Quiz

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Previous quizzes appear here in reverse chronological order.

Lesson 36

Consider the triangular plate shown below. Each square on the grid is 1 cm×cm.

1. The x coordinate of the x-centroid is closest to
   a. 3 cm
   b. 4 cm
   c. 5 cm
   d. 6 cm
   e. 7 cm
   
2. The shaded area to the left of the x-centroid is the same as the shaded area to the right.
   a. True
   b. False
   

Lesson 33

The surface between the block and the inclined plane is rough. (I.e., it is subject to friction.) The block is in static equilibrium.

1. The magnitude of the normal force between the block and the inclined plane is
   a. N = mgcosθ
   b. N > mgcosθ
   c. N < mgcosθ
   d. insufficient info to determine
2. Since the block is in static equilibrium, the friction force between the block and the surface is f = μ_sN
   a. True
   b. False
   c. insufficient info to determine
3. In this problem the friction force will act
   a. in the positive x direction
   b. in the negaticve x direction
   c. insufficient info to determine

Lesson 32

A pulley with a crank is shown in the figure below. A student has created a FBD for this system as shown.

 

The student has also determined that the moments about point C due to the force and the reaction at B are, respectively,

r × F = -4000 i + 1500 j - 1000 k [N-mm]

and

r × B = -100B_z j - 100B_y k [N-mm].

1. Given that the tension force T is vertical, what is the correct expression for the moment arm (i.e., r) to find the moment due to T about point C?
   a. 100 mm
   b. 150 mm
   c. 180.3 mm
   d. -150 mm i + 100 mm k
   e. None of the above
   
2. What is the correct expression for the moment due to T about point C?
   a. 100 mm × T i
   b. 150 mm × T j
   c. 180.3 mm × T k
   d. -150 mm × T i + 100 mm × T k
   e. 100 mm × T i + 150 mm × T k
   
3. What is the magnitude of T?
   a. 0 N
   b. 40 N
   c. 100 N
   d. 150 N
   e. Cannot be determined from the given info.

Lesson 29

Recall the two trusses from our example:

1. How does the force in member BC compare for the two loadings?
   
   a. F_BC,2 > F_BC,1
   b. F_BC,2 < F_BC,1
   c. F_BC,2 = F_BC,1
   d. Insufficient info to determine
   
2. How does the force in member BE compare for the two loadings?
   a. F_BE,2 > F_BE,1
   b. F_BE,2 < F_BE,1
   c. F_BE,2 = F_BE,1
   d. Insufficient info to determine
   

Lesson 27

1. Is this system statically determinate? All components are weightless and the wall is rigid.
   
   
   
   a. Yes
   b. No
   
2. Is this system statically determinate? All components are weightless and the walls are rigid.
   
   
   
   a. Yes
   b. No
   

Lesson 22

A frame is loaded as shown in the figure.



A free body diagram of the frame is given by



A free body diagram of piece AC is given by



Which of the following free body diagrams is correct for piece BDE?



a.
b.
c.
d.

Lesson 21

Three pipes all of weight W rest in a weightless pipe rack as shown in the figure.

1. Which figure gives the correct free body diagram of the pipes and the rack together?

   a.	b.	c.	d.

   a.
   b.
   c.
   d.
   Both c. and d.
   b., c., and d.
   
2. Which figure gives the correct free body diagram of the bottom pipe?

   a.	b.	c.

   a.
   b.
   c.
   Both a. and b.
   a., b., and c.

Lesson 19

Consider the two booms shown in the figure. There are massless and frictionless pulleys at C and D.

1. How does the tension in the cable compare for the two cases?
   a. T₂ > T₁
   b. T₂ < T₁
   c. T₂ = T₁
   d. Insufficient info to determine
   

Lesson 18

1. Consider drawing a free body diagram in which you must "cut" a massless cable. How many unknown reactions does cutting the cable introduce?
   a. 1
   b. 2
   c. 3
   d. Insufficient info to determine
   
2. Consider drawing a free body diagram in which you must "remove" a 2-D pin connection. How many unknown reactions does this introduce?
   a. 1
   b. 2
   c. 3
   d. Insufficient info to determine
   
3. Consider drawing a free body diagram in which you must "remove" a 3-D ball and socket joint (like your shoulder) from a body. How many unknown reactions does this introduce?
   a. 1
   b. 2
   c. 3
   d. Insufficient info to determine
   
4. Consider drawing a free body diagram in which you must "cut" through a 3-D cantilever beam where it is attached to a wall. How many unknown reactions does this introduce?
   a. 2
   b. 3
   c. 6
   d. Insufficient info to determine
   

Lesson 15

1. For a moment about point P due to a force F, M_P = r×F.
   a. True
   b. False
   
2. For a moment about point P due to a force F, M_P = F×r.
   a. True
   b. False
   
3. For a moment about point P due to a force F, M_P makes a right angle with r.
   a. True
   b. False
   
4. For a moment about point P due to a force F, M_P makes a right angle with F.
   a. True
   b. False
   
5. A force of 10 N is applied at point B. We wish to maximize the moment about point A due to the force at B. At what angle,θ, shall we place the force at B?
   a. 0°
   b. 45°
   c. 90°
   d. 135°
   e. 180°
   

Lesson 14

A compound bar is loaded as shown in the figure.

1. What is the magnitude of the axial force in Bar AB?
   a. 1800 N
   b. 1000 N
   c. 800 N
   d. 2800 N
   e. 0 N
   f. None of the above
2. Bar AB is in...
   a. compression
   b. tension
   c. neither compression nor tension
3. Under this loading Bar AB will...
   a. get longer
   b. get shorter
   c. stay the same length

Lesson 11

A massless bar with Young's modulus E, length L and cross sectional area A is welded in place between two rigid plates. A weight W is then hung from a pin on the bar.

1. Which figure gives the correct free body diagram for the bar?
   a.
   b.
   c.
   d.
   
2. Which figure gives the correct free body diagram for the section of bar above the pin?
   a.
   b.
   c.
   d.
   
3. What is the total deflection for the whole bar?
   a. WL/EA
   b. F₁L/EA
   c. F₂L/EA
   d. 0
4. The equilbrium equations by themselves are sufficient to solve for all unknown forces.
   True
   False

Lesson 10

Two metal bars are made of different materials but have identical geometry (dimensions) and identical tensile loading.

1. At the applied load, Bar A deflects more than bar B. When load is removed, both bars return to their original dimensions. Therefore, the metal in bar A is
   a. stronger
   b. weaker
   c. stiffer
   d. less stiff
   e. more ductile
   f. less ductile
   
2. In a second test, the bars are identically loaded until one bar fails. The bar that fails first is
   a. stronger
   b. weaker
   c. stiffer
   d. less stiff
   e. more ductile
   f. less ductile
   
3. Rubberbands are
   a. ductile
   b. brittle
   c. delicious
   

Lesson 9

1. A pinned link is loaded axially through its pins only.

   True/False: There is only normal stress (σ) and no shear stress (τ) in the link

   a. True, there is no shear stress
   b. False, there is shear stress
   
2. In order to calculate the shear stress in the pin, what area do you use?
   a. Projected area
   b. Cross sectional area
   c. Surface area
   d. Axial section area
   e. Area 51
   
3. Stress is a...
   a. Scalar
   b. Vector
   c. None of the above
   

Lesson 8

1. A four-legged table rests on a floor. The table legs all have circular cross sections with 1-in diameters. With the intent of lessening damage to the floor, 2-in diameter disks are placed under each leg. With the addition of the disks, the contact stress on the floor will...
   a. not change.
   b. be two times as large.
   c. be four times as large.
   d. be eight times as large.
   e. be 1/2 as large.
   f. be 1/4 as large.
   g. be 1/8 as large.
   h. None of the above
   
2. Weights in a weight room are stacked on a spindle with a rubber mat as the base. With the intent of lessening damage to the floor, the facility director replaces the mat with a rubber mat twice as thick. For the same weight stack, the contact stress on the floor will...
   
   a. not change.
   b. be two times as large.
   c. be four times as large.
   d. be eight times as large.
   e. be 1/2 as large.
   f. be 1/4 as large.
   g. be 1/8 as large.
   h. None of the above
   

Lesson 7

A hydraulic cylinder slowly pushes the frictionless pulley as shown in the figure.

1. As θ decreases, what happens to the tension in the cable?
   a. It increases.
   b. It decreases.
   c. It remains the same.
   d. Insufficient info to determine.
2. Did you sketch a free body diagram to help you answer part a?
   
   a. Yes.
   b. Yes.
   c. Yes.

Lesson 6

A gorilla is suspended from a cable making use of frictionless pulleys as shown in the figure.

1. Which figure gives the best free body diagram for the system?
   
   a.
   b.
   c.
2. As θ decreases, what happens to the tension in the cable?
   a. It increases.
   b. It decreases.
   c. It remains the same.
   d. Insufficient info to determine.

Lesson 5

1. A particle is defined as an object with mass but no size. A consequence of something being a particle is that all the forces acting on it pass though a single point.

   Can a bowling ball be treated as a particle?

   a. Yes, always
   b. No, never
   c. Maybe sometimes
2. What is true of a particle in static equilibrium?
   a. It has static cling
   b. It is not accelerating
   c. ΣF = 0
   d. All of the above.
   e. b. and c. only
3. In the first figure a person pulling on the rope results in a tension of 100 lb. With a person exerting a 100 lb force on each end of the rope as shown in the second figure, the tension in the rope will be
   
   a. 0 lb
   b. 50 lb
   c. 100 lb
   d. 150 lb
   e. 200 lb
   

Lesson 4

1. Consider a unit vector given by e = e_xi + e_yj + e_zk. What is the magnitude of (e_x² + e_y² + e_z²)^½?
   a. 0
   b. √2
   c. √3
   d. 1
   e. Insufficient info to determine.
2. What are the dimensions of e?
   a. Length
   b. Depends on the physical quantity of the vector
   c. There are no dimensions.
3. What is the angle e makes with the z-axis?
   a. 90°
   b. 180°
   c. cos^-1(e_z/|e|)
   d. Insufficient info to determine.

Lesson 2

Consider the figure below in which the top view of a fence post is shown. Both F₁ and F₂ have a magnitude of 100 lb.

1. 
   True
   False
   
2. 
   True
   False
   
3. The magnitude of the resultant of the two forces is closest to
   a. 0 lb
   b. 50 lb
   c. 100 lb
   d. 150 lb
   e. 200 lb
   

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