Question:
A body of $20\ lb-wt$ is suspended by two strings that are $6ft$ and $8ft$ long, their other ends being tied to the extremities of a rod of length $10ft$. If the rod was so held that the body hangs just below its midpoint, find the tensions of the strings.
If the rod was held parallel to the ground:
If the rod was tilted so that C and D points were aligned (according to me):
If the rod was tilted so that C and D points were aligned (according to my book):
My experiment:
Using the above apparatus, I attempted to simulate the problem in the question. I found it impossible for the bottle/weight to move towards the midpoint of the stick by tilting the stick towards the shorter string (this is what my book claims through its figure). I found the bottle moving towards the midpoint of the stick when I tilted the stick in the opposite direction i.e. towards the longer string. So, that's why I think the book's figure is wrong.
My question:
- Isn't the book's figure wrong? Didn't they tilt the rod in the opposite/wrong direction?
Your strings are not tightened. This is why your experiment does not work.
You can solve the problem in a different way. Draw the triangle $ABC$. It will have the same shape as the final triangle irregardless of how you tilt the rod. Then draw the line between $D$ (the midpoint of $AB$) and the point $C$. Now rotate the figure until the line $DC$ is vertical, and the rod $AB$ is facing north. This is the correct positioning of the rod. Afterwards you can compute the angles and find the forces.