# Pulling an object with a rope

I have a question with our practical life, see the below question.

I tried to pull an object with these two ways but the force I should add was different in the two situations. As the second picture I tied the end of the rope in a tree, and I pulled the rope by the middle point of the rope. As the second time I felt more easy than the first situation. What is the reason for that?

• Sure this isn't relevant? en.wikipedia.org/wiki/Pulley Nov 26, 2017 at 10:32
• Sir, the rope has tied to the tree. Not placed as a pulley. Nov 26, 2017 at 10:39

It's because there is an effective gearing system created.

Moving the rope sideways the tension increases significantly, redirecting the effort to pull the load. A large sideways deviation creates a small change in tree-load distance, so it is geared. To take advantage of this, move the rope laterally, re-tie it and repeat.

Without the tree lateral movement of the rope is wasted, and hads to be minimised.

The gear ratio is

$\frac{dy}{dx} = \frac{2y}{x}$

which is very small for a straight rope.

• Just checking. You'd be suprised some of the posts. Nov 26, 2017 at 10:51
• Sir can you draw a free body diagram for explain your answer more... Nov 26, 2017 at 11:18