#310 The hoist shown is used in a machine

The hoist shown is used in a machine - Mechanical Engineering

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Free Chegg Question

The hoist shown is used in a machine shop to position heavy workpieces in a lathe. If the cable between pulleys A and B can support a force of 300 lb, all other cables can support a force of 500 lb, and bar CE can support a compressive force of 600 lb, determine the largest weight W that may be lifted.

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Free Chegg Answer

1. 1. 1. 1. Step 1 of 6

            Draw the free body diagram of the hoist.

         2. Step 2 of 6

            

         3. Step 3 of 6

            Consider Fig. (1):

            Write the equilibrium equation in y-direction.

             …… (1)

            Consider Fig. (2):

            Write the equilibrium equation in y-direction.

            

            Substitute  for .

             …… (2)

            Find the angles made by the tension in cord CD and bar CE.

            

         4. Step 4 of 6

            Consider Fig. (3):

            Write the equilibrium equation in x-direction.

            

            Substitute  for  and  for .

             …… (3)

            Write the equilibrium equation in y-direction.

            

            Substitute  for , for , for  and  for .

             …… (4)

         5. Step 5 of 6

            Substitute  for  in equation (3).

             …… (5)

            Calculate the values of weight by substituting the maximum forces in the cables and bar.

            Substitute  for  in equation (1).

            

            Substitute  for  in equation (2).

            

             

         6. Step 6 of 6

            Substitute  for  in equation (4).

             

            

            Substitute  for  in equation (5).

            

            Therefore, the largest weight that may be lifted is .If load above this is considered the any of the cables may fail.