Another question about EK1001 physics

[deleted647690]

This is about question 280 on page 28. It shows a diagram with a mass held by a tension T3, and attached to that rope is a junction splitting into two other ropes with tensions T1 and T2, each at a different angle theta with the horizontal.

The question says, "If m = 10 kg, theta 1 = 60, theta 2 = 30 degrees, the tension T2 is:
A. 50 N
B. 100 N
C. 137 N
D. 237 N"
The answer they give is A, but I don't see how you would do this question. Their reasoning is just, "A is correct. Since the system is in equilibrium, the horizontal forces are equal: T1costheta1 = T2costheta2, and the vertical forces are equal: mg= T1sintheta 1 + T2 sin theta 2

I know that mg would be equal to T1 sin theta 1 + T2 sin theta 2, but we don't know T1 or T2.....

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[rhinzaz]

Hi Acetylmandarin,

We are assuming the system is static (in equilibrium) and not moving; they equate the horizontal forces T1costheta1 = T2costheta2.

Now you can isolate for T1 from this equation and insert that into the vertical forces equation mg= T1sintheta 1 + T2 sin theta 2

After that, you should arrive at T2=50N