#440 A force P of magnitude 280 lb is applied

A force P of magnitude 280 lb is applied - Mechanical Engineering

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Free Chegg Question

A force P of magnitude 280 lb is applied to member ABCD, which is supported by a frictionless pin at A and by the cable C.ED. Since the cable passes over a small pulley at E. the tension may be assumed to be the same in portions CE and ED of the cable. For the case when a = 3 in., determine (a) the tension in the cable. (b) the reaction at A.

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Free Chegg Answer

1. Step 1 of 7

   Given P = 280 lb

   Let A_x and A_y be the support reactions at A.

   Let us draw the free-body diagram of the member.

2. Step 2 of 7

   

3. Step 3 of 7

   a) Take moment about A and apply the equilibrium condition 

   Taking sign conventions, anticlockwise moment is taken as positive and clockwise moment is taken as negative.

   

   

   Therefore the tension in the cable is 

4. Step 4 of 7

   b) Apply equilibrium condition 

   

5. Step 5 of 7

   Apply equilibrium condition 

   

   The negative sign shows that the assumed direction of the force was wrong.

6. Step 6 of 7

   Now, the reaction at A is 

   

   Therefore the reaction at A is 

7. Step 7 of 7

   Now, the direction of A is obtained by 

   Since the horizontal reaction acts in the negative x-direction and the vertical reaction acts in the positive y-direction, the angle made by the resultant reaction will be in the second quadrant.