Don\'t forget the formulas. Imagine you have a taught rope that is completely ho

Question

Don't forget the formulas.

Imagine you have a taught rope that is completely horizontal. It is so taught, it makes a musical tone when you pluck it! Now, at the mid-point of the rope, you hang a 5 ib weight. No matter how taught the rope is, it still deflects downward at the point of load From what you know of statics (and thus also from what you know is not statics), explain why does the rope always deflect downward? Explain with words and equations. Please write at least 200 words. You cannot see others posts until you post. This will be graded for insights and effort

Explanation / Answer

When the weight is suspended at mid point of the rope, there will be tensions (T) in the two inclined segments of the rope. Suppose each segment is making an angle (A) with the vertical, than vertical components of tensions will be T cosA each, so total vertical force is 2TcosA and horizontal components TsinA will cancel each other. So in static equilibrium, downward weight = upward tension

So 2TcosA = mg, so tension T = mg/2cosA

So if we want the rope to be straight, than angle A = 900,

so cos 900 = 0, hence tension T = infinite, which is impossible. So our conclusion is that the rope can't be straight.

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