Chapter 5, Problem 5.1P

Bar AB of negligible weight is supported by a ball-and-socket joint at B and two cables attached at A. Draw the FBD for the bar, recognizing that it is a two-force body. Determine the number of unknowns.

To determine

Number of unknowns.

Answer to Problem 5.1P

Number of unknown forces are 2.

Explanation of Solution

Given Information:

Bar AB of negligible weight is supported by ball and socket joint at B and two cables attached at A. See the figure below:

  

Calculation:

Draw free body diagram as shown in the following figure:

  

There are three unknown reaction forces at B as $R_{BX}\text{ , }{R}_{BY,}\text{ and }{R}_{BZ}.$

Also there are two unknown tension forces at A as, $F_{AD}\text{ and }{F}_{AC}.$

So there are 5 unknowns in total.

Also, forces at A and B can be reduced to their corresponding resultant at A and B respectively. So there are only 2 unknowns.

Conclusion:

Therefore, there are 2 unknown forces in the system.