a block hangs from a cord 10 m long. a second cord is tied to the midpoint of the first, and a horizontal pull equal to the half the weight of the block is exerted on it, the second cord being always kept horizontal.
a) how far will the block be pulled to one side?
b)How far will it be lifted?

Question

a block hangs from a cord 10 m long. a second cord is tied to the midpoint of the first, and a horizontal pull equal to the half the weight of the block is exerted on it, the second cord being always kept horizontal.
a) how far will the block be pulled to one side?
b)How far will it be lifted?

queelius · Answer

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So, what is T, tension force? It is, as a force vector, <(1/2)w, w>. As a scalar, it is:

$$\left| T \right| = \sqrt((\frac{ 1 }{ 2 }w)^2+w^2) = \frac{\sqrt{5}}{2}w$$

That means $$\left| T \right| \sin(\theta) = w; \frac{\sqrt{5}}{2}w{\sin(\theta)}=w; \sin(\theta) = \frac{\sqrt{5}}{2}$$

We know the length of the top half of the cord, 5 m, and we know the angle (theta), thus we know how long the vertical component of the 5 meter cord is. Can you take it from here?