Question

3. Figure 3 shows the symmetric hook of a hoist to lift a package of weight G (width 2a). The hook consists of a plate and two tongs to hold the package by means of friction developed between the package and the tongs (coefficient of static friction Ho). The hook (own weight Go) is held by a central rope (force So). Two ropes (respective forces Si and S2) are connected at a right angle (90°) to the two tongs in points B and C respectively and lead upwards after passing through the rolls at points D and E. The tongs can turn without friction about the smooth hinge in point A (distance a from points B and C). The package can be released by controlling the force of the attached ropes a) Draw the free body diagram (FBD) for the hook and from the equilibrium conditions find the relationship between the forces in the ropes (S1, S2 depending on So). Which equilibrium condition leads to the symmetry condition that S1 S2? 3 marks] b) Draw the FBD for the package only and from the equilibrium conditions find the frictional forces between the package and the tongs. Using the coefficient of static friction μο, find the minimum necessary normal forces between the tongs and the package to hold it. [3 marks] [3 marks] [5 marks] 3 marks] [3 marks] c) From one equilibrium condition for one of the tongs find the actual normal forces between the tongs and the package depending on the rope forces d) Find the maximum load G that can be lifted. How does the rope force So have to be chosen for this and how large do S1 and S2 have to be? e) How would So have to be chosen so that any load falls out from the hook, i.e., the hoist can be unloaded? f) For which coefficient of static friction μο can the diameter of all three ropes be chosen equal, i.e., the maximum forces are the same? S. Но Ho Figure 3: Hook for Q3.

Answer 1