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_AH  - T cos 20º = 0          R_AH  = T cos 20º                          ...(i)

∑V = 0      R_AV  - 10 - T sin 20º = 0 R_AV  = 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_AH = 5.54 Kg                             .......ANS

R_AV = 15.89 Kg                          .......ANS