SOLUTION: Question 1062547: A workshop table has an equilateral triangular top, each side of which is 900mm, the legs being at the three corners. A load of 500N is placed on the table at a

Algebra ->  Trigonometry-basics -> SOLUTION: Question 1062547: A workshop table has an equilateral triangular top, each side of which is 900mm, the legs being at the three corners. A load of 500N is placed on the table at a       Log On


   



Question 1075922: Question 1062547: A workshop table has an equilateral triangular top, each side of which is 900mm, the legs being at the three corners. A load of 500N is placed on the table at a point distant 325mm from one leg and 625mm from another. What is the load in each of the three legs.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
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Summing the forces in the z direction,
R%5B1%5D%2BR%5B2%5D%2BR%5B3%5D=500
Summing the moments about the x axis,
500%2AC-R%5B3%5D%2AD%2BR%5B2%5D%2AD=0
Summing the moments about the y axis,
500%2AE-R%5B2%5D%2AF-R%5B3%5D%2AF=0
Find C using the law of cosines to find A,
cos%28A%29=%28900%5E2%2B625%5E2-325%5E2%29%2F%282%28900%29%28625%29%29
cos%28A%29=73%2F75
A=13.26
So then
30-A=16.74
So then,
C=625sin%2816.74%29
C=625%280.2880%29
C=180.0mm
and
E=625cos%2816.74%29
E=598.5mm
and
F=900cos%2830%29
F=779.4mm
So then,
Summing about x,
500%2A180-R%5B3%5D%2A450%2BR%5B2%5D%2A450=0
450%28R%5B3%5D-R%5B3%5D%29=500%2A180
R%5B3%5D-R%5B2%5D=%28500%2A180%29%2F450
1.R%5B3%5D-R%5B2%5D=200
and summing about y,
500%2AE-R%5B2%5D%2AF-R%5B3%5D%2AF=0
500%28598.5%29=%28R%5B2%5D%2BR%5B3%5D%29%28779.4%29
2.R%5B2%5D%2BR%5B3%5D=383.9
So then adding eqs. 1 and 2,
R%5B3%5D-R%5B2%5D%2BR%5B2%5D%2BR%5B3%5D=200%2B383.9
2R%5B3%5D=583.9
R%5B3%5D=291.97N
Then,
291.97-R%5B2%5D=200
R%5B2%5D=91.97N
and,
R%5B1%5D%2B91.97%2B291.97=500
R%5B1%5D=116.06N