Just wondering whether anyone could help with a physics problem.
The question says:
Determine forces T1 and T2 when a heavy metal beam of weight 12kN is suspended at rest from the hook of a crane. The beam is held at an angle to the horizontal by two ropes AB and BC. AB is 55 degrees to the vertical and BC is 20 degrees to the vertical.
So far I've got that the system is in equilibrium so there are no resultant forces meaning the sum of the downward vertical components of T1 and T2 = 12000N. I also know that I need to do T1sin55 to get that vertical component (or work back from it in this case) but I'm not sure whether I've got the next bit right. Could I say T1cos55=T2cos20 for the horizontal components because there are no resultant forces in the horizontal direction either? Could I do this by simultaneous equations?
T1sin55 + T2sin20 = 12000
meaning T1 can be replaced with T2cos20/cos55
so T2sin55cos20/cos55 + T2sin20 = 12000
giving 1.342020T2 + T2sin20 = 12000
so T2=12000/1.68... = 7125.7N
And then substitute that into T1sin55 + T2sin20 = 12000?
T1sin55 + 2437.139867 = 12000
T1sin55 = 9562.86....
Does this seem reasonable?
Resolving Tension Forces Question
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