Question

Hi, so i have to find T1, can some1 help?

Answer 1

30.1 N

Explanation:

Given:

$W_1 = 16\:\text{N}$

$W_2 = 8\:\text{N}$

Let's write the components of the net forces at the intersections. Note that the system is equilibrium so all the net forces are zero.

Forces involving W1:

$x:\:\:\:-T_1 + T_3\cos \alpha = 0\:\: \\ \text{or}\:\:T_2 = T_3\cos \alpha\:\:\:\:\:(1)$

$y:\:\:\:T_3\sin \alpha - W_1 = 0\:\:\: \\ \text{or}\:\:\:T_3\sin \alpha = W_1\:\:\:\:\:\:(2)$

Forces involving W2:

$x:\:\:\:T_1\sin 53 - T_3\sin \alpha = W_2\:\:\:\:\:\:\:(3)$

$y:\:\:\:T_4 - T_1\cos 53 - T_3\cos \alpha = 0\:\:\:\;(4)$

Substitute (2) into (3) and we get

$T_1\sin 53 - W_1 = W_2$

Solving for $T_1$,

$T_1 = \dfrac{W_1 + W_2}{\sin 53} = 30.1\:\text{N}$