1000000
	c. 100
	d. 1000
	e. 8000

Question 178

We wish to fit the central portion of the S-N curve below to an equation of the form S = kN^c. What value of c would be most appropriate?

Choose one answer.

	a. -0.2
	b. 0.2
	c. -2
	d. 2
	e. -1

Question 179

How do distributed or continuous loads differ from discrete loads?

Choose one answer.

	a. Distributed loads occur over a range in space; discrete loads occur at specific locations.
	b. Discrete loads occur over a range in space; distributed loads occur at specific locations.
	c. There is no real difference.
	d. Discrete loads may only have values in multiples of 2; distributed loads may have any value.
	e. Distributed loads are evenly spaced; discrete loads may occur at any location.

Question 180

The stress tensor in a test configuration is given (in MPa) by

724

263

438

Compute the Von Mises stress according to

σ_M =sqrt( ½ [(σx − σy)²+ (σx − σz)²+ (σy − σz)²+ 6(τxy + τyz + τxz)]).

Choose one answer.

	a. 3.2 MPa
	b. 6.2 MPa
	c. 9.3 MPa
	d. 7.4 MPa
	e. 5.5 MPa

Question 181

How does a truss element differ from a beam?

Choose one answer.

	a. Truss elements may only support axial loads; beams may support transverse loads.
	b. They are the same.
	c. Beams have complex cross sections; truss elements are rods.
	d. Truss elements buckle under compression; beams do not do so as easily.
	e. Beams do not support tension; truss elements do.

Question 182

In wire drawing, the drawing stress can often be represented by σ = σ_Y ln(A₀/A), where A₀ and A are the initial and final areas of the wire. If we constrain σ/σ_Y to be 0.4, then what is the percentage reduction (100*(1-d/d₀)) in wire diameter that can be achieved in a single drawing operation?

Choose one answer.

	a. 30%
	b. 18%
	c. 10%
	d. 5%
	e. 15%

Question 183

For a uniformly loaded cantilevered beam, how does shear within the beam depend upon position along the length of the beam?

Choose one answer.

	a. It is constant.
	b. It decreases linearly from the free end to the supported end.
	c. It increases linearly from the free end to the supported end.
	d. It increases quadratically from the free end to the supported end.
	e. It is zero.

Question 184

For an end-loaded cantilevered beam, how does the bending moment depend upon position along the length of the beam?

Choose one answer.

	a. It increases linearly from the load end to the cantilevered end.
	b. It decreases linearly from the load end to the cantilevered end.
	c. It is constant.
	d. It increases quadratically from the load end to the cantilevered end.
	e. It decreases quadratically from the load end to the cantilevered end.

Question 185

For an end-loaded cantilevered beam, how does shear within the beam depend upon position along the length of the beam?

Choose one answer.

	a. It is constant.
	b. It decreases linearly from the free end to the supported end.
	c. It decreases linearly from the free end to the supported end.
	d. It increases quadratically from the free end to the supported end.
	e. It is zero.

Question 186

For a uniformly loaded cantilevered beam, how does the bending moment depend upon position along the length of the beam?

Choose one answer.

	a. It increases linearly from the load end to the cantilevered end.
	b. It decreases linearly from the load end to the cantilevered end.
	c. It is constant.
	d. It increases quadratically from the load end to the cantilevered end.
	e. It decreases quadratically from the load end to the cantilevered end.

Question 187

What is the maximum shear stress occurring in a cylindrical pressure vessel of length 1m, diameter 0.5 m, and wall thickness 2 cm when pressurized to 200 psi?

Choose one answer.

	a. 1 MPa
	b. 5 MPa
	c. 9 MPa
	d. 15 MPa
	e. 25 MPa

Question 188

1.Determine the magnitude of the force in AB in the truss illustrated below. The triangles are equilateral.

1.Determine the magnitude of the force in AG in the truss illustrated below. The triangles are equilateral.

1.Determine the magnitude of the force in BC in the truss illustrated below. The triangles are equilateral.

1.Determine the magnitude of the force in GF in the truss illustrated below. The triangles are equilateral.

Convert a pressure of 3 atmospheres to units of meters of a fluid of density 0.53 grams/ml (at the earth’s surface). Which of the following best corresponds to that result?

Choose one answer.

	a. 67.8
	b. 32.4
	c. 58
	d. 101325
	e. 202650

Question 199

Find the angle between the two vectors y = 2 i + 4 j + 8 k and z = 6 i + 4 j + 6 k in degrees. Which of the following best matches the result?

Choose one answer.

	a. 55 degrees
	b. 50 degrees
	c. 70 degrees
	d. 28 degrees
	e. 5 degrees

Question 200

Two forces of magnitude 9 N and 12 N act on a point. The angle between the two forces is 135 degrees. Estimate the resultant force.

Choose one answer.

	a. 5 N
	b. 8.5 N
	c. 20 N
	d. 17 N
	e. 30 N

Question 201

Two forces of magnitude 9 N and 12 N act on a point. The angle between the two forces is 75 degrees. Estimate the resultant force.

Choose one answer.

	a. 5 N
	b. 8.5 N
	c. 20 N
	d. 17 N
	e. 30 N

	a. F1, F2, and F3 must all be of equal magnitude.
	b. All forces must be zero.
	c. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(30 degrees) \|F2\|.
	d. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(60 degrees) \|F2\|.
	e. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 sin(30 degrees) \|F2\|.

	a. F1, F2, and F3 must all be of equal magnitude.
	b. All forces must be zero.
	c. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(25 degrees) \|F2\|.
	d. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(60 degrees) \|F2\|.
	e. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 sin(30 degrees) \|F2\|.

	a. F1, F2, and F3 must all be of equal magnitude.
	b. All forces must be zero.
	c. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 cos(30 degrees) \|F2\|.
	d. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 sin(30 degrees) \|F2\|.
	e. F1 and F2 must have equal magnitude. The magnitude of F3 must be 2 sin(45 degrees) \|F2\|.