Asked by Anonymous
a 10-kg mass is supported by two strings of length 5m and 7m attached to two pints in the celing 10m apart. find the tenion in each string
Answers
Answered by
drwls
The net upward force exerted by the two strings must equal M g = 98 N
The strings make angles of A1 and A2 with the horizontal.
5 sin A1 = 7 sin A2.
5 cos A1 + 7 cos A2 = 10
Now you have to do some geometry.
25 sin^2 A1= 49 sin^2 A2
25 cos^2 A1 = 100 - 140 cosA2 + 49 cos^2 A2
25 = 100 -140cosA2 + 49
140 cosA2 = 124
A2 = 27.7 degrees
A1 = 40.5 degrees
Now write vertical and horizontal force balance equations and solve for the two rope tensions, T1 and T2.
T1 sinA1 + T2 sinA2 = 98 N
T1 cosA1 = T2 cosA2
Take it from there
The strings make angles of A1 and A2 with the horizontal.
5 sin A1 = 7 sin A2.
5 cos A1 + 7 cos A2 = 10
Now you have to do some geometry.
25 sin^2 A1= 49 sin^2 A2
25 cos^2 A1 = 100 - 140 cosA2 + 49 cos^2 A2
25 = 100 -140cosA2 + 49
140 cosA2 = 124
A2 = 27.7 degrees
A1 = 40.5 degrees
Now write vertical and horizontal force balance equations and solve for the two rope tensions, T1 and T2.
T1 sinA1 + T2 sinA2 = 98 N
T1 cosA1 = T2 cosA2
Take it from there
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