Ex 5

Statics – Exercise No. 5 4.62 A uniform rod AB of length 3R and weight W rests inside a hemispherical bowl of radius R as shown. Neglecting friction, determine the angle θ corresponding to equilibrium. Note: use the fact that AB is three force body. Answer: θ = 23.20.

4.63 A 1.2 × 2.4 m sheet of plywood with a mass of 18 Kg has been temporarily against column CD. It rests at A and B on small wooden blocks and against protruding nails. Neglecting friction at all surfaces of contact, determine the reactions at A, B and C. Answer: A = 106j – 10.19k [N] ; B = 70.6j – 40.8k [N] ; C = 51k [N]

4.67 A 200-mm lever and a 240-mm-diameter pulley are welded to the axle BE wich is supported by bearings at C and D. If a 720-N vertical load is applied at A when the lever is horizontal, (a) the tension in the cord, (b) the reactions at C and D. Assume that the bearing at D does not exert any axial thrust. Answer: (a) T = 1200 [N] ; (b) C = 400i + 1200j [N], D = -1600i - 480j [N]

4.75 The 4-m boom AB is acted upon by the 5-kN force shown. Determine (a) the tension in each cable, (b) the reaction at the ball and socket at A. Answer: TBD = 4.12 [kN] ; TBC = 5.75 [kN] ; A = 8.84i + 2.5j [kN]

4.104 Two rods are welded together to form a T-shaped lever which leans against a frictionless vertical wall at D and is supported by bearings at A and B. A vertical force P of magnitude 600 N is applied at the midpoint E of rod DC. Determine the reaction at D. Answer: D = 375i [N] 1

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All the questions are taken from Ferdinand P. Beer and E. Russell Johnston Jr. “Vector Mechanics for Engineers, Statics” Second SI Metric Edition, McGraw-Hill Book Company.