(please print) puid #: problem 1 (20 points) 1a. if the

ME 270 – Fall 2021 Exam 1 NAME (Last, First): ________________________________

(Please PRINT) PUID #: __________________

ME 270 Exam 1 PM – Fall 2021 Page 2

PROBLEM 1 (20 points)

1A. If the tension of cable AC was measured at TAC = 94.6lbs, determine the tension of cable AB(TAB) and the weight of the crate (Wcrate). Also, if the weight of the crate were doubled, what would the tension of cable AC(TAC) be? (5 pts) y

x

TAB = __________________________lbs (2 pts) Wcrate=_________________________ (2 pts) TAC =___________________________ (1 pts)




1B. Determine the equivalent force-couple system at base A that could be used to replace the applied loading shown on the jib crane. (Hint: This is not a static equilibrium problem.) (5 pts)

�̅�𝑨= ____________𝒊̅ + __________________𝒋 ̅𝒍𝒃𝒔 (2pts) �̅�𝑨 = _______________________�̅� ft-lb (3pts)




1C. For the shaded area shown, determine the area (A) and the x-component of the location of the

centroid (�̅�) of this shape with respect to the x-y axes shown using the method of composite parts. (5

pts.)

𝐴 = _______________𝑓𝑡2 (2pts) �̅� = __________________𝑓𝑡 (3pts)




1D. For the distributed loading shown, determine the magnitude of the equivalent force (Feq) and the

equivalent x-location (xeq) along the bar (as measured from the origin) that would be equal to the

original loading shown below. (5 pts).

𝐹𝑒𝑞 = ______________𝑁 (2pts) xeq= _____________𝑚 (3pts)

O .




PROBLEM 2. (20 points)

Given: Frame ABC is loaded with two forces, a couple, and a distributed load as shown and is held in static equilibrium by a fixed support at C.

Find: a) Determine the equivalent force (Feq)

for the distributed load and its distance from B

(�̅�eq). (3 pts)

Feq = lbs (2 pts)

(�̅�eq)from B = ft (1 pt)

b) On the artwork provided, complete the free body diagram for frame ABC. Use the Feq determined

above in your free body diagram. (2 points)




c) Clearly write the equilibrium equations and solve for reactions at fixed support C in vector form. (12 pts)

�̅�C = _________________𝒌 ̂ft-lbs (6 pts) �̅�c =____________ 𝑖̂+ ____________ 𝑗̂ lbs (6 pts)

d) If the 120 ft-lb couple at A were removed, what qualitative effect would this have on the magnitudes of the reactions (no work need be shown)? (3 pts)

MC would: increase remain the same decrease (circle one) (1 pt)

Cx would: increase remain the same decrease (circle one) (1 pt)

Cy would: increase remain the same decrease (circle one) (1 pt)




PROBLEM 3. (20 points)

GIVEN: A pole of negligible mass is held in static equilibrium by two cables (AB and CD) attached to walls B and D and a ball-and-socket support at point O. A 210-N load is applied on the pole at x =10 m.

a) Complete the free body diagram of the pole using the artwork below. (2 pts)

b) Write expressions for tension vectors AB and CD acting on the pole using their unknown magnitudes and known unit vectors. (4 pts) The applied load is shown as an example, you may express as a simplified fraction or use the decimal representation.

T̅AB = |�⃗⃗� AB| ∗ [( __________) 𝑖̂ + (____________) �̂� + (___________)�̂�]N (2 pts)

T̅𝐶𝐷 = |�⃗⃗� CD| * [( __________) 𝑖̂+ (____________) �̂� + (___________) �̂�]N

Applied Load= 210 * [( ____0___) 𝑖̂+ (_____0___ ) �̂� + (____- 1_____) �̂�]N

(2 pts)

(example)




c) Determine the magnitudes of the tensions in cables AB and CD. (8 pts)

d) At point O, determine the reaction at O and express as a vector. (6 points)

|�⃗� 𝐴𝐵| = 𝑁 (4 pts)

|�⃗� 𝐶𝐷| = 𝑁 (4 pts)

O⃗⃗ = [( __________) 𝑖̂ + (____________𝑗̂ + (___________) �̂�] N. (6 pts)




ME 270 Exam 1 Equations

Distributed Loads

( )L

eq0

F = w x dx

( )L

eq0

xF = x w x dx

Centroids

cx dAx =

dA

cdAy =

dA

y

ci i

i

i

i

x A

x = A

ci i

i

i

i

y A

y = A

In 3D,

ci i

i

i

i

x V

x = V

(please print) puid #: problem 1 (20 points) 1a. if the

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