7laha - Equilibrium

"7laha - Equilibrium"

Smart structure problems for never stop thinking

Source:  Mechanics of material by

Ferdinand p. Beer and E .Russell Johnston

Solved Example (3-41) :

A continuous cable of total length 4m is wrapped around small pulleys at A,B,C and D if each block has mass =15.6Kg what is the change in the length of the two springs. you should know that the springs are un stretched when d=2m .
K for the springs =500 N/M .

Solution :

Each spring has k=500N/m   each mass =15.6KG
At d=2m the cable has  square form
 

when we put the masses
The change in the form is too slight
So    2 T/√2=15.6 *9.81   so T =108.2N

So ∆=(√2T/500)=0.3m
Note that : this problem can be solved in one step that : mg=K∆

Try this problem :

From the previous problem
At different masses and horizontal springs .Can  the cable take this form?
Consider α=60deg ,θ=30deg ,a and b are known and the weight at pulley D is lighter than the weight at pulley B
If your answer is yes find the mass at pulley D in terms of ∆1 and∆2
If your answer is No say why?

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