Question

Note the situation where the clothes hanging on the line may be too low. If the weight of the clothes does not change, would raising the line create more or less tension, T? To answer this, consider the required vertical component of T, then the horizontal. Why is an angle of 0o impossible?

Answer 1

Let, the tension be T, in the line, which makes an angle $\theta$ with horizontal.

The vertical component component becomes T sin $\theta$ = mg, where, m is mass of the clothes on it.

When the line is raised, angle $\theta$ of the line with the horizontal is decreased, so, sin $\theta$ also decreases. But, the weight mg of the clothes remains same. So, T increases to keep T sin $\theta$ same as before.

Also, the horizontal component T cos $\theta$ of the tension of the line increases, since, decreasing $\theta$ increases cos $\theta$ .

So, T cos $\theta$ increases.

Hence, raising the line creates more tension the line.

For $\theta$ = 0^o, sin $\theta$ = 0, so, T sin $\theta$ = T x 0 = mg = 0, which is impossible, because, the mass m of the clothes is non - zero. For this reason, an angle of 0^o is impossible.