A man sits in a seat that is hanging from a rope. The rope passes over a pulley suspended from the ceiling, and the man holds the other end of the rope in his hands. What is the tension in the rope, and what force does the seat exert on him? Draw a free-body force diagram for the man.
Solution 1DQ The free body diagram can be drawn as shown below. Let the weight of the man be M and that of the seat be S . Therefore, from the free body diagram above, T + T = M + S 2T = M + S T=(M + S)/2…..(1) This is the tension in the rope. In other words, the tension in the rope is the half of the sum of the weights of the man and the seat. Let the seat exerts a force of R on the man. Tension in the string T and R will be acting upward. This combination will be balanced by the weight of the man M. Therefore, M = T + R R = M T Now, substituting T value from equation (1), R = M (M + S)/2 R = (2M M S)/2 R = (M S)/2 Therefore, the force exerted by the seat on the man will be half of the difference between the weights of the man and the seat.