Answer to Question #96210 in Classical Mechanics for John

Question

Questions in the link
https://eksiup.com/p/zh2525055pgx

Answer 1

In general case, as the net force is zero:

$${T}_{AB}\cos\theta_2=F\sin\theta_1$$ $$T_{AC}+T_{AB}\sin\theta_2=F\cos\theta_1$$

It has the solution:

$${T}_{AB}=\frac{F\sin\theta_1}{\cos\theta_2}$$

$$T_{AC}=-\frac{F\sin\theta_1}{\cos\theta_2}\sin\theta_2+F\cos\theta_1$$

So, for case a):

$${T}_{AB}=\frac{100*\sin0^{\circ}}{\cos45^{\circ}}=0N$$

$$T_{AC}=-0+100\cos0^{\circ}=100N$$

for case b)

$${T}_{AB}=\frac{100*\sin30^{\circ}}{\cos60^{\circ}}=100N$$

$$T_{AC}=36.6N$$