1. Show that if the coefficient of friction between the block and the plane is 0.35, the force required to just start the block moving up the 40° inclined plane is F = ?? W while the force required to hold the block from sliding down the plane is F = ?? W.
2. The rigid weight less beam carries a load P at its right end and is supported at the left end by two frictionless pins. The pin at the top is pulled upwards and held in a place by a cable inclined at a 45° angle with the horizontal.
Draw a free body diagram of the beam, isolated from its environment i.e. show all the forces acting on the beam alone; show all relevant dimensions; show a reference Cartesian axes system. Explain how would you go on to determine the magnitude of the cable force acting at the pin A and the magnitude and direction of the reaction force at B.
3. Find the reactions acting at A and B in terms of P and dimensions shown (xp/L). Isolate member BC and draw a free body diagram which will enable you to determine the forces acting on this member. Find those forces, again in terms of P and the dimensions shown.
Find the force in the horizontal beam of the structure.
4. For the truss shown below,
(i) Isolate the full truss structure and replace the applied loads with an equivalent load(no moment acting at some distance b from the left end. What is b?
(ii) Determine the reactions at f and I.
(iii) Find the force in member ch with but single additional free body diagram.
5. Find the force in the member CD of the structure shown in terms of P. All members, except CF, are of equal length. In this, use method of joints starting from node B. Note: You must determine the reaction at B to get started.
6. The rigid weight less beam carries a load P at its right end and is supported at the left by two frictionless points. What can you say about reactions acting at A and B? E.g., "they are equivalent to..."
7. A simply supported beam (indicated by the rollers at the ends ) carries a trolley used to lift and transport heavy weights around within the shop. The trolley is motor powered and can move between the ends of the beam. For some arbitrary location of the trolley along the beam a.
(i) What are the reactions at the end of the beam?
(ii) Sketch the shear force and bending moment distributions.
(iii) How does the maximum bending moment vary with a; i.e. change as the trolley moves from one end to the other?
