a 20N crate is suspended by 2 ropes, one with a angle of 40 degrees and the other with a angle of 15 degrees. Find T1 and T2.
This was a extra credit problem and i must know how to solve it! it's bugging me! lol
This was a extra credit problem and i must know how to solve it! it's bugging me! lol
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Zero horizontal force:
T1 sin(40) = T2 sin(15)
Zero vertical force
T1 cos(40) + T2 cos(15) = 20
From these two equations in two unknowns you can easily solve for both.
E.g.
The first equation tells you that
T1 = T2 sin(15)/sin(40)
Substituting this in the second equation gives:
T2 sin(15)/sin(40) * cos(40) + T2 cos(15) = 20
T2 ( sin(15)/tan(40) + cos(15) ) = 20
T2 = 20 / (sin(15)/tan(40) + cos(15))
and then
T1 = 20 (sin(15)/sin(40) ) / ( (sin(15)/tan(40) + cos(15))
T1 sin(40) = T2 sin(15)
Zero vertical force
T1 cos(40) + T2 cos(15) = 20
From these two equations in two unknowns you can easily solve for both.
E.g.
The first equation tells you that
T1 = T2 sin(15)/sin(40)
Substituting this in the second equation gives:
T2 sin(15)/sin(40) * cos(40) + T2 cos(15) = 20
T2 ( sin(15)/tan(40) + cos(15) ) = 20
T2 = 20 / (sin(15)/tan(40) + cos(15))
and then
T1 = 20 (sin(15)/sin(40) ) / ( (sin(15)/tan(40) + cos(15))