Calculate the tension T in the rope:
Q: A man raises 10 Kg joist of length 4m by pulling on rope, Find out the tension T in the rope and reaction at point A for the position as shown in the figure given below.
Sol.: Apply the condition of equilibrium
∑H = 0 R_{A}_{H} - T cos 20º = 0 R_{A}_{H} = T cos 20º ...(i)
∑V = 0 R_{A}_{V} - 10 - T sin 20º = 0 R_{A}_{V} = 10 + T sin 20º ...(ii)
By taking moment about the point A
T sin 20º × AC + 10 sin 45º × AE - Tcos20 × BC = 0,
AC = 4 cos 45º = 2.83 m BC = 4 sin45º = 2.83 m AE = 2 cos 45º = 1.41 m
T × 0.34 × 2.83 + 10 × 0.71 × 1.41 - T × 0.94 × 2.83 = 0,
0.9622 T + 10.011 - 2.66 T = 0
T = 5.9 Kg .......ANS
By putting value of T in equation (i) and (ii)
R_{A}_{H} = 5.54 Kg .......ANS
R_{A}_{V} = 15.89 Kg .......ANS