There are two vertical poles, one of height 100 feet and the other 70 feet, positioned a horizontal distance of 80 feet apart on level ground. A rope of length 100 feet connects the tops of the two poles. A weight, placed on the rope so that it can slide freely along it, is allowed to come to rest.
Find the horizontal distance of the weight from the 100 feet pole and the vertical distance from the ground.
(In reply to
re: method .... by Kenny M)
You are right. While the angles are equal (and so my solution was correct for h and v), I did not correctly handle to vertical forces and the total tension correctly.
For the weight not to move, the horizontal tension must cancel, so the angles are equal. T_x = (+/-) T cos(theta), where T is the total tension. For each side of the string from the weight:
T_y = mg/2 (on each side the vertical tension is equal due to the angle being equal, and is half the downward force). Since Ty = T sin(theta), T = mg/(2 sin (theta)),
and so
T_x= cot(theta) mg/2
Edited on June 26, 2019, 5:27 pm
re(2): method ....
