With the help of a system of blocks, a load weighing 100 kg was raised by 3M

With the help of a system of blocks, a load weighing 100 kg was raised by 3M, applying a force of 250N. How long did you have to pull the free end of the rope?

m = 100 kg.

g = 10 m / s2.

h = 3 m.

F = 250 N.

L -?

A simple mechanism, to which the block system belongs, does not give a gain in work, it gives a gain in strength.

With uniform lifting of the load, the moments of forces Mg, with which the load acts on the block, is equal to the moment of force M, with which the load is pulled: Mg = M.

Mg = Fg * r, M = F * R, where Fg is the weight of the load, r is the radius of the block to which the load is attached, R is the radius of the block to which the force F is applied.

Fg = m * g.

m * g * r = F * R.

100 kg * 10 m / s2 * r = 250 N * R.

The radius of the block R, on which the force acts, is 4 times the radius of the block r, to which the weight is attached: R = 4 * r.

L = 4 * h.

L = 4 * 3 m = 12 m.

Answer: in order to lift the load, the free end of the rope had to be extended by L = 12 m.