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A body of mass m is suspended by two st...

A body of mass m is suspended by two strings making angles `alpha and beta` with the horizontal. Find the tensions in the strings.

Text Solution

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Take the body of mass m as the system. The forces acting on the system are
i. mg downwards (by the earth),
ii. `T_1` along the first string (by the first string ) and
iii. `T_2` along the second string (by the second string)


These forces are shown in figure. As the body is in equilibrium, these forces must add to zero. Taking horizontal components,
`T_1 cos alpha - T_2 cos beta =0`
`T_1 cos alpha= T_2 cos beta` .........i
Taking vertical components,
`T_1sinalpha+T_2sinbeta-mg=0` .............ii
Eliminating `T_2` from i and ii,
`T_1 sin alpha + T_1(cos alpha)/(cos beta)` `sinbeta =mg`
or , ` T_1 = (mg)/(sin alpha + (cos alpha)/(cos beta)sin beta` = `(mg cos beta)/(sin(alpha+beta))`
From i. `T_2 = (mgcosalpha)/(sin (alpha+beta)`
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