Problem NEWTON's Laws Of Motion?

Question

A man has fallen into a ditch of width 'd' & 2 of his friends are slowly pulling him out using a light rope & two fixed pulleys. Show that the force exerted by each friend on the rope increases as the man moves up. Find the force when the man is at depth 'h'. 'h' is the height between the pulley & the man fallen in the dicth.

Answer 1

We need more information on the layout of this problem.  I don't know how the pulleys are placed.  I don't know if they are lifting the man straight up, or up a slope.  I am guessing there is a diagram with this problem.  We need to see it.

Answer 2

http://answers.yahoo.com/question/index;...

Answer 3

The friends need to pull with a certain upward force, Fy, the whole time.  At first, most of the force is vertical, because the ropes are closer to vertical than horizontal.  But the higher the man gets pulled, the more horizontal the ropes are, and the stronger they need to pull in order to maintain the same Fy.

Draw right triangle ABC, where A is the bottom of the rope, B is the top, and C is an imaginary point where the right angle is formed.  Segment BC has length h.  Angle BAC is theta.  

Fy = F * sin(theta)

F = Fy / sin(theta)

Theta depends on two things: how deep h is, and how wide d is.  

The base of the triangle, segment AC, has length 1/2 d.

So hypotenuse (segment AB) = sqrt[ (.5d)^2 + h^2) ]

sin(theta) = h / hypotenuse

F = Fy / sin(theta) = Fy / (h / (sqrt (.25d^2 + h^2)) )

We know that theta will decrease as the man gets higher (picture the triangle getting shorter), which means sin(theta) will also decrease.  Fy, as mentioned, will stay the same.  Therefore, Fy / sin(theta) will increase, and since this equals F, F will increase.