Question

A rope is connected between two points A and B 120 cm apart at the same level. A load of
200 N is suspended from a point C on the rope 45 cm from A . Find
the load, that should be suspended from the rope D 30 cm from B, which will keep the
rope CD horizontal.

Answer 1

Answer:

The rope has load weight 200 N at point C, 45 cm horizontally from A toward B, and h cm beneath the AB line.

Unknown load weight F is at point D, 30 cm horizontally from B toward A, and h cm beneath the AB line, so that line segment CD is parallel to AB and h cm beneath it.

Obviously, the rope from A to C to D to B is longer than the direct AB line (120 cm). The rope length does not matter because it does not affect the horizontal portions of distances, such that ((AC)^2-h^2) + CD + ((DB)-h^2) = 120 cm.

The right triangle of distances formed by hypotenuse AC, horizontal side 45 cm and vertical side h determines a similar triangle of forces at point C: hypotenuse equal to tension from C to A, horizontal component opposing tension T from C to D, and vertical component opposing weight 200 N.

The ratios of the distance and force triangles’ orthogonal sides around point C are equal because the triangles are similar:

45/h = T/200

hT = 45*200 [1]

The same kind of relationship exists for distance and force triangles around point D, with two identical values: the vertical distance h and the horizontal tension T from D to C:

30/h = T/F

hT = 30F [2]

Combine [1] and [2] to eliminate left sides:

45*200 = 30F

F = 45*200/30 = 300

The load weight at point D is 300 N.

h/45 = 200/Tcom a horizontal tension T between C and D, a vertical load

The reason for describing distances as frsction of ropTo maintain points C and D at same level