Concepts Of Physics MCQ Edition [Volume 1]PhysicsNewton's Laws of Motion
A man has fallen into a ditch of width d , and two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in the figure. Assuming the force exerted by both friends is equal, find the force applied by each friend on the rope when the man is at a depth h .
Options
- Amg d^2 + 4h^2 4h
- Bmg d^2 + h^2 2h
- Cmg h d^2 + 4h^2
- Dmg d^2 + 4h^2 2h
Correct answer
A. mg d^2 + 4h^2 4h
Step-by-step solution
Let T be the force applied by each friend. Since the man is pulled up slowly, he is in equilibrium. The horizontal components of the tension forces balance each other, which implies the man is exactly in the middle of the ditch. Thus, the horizontal distance from the man to each pulley is d 2 . Let be the angle each rope makes with the vertical. From the geometry of the system, the length of the rope from the pulley to the man is given by: L = h^2 + ( d 2 )^2 = 4h^2 + d^2 2 The cosine of the angle is: = h L = 2h d^