ME 270 – Spring 2016 Exam 1

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ME 270 – Spring 2016 Exam 1

PROBLEM 1 (20 points) – Prob. 1 questions are all or nothing.

1A. Determine the force vector expression for cable AB (i.e., ) assuming the tension in the cable is 700lbs. Determine the moment of  about point C (i.e., the origin of the coordinate axes).

1B. For the system shown, determine the equivalent force-couple system at the base at C. Express the resultants in vector form. (Hint: This is not a static equilibrium problem.)

1C. The force on the rope attached at C is 

(i) Find the unit vector  that points from C to B.

(ii) Find the magnitude FCB of the projection of  in the direction of the unit vector .

1D. For the shaded area shown determine:

(i) the area A

(ii) the x-centroid.

Note: Keep the answer in terms of constants b and h.

PROBLEM 2 (20 points)

GIVEN: A ring holds a crate of weight W equal to 400N. Addtionally, the ring is held in place by cables AD, AC, and rigid rod AB, which acts along the x-axis as shown. Answer the following:

a) In the space below draw a FBD of the ring (4 pts).

b) Resolve the tension in ropes AB, AC and AD in Cartesian vector form.

c) Find the magnitude of the tensions in cable AB, AC, and AD.

d) Find the angle α between cables AB and AC (4 pts).

PROBLEM 3. (20 points)

GIVEN: Angled bar ABCD is loaded as shown and held in static equilibrium by a fixed support at A.

FIND:

a) Determine the equivalent force for the distributed load along the vertical bar (AB) and its location from support A. (5 pts)

b) On the sketch provided, complete the free-body diagram of bar ABCD using the equivalent force computed above. (3 pts)

c) Determine the reactions at the fixed support A required to hold bar ABCD in static equilibrium.    (10 pts)

d) If the 90 ft-lb couple were shifted toward point B, what impact would this have on the reactions at A? (2 pts)