See Fig. A mass of 6 kg is suspended by aropeoflength 2 m from the ceiling.A force of 50 N in the horizontal direction isappliedatthe mid- point P of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium ?(Take g = 10 m s^(-2) ). Neglect the mass of the rope.

See Fig. A mass of 6 kg is suspended by aropeoflength 2 m from the cei

1.	See Fig. A mass of 6 kg is suspended by aropeoflength 2 m from the ceiling.A force of 50 N in the horizontal direction isappliedatthe mid- point P of the rope, as shown. What is the angle the rope makes with the vertical in equilibrium ?(Take g = 10 m s^(-2) ). Neglect the mass of the rope.
Answer» Solution :Figures (b) and (c) are known as free-body DIAGRAMS. Figure (b) is the free-body diagram of W and Fig. (c) is the free-body diagram of POINT P. Consider the equilibrium of the weight W. Clearly `T_2 = 6 XX 10 = 60 N` Consider the equilibrium of the point P under the action of three forces - the tensions `T_1` and `T_2`, and the horizontal force 50 N.The horizontal and vertical components of the resultant force must vanish separately : `T_1 cos theta = T_2 = 60 N` `T_1 sin theta = 50 N` which gives that `tan theta = 5/6 ortheta = tan^(-1) (5/6) = 40^@`