# string tension?

Calculate the magnitude of the tension in string1 if θ1 = 33.91°, θ2 = 52.83° and the mass of the sign is 5.10 kg.

### 1 Answer

- SlowfingerLv 62 months agoFavourite answer
Answer:

S1 = 30.25 N

S2 = 41.55 N

Explanation:

Let tension forces in string 1 and 2 are S1 and S2 respectively. Supposed directions are away from the sign.

Condition of static equilibrium is that:

1) the sum of all forces in x-direction is zero.

2) the sum of all forces in y-direction is zero

This yields 2 equations

S1 cos θ1 - S2 cos θ2 = 0

S1 sin θ1 + S2 sin θ2 - mg = 0

From 1st equation

S1 = S2 cos θ2 / cos θ1 ...... (*)

substitute this into 2nd equation

S2 (cos θ2 sin θ1 / cos θ1 + sin θ2) - mg = 0

S2 = mg / (cos θ2 tan θ1 + sin θ2)

S2 = 5.1 * 9.8 / (cos 52.83° tan 33.91° + sin 52.83°) = 41.55 N

Back to (*)

S1 = 41.55 cos 52.83° / cos 33.91° = 30.25 N