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If you have a mass hanging on a string between two poles, pulls the rope slightly downward and creates a tension in the rope and an angle to the horizontal (theta). If you doubled the distance between these two poles, what would happen to theta (assume the same tension in the rope)?
This question is a cliffnotes version from TPR CBT IV passage 5. The answer is that the angle does not change. However, from a geometric perspective, I was approaching the question looking at triangles. If the same tension is in the rope, then the mass should cause the rope to sag an equal distance as previously. Thus, the height of the triangle is the same. Since the length of the base of the triangle increases, shouldn't the angle then have to decrease?
For example, a triangle with height 3 and base 4 has a theta of ~37 degrees and a triangle with height 3 and base 8 has a theta of ~ 21 degrees.
What is wrong in my reasoning?
This question is a cliffnotes version from TPR CBT IV passage 5. The answer is that the angle does not change. However, from a geometric perspective, I was approaching the question looking at triangles. If the same tension is in the rope, then the mass should cause the rope to sag an equal distance as previously. Thus, the height of the triangle is the same. Since the length of the base of the triangle increases, shouldn't the angle then have to decrease?
For example, a triangle with height 3 and base 4 has a theta of ~37 degrees and a triangle with height 3 and base 8 has a theta of ~ 21 degrees.
What is wrong in my reasoning?
