rope ab is 4.5m long and is at the same level 4 m apart . a load of 1500N is suspended from a point c on the rope at 1.5 m connected at a point p on the rope 1m from the b willbe necessary to keep the position cd horizontal level
Answers
Given:
length of rope = 4.5 cm
load of rope = 1500 N
Explanation:
Let CE = y and
AE = x
From Δ AEC x² + y² = 15 = 2.25 (1)
AB = 4 cm
and AC + CD + BD = 4.5 m
CD = 4.5 - 1.5 - 1.0 = 2.0 m
EF = 2.0m
BF = AB - ( AE + EF)
= 4( - ( x= 2.0) = 2- x (2)
From Δ BFD BF² + DF² = 1²
(2 - x)² + Y² = 1 (3)
From (1) and (3)
x² - (2 - x)² = 1.25
x² - 4 + 4x - x² = 1.25
x = 1.3125 m
α = cos⁻ [ 1.3125 / 1.] = 28.955°
β = cos⁻ [ 2 - 1.3125 / 1] = 46.567°
at C, we get
T₁ / sin 90° = T₂ / sin 118.955° = 1500 / sin( 180 - 28.955)°
T₁ = 3098.39 N
T₂ = 2711.09 N
Answer = 3098.39 N , 2711.09 N