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A circular plate of radius r is suspended in equilibrium as shown in the figure by the three wires that areconnected to the ring at point A. If the spring at point E is stretched by a distance of 20 mm and the springconstant is kE = 100 N/mm, determine the mass of the plate.Take   α = 32◦,   β = 115◦, ℎ = 45.2 m and r = 10.6 m You must show all your work, including free body diagram, for full credit.

Find the centroid, C, of the cross-section shown in the figure and the moment of inertia about the centroidal axis x’’. Show all your calculations to receive full credit. The figure is not in scale. 

A circular plate of radius r is suspended in equilibrium as shown in the figure by the three wires that areconnected to the ring at point A. If the spring at point E is stretched by a distance of 20 mm and the springconstant is kE = 100 N/mm, determine the mass of the plate.Take   α = 31◦,  β = 122◦, ℎ = 36.3 m and r = 12.1 m You must show all your work, including free body diagram, for full credit.

Find the magnitude of the resultant force of the distributed loads acting on the beam AB.  Justify your answer to receive full points.

The shaft is supported by a journal bearing at A and a thrust bearing at B. Determine the tension in cable CE and the reactions at A and B when a load P = 93 lb and a couple moment M = 50 lb·in is applied. Assume the bearings are properly aligned. For full credit, you must show these steps: Draw a free body diagram. Write sum of forces acting on the body. Take the sum of moments about point B.

Find the magnitude of the resultant force of the distributed loads acting on the beam AB.  Justify your answer to receive full points.

Given θ = 21◦,  α = 16◦, d1 = 520 mm, and d2 = 350 mm, find the moment about point B generatedby the F = 230 N forces. Note that positive moments are counterclockwise. Justify your answer to receive full points.

Given  α = 25◦, b = 2.13 in. and d = 2.51 in. find the moment generated by the P = 173 lb forces. Note that positive moments are counterclockwise. Justify your answer to receive full points.  

Determine the resultant force of forces F2  and F3 as a cartesian vector.  Note that the angles shown in the force F2 are the coordinate angles α, β and γ with respect to the coordinate axes. You may ignore force F1. 

Given d1 = 23 mm, d2 = 10 mm, d3 = 12 mm, θ = 40◦, P = 36 N, and M = 210 N⋅mm, determinethe resultant moment about point C. Note that counterclockwise moments are considered to be positive. Justify your answer to receive full points.