ME 270 Final Exam Fall 2019 NAME (Last, First):€¦ · ME 270 – Final Exam Fall 2019 NAME (Last, First): _ (Please PRINT) PUID #: _ ME 270 Final Exam – Fall 2019 Page

ME 270 – Final Exam Fall 2019 NAME (Last, First): ______________________________

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ME 270 Final Exam – Fall 2019 Page 2

Problem 1 (25 points) – each answer in this problem is to be graded all-or-nothing (no partial credit)

Part 1A (6 points)

Bar AB (lying in the y-z plane) is attached to a fixed support at point A on the z-axis. A cable is attached at point B on the bar, and has a tension of T = 125 lbs. Determine the unit vector �⃗� 𝐴𝐵, the tension vector �⃗� 𝐵𝐶, and the magnitude of the projection of tension �⃗� 𝐵𝐶 to the direction of the bar �⃗� 𝐴𝐵.

�⃗� 𝐴𝐵 = (2pts)

�⃗� 𝐵𝐶 = lbs (2pts)

Projection Magnitude = lbs (2pts)




Part 1B (4 points)

Two cables, AB and BD, are used to hold a block of unknown weight (𝑊1) in static equilibrium. The cable BD passes over an ideal (i.e., frictionless) pulley at point C, and another crate with a weight of 𝑊2 = 50 N is attached to the cable at point D. Determine the magnitude of the tension 𝑇𝐴𝐵 and the weight 𝑊1required for the system to be in static equilibrium as shown.

𝑇𝐴𝐵 = N (2pts)

𝑊1 = N (2pts)

÷! ÷ . Titov

E Fx ⇒ :-T

,Gsboo 1- Tz I ⇒

⇒ T,= 80 N

E Fy -- o : T,Sin boo + Tz tf - W 1=0

⇒ w , = 99.282 N

80

99,282




Part 1C (6 points)

A truss (shown in the figure) is loaded with an external force of 300 lbs in the vertical direction at joint A. The truss is held in static equilibrium by a pin support at D and a roller support at E. Determine the magnitude of the internal forces for members AB and AC, and then indicate whether they are in tension or compression (Circle one of the options provided).

𝐹𝐴𝐵 = (2pts) (Tension, Compression, Zero) (1pt)

𝐹𝐴𝐶 = (2pts) (Tension, Compression, Zero) (1pt)

Joint A :

→FABI Ey -

- O : ftp.I-3ou-o

F) Fae ⇒ Ears = too Ibv IK

,⇒ : Faiz Ift Fac -- o300lb

⇒ Face -- - Goo lb

%!! 00




Part 1D (5 points)

Determine the force P required to cause the 50-lb homogeneous bar to tip (PT) and slide (PS) for the configuration shown. What is the nature of the impending motion that would occur first?

𝑷𝑻 = (2 pts)

PS = (2 pts)

𝑰𝒎𝒑𝒆𝒏𝒅𝒊𝒏𝒈 𝑴𝒐𝒕𝒊𝒐𝒏 = Tip Slip Both (Circle One) (1 pts)

𝛉 =30o Assume Impending tipping ,i¥y¥ip=Tf EMA - o : to " (as ) - Asian .ci )V f L

WHOA N p ⇒ PT = to lb

Assume Impending slippingA f- ns.N

Efx -0 : f - jassi -- o

hkfolb Ncp Efy -

- o : N-W- pssinso →⇒ Pg -- 20.95 lb

50lb

20*95 lb




Part 1E (4 points)

A force, 𝑇, is applied to a cable which holds a crate in a position where half of the crate is submerged into water (as shown in the figure). The density of water is 1000 kg/m3, the density of the crate is 2500 kg/m3. Please find the buoyancy force exerted on the crate (𝐹𝑏) and the tension in the cable (𝑇) needed to hold the crate in the position shown.

𝐹𝑏 = N (2pts)

𝑇 = N (2pts)

*¥W

Fb

Fb -- Pg - Vdisp .

,Vdisp = 015 Ms

= tooo x 9.81 × 0.5 = 49 of N

W '- Pg V = 2500×9.81×1 = 24525 N

T-- W- Fb - 19620 N

4905

19620




Problem 2 (25 Points)

Given: A horizontal boom OA is loaded at end A by a crate with a weight of 𝑊 = 10,000 N. The boom is held in static equilibrium by a ball-and-socket connector at end O, a cable AB and another bar CD. The two connectors, C and D, on the linkage bar are both ball-and-socket joints. All geometric information is shown in the figure.

FIND: (a) Draw free body diagram of the linkage bar CD and the horizontal boom OA. (4 Points)

(2pts)

(2pts)

ED → ED

c-

Ox→170g FIBµ c-qRD d

w




(b) Express the force of cable AB acting on boom OA at point A and the force from the linkage bar to the boom at point C as force vectors (i.e., their known unit vectors and their unknown magnitudes). (4 points)

�⃗� 𝐴𝐵 = (_____) ______________i + ________________ j + ________________k⃗ (2pts)

𝐹 𝐶𝐷 = (_____) ______________i + ________________ j + ________________k⃗ (2pts)

(c) Find the magnitude of the tension of cable AB and the magnitude of the axial force of the linkage bar CD, also indicate whether CD is in tension or compression (Circle one of the options). (4 Points)

𝑇𝐴𝐵 = N (3pts)

𝐹𝐶𝐷 = N (2pts) (Tension, Compression, Zero) (1pt)

II. = -si'

-8J't tic'

m ⇒ it'

=- Fi i' es

'

I'

= 3T- ki't OE m ⇒ UT, = Isi'-fi ' + oi'

TAB -9667 - o. 667 0.333

E,O ' 6 -98 o

=mI=o.

.

Foxx Fast Texters t Kiani's .Fat -- o E't 85

' tok'm,Trai OE 't xj 'toI m

⇒ ( Oi't 85'

tok'

) x tf i''-FI't 'sE) TAB

+ ( o -i'tis'toI'

) x I ZE'

- ¥54017 Fu,

+ ( o E't 85' tote ) ( o i'

'

+ of - toooo I'

y co

⇒ ( II'tFi'

Hiatt 'EI' HI. H- soooo i's =

⇒ f- TAB - 80000=0 , Az Tmz- ¥ Faso ⇒TAB = 3×104 N

6,366×40×404 ①

Ko-

- 6.667×64




(d) The cross section of the linkage bar CD is a circle with a radius of 0.1m. Please find the average normal stress in bar CD. (2 points)

𝜎𝐶𝐷 = (2pts)

(e) Calculate the reaction force from the ball-and-socket support at O to the bar OA (express the force in vector form). (6 points)

�⃗� = (6pts)

(f) If cable AB has a diameter of 0.01m and a failure stress of 𝜎𝐴𝐵 = 2 × 108 Pa, what is the heaviest load (𝑊𝑚𝑎𝑥) that the boom could hold without exceeding this failure stress? Assume bar CD will not fail. (3 points)

𝑊𝑚𝑎𝑥= (3pts)

A -- Tito . 1) 2=3.14×152 m'

5-- Eff = 2,123×66 Pa6

2.123×10 Pa

EFX i 0×-25 They -1¥ Feb ⇒ Ox = - 2.000×64N

ZFy⇒ : Oy - 25¥ - ¥f=o ⇒ Oy -

-7,333×6 4N

[ Fz=oi Oz f } Tpg - 10,000=0 ⇒ 0*0 N

- 2.000×1045+7,333×10 told w

AaB -- a ( o 5=785×155 m' , (TABI Max -_%Aµs=h57Xb4N ,

Wife -H?; ⇒ Wmax - 5.23×63a5. 231403N

Tony Xue

Tony Xue

800

Tony Xue

Tony Xue

1000

Documents

ME 270 Final Exam Fall 2019 NAME (Last, First):€¦ · ME 270 – Final Exam Fall 2019 NAME (Last, First): _____ (Please PRINT) PUID #: _____ ME 270 Final Exam – Fall 2019 Page

ME 270 Final Exam Fall 2019 NAME (Last, First):€¦ · ME 270 – Final Exam Fall 2019 NAME (Last, First): _ (Please PRINT) PUID #: _ ME 270 Final Exam – Fall 2019 Page