Look at the point where the two ropes meet. Since the system is in static
equilibrium, the net force on this point must be zero. This means the horizontal
forces must balance and the vertical forces must balance. Since the horizontal
forces balance, this means T 1 x = T 2 x, so
T 1 cos 45° = T 2 cos 45°which gives us T 1 = T 2. Since the tensions are the same, we can drop the subscripts
and simply refer to the tension in each rope as T.
Now, to balance the vertical forces, we notice that the total upward is T 1 y + T 2 y =
Ty + Ty = 2Ty and the force downward is Mg, the weight of the block. Therefore,