A cylinder is suspended from the ceiling by cables attached at points B, C, and

Question

A cylinder is suspended from the ceiling by cables attached at points B, C, and D. a) What are the tensions in cables AB, AC, and AD if the mass m of the cylinder is 100 kg? b) If the specifications from the cable manufacturer indicates that the maximum allowable tensile strength of each cable is 1,000 N (this value includes the safety factor), what is the largest safe value of the cylinder mass that can be supported based on this criterion? Hint: each cable will not see 1,000 N simultaneously. Be sure to provide complete free body diagram(s) to support your equations of equilibrium for full credit.

Picture:http://tinypic.com/r/27zaee1/6

Explanation / Answer

write all the vectors direction

AD=(-3-0)i+(0+4)j+(3-0)k =-3i+4j+3k ---------------- -3i+4j+3k/34 (unit vector)

AC=(-2-0)i+(0+4)j+(-2-0)k=-2i+4j-2k------------------ -2i+4j-2k/ 24 (unit vector)

AB=(4-0)i+(0+4)j+(2-0)k =4i+4j+2k-------------------4i+4j+2k/36 (unit vector)

let tension in AD=F1
AC=F2
AB=F3

F1+F2+F3 = 100 j

F1(-3i+4j+3k/34 ) +F2(-2i+4j-2k/ 24 )+F3(4i+4j+2k/36 )=100j

solving it we get

-3*F1/34 -2*F2/24 +4*F3/6=0

4*F1/34 +4*F2/24 +4*F3/6=1000

+3*F1/34 -2*F2/24 +2*F3/6=0

solve it we get

F1=200.79

F2=654.54

F3=491.73

b

F2 is maximum ie

so it will get 1000 N first

654.54N for 100kg

for 1000N weight will be 100*1000/654.54 =152.78 kgs

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