Question

A 90N body is suspended by means of two strings which make an angle of 40 and 35 degrees with the vertical. Determine the tensions in the two strings.

Answer 1

The equilibrium conditions give

T_1 sin⁡〖35°〗-T_2 sin⁡〖40°〗=0

T_1 cos⁡〖35°〗+T_2 cos⁡〖40°〗-mg=0

or

T_2=sin⁡〖35°〗/sin⁡〖40°〗 T_(1 )

〖T_1 cos〗⁡〖35°〗+cos⁡〖40°〗 sin⁡〖35°〗/sin⁡〖40°〗 T_(1 )=mg

We get

T_1=mg/cos⁡〖35°+tan⁡〖40°〗 sin⁡〖35°〗 〗 =(90 N)/cos⁡〖35°+tan⁡〖40°〗 sin⁡〖35°〗 〗 =69 N

T_2=sin⁡〖35°〗/sin⁡〖40°〗 T_(1 )=sin⁡〖35°〗/sin⁡〖40°〗 ×69 N=62 N