3) For the following system, the rod is uniform and weighs 1200N and the sign weighs 2000N. The diameter of the cylindrical supporting steel cable is 4.00cm. a) Determine the tension needed in the steel cable to keep the system in equilibrium. b) Determine the horizontal and vertical forces on the rod due to the pivot. c) Determine the fractional change in the steel cable.

A) Determine the force in the spring with unstretched length 3 inches and a spring constant of 240 lb/ft. B) Determine the forces at A, B, C, D, and F. A 6 in. B 6 in. D 6 in. E G 8 in. 8 in.

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4.8 m 2. The frame shown below is loaded with an unknown horizontal force, P. At point E, the surface exerts a force of 130 lb. on the roller. a) Draw and label all the reactions and forces acting on the frame and on the individual components, using the diagrams provided on the back of this handout. b) Determine the magnitude of the force, P, required for the frame to be in equilibrium. c) Determine the x- and y- components of the force acting at point C on member CDE, and specify the directions (→, +, t. 1). Note: For each calculation, state which diagram number (1, 2, 3, 4) you are using. Ans: P = 80 lb, C = 100 lb , C, = 75 lb 1 (by the way, FBC = 125 lb (T)) 4 in. 8 in. C 3 in. В 6 in. 1 3

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2. For the frame and loading shown to below, determine the components of the reactions at B and D if the force P = 100 lb. a) Draw the free body diagram of the entire frame and free body diagrams for all the components of the frame. Identify any two-force members and use this information in your calculations. Draw and label all forces. b) Find the x- and y- components of the reactions at B and D. Ans: Bx = 64 lb →, By = 48 lb ↑, D, = 64 lb , D, = 52 lb ↑ (By the way, FBC = 80 lb (T)) %3D %3D %3D 2 in. y А В 3 in. C 4 in. 5 in. 10 in.

Q2: The structure is designed to support a 40 kN load vertically and 50 kN load horizontally. The structure consists of a boom AB and rod BC joined by pins at the junctions and supports. Pin at support “c" can move in slot vertically without any friction. Ignoring the weights of the components of the structure: a) Draw Free Body Diagram of the structure, b) Determine the reaction forces at the supports. - Frictionless pin in slot 600 mm B 50 kN 800 mm 40 kN

Two weights, A and C, are fixed to a bar, B. Their masses are: A = 60 kg, B = 230 kg,C = 45 kg. B is, in turn, connected to a fixed vertical post by a hinge and a support cableD. The geometry of the system is shown at right. Treat weights A and C as point masses a)What is the tension in support cable D? Be sure to include a detailed freebody diagram to accompany your analysis.b) What is the magnitude of the force provided by the hinge?c) What is the moment of inertia of the A + B + C as a rigid system, for rotationabout the hinge? For analysis, break the beam into a short piece to the left of thehinge, and a separate longer piece to the right of the hinge. If the support cable D on should break,d) what is the angular acceleration of the beam and weights at the moment the cable breaks?e) what is the magnitude of the linear acceleration experienced by each of the weights, A and C, at moment the cable breaks?

A uniform trapdoor shown below is 1.0 m by 1.5 m and weighs 300 N. It is supported by a single hinge (H), and by a light rope tied between the middle of the door and the floor. The door is held at the position shown, where its slab makes a 30° angle with the horizontal floor and the rope makes a 20° angle with the floor. Find the tension in the rope and the force at the hinge.

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