How does the tension in a pulley system change with different masses?

[Saitama]

Homework Statement

In the arrangement shown in Fig. 1.18(see attachment) the mass of ball 1 is η=1.8 times as great as that of rod 2. The length of the latter is l = 100 cm. The masses of the pulleys and the threads, as well as the friction, are negligible. The ball is set on the same level as the lower end of the rod and then released. How soon will the ball be opposite the upper end of the rod?

Homework Equations

The Attempt at a Solution

Well, i couldn't solve it so i had to peep into the solution. Here's the solution:
http://irodovsolutionsmechanics.blogspot.in/2007/08/irodov-problem-175.html

I don't quite understand the solution. It says that the ball goes up but that doesn't make sense to me. It is mentioned in the question that ball is heavier than the rod. The ball should move down as it is heavier. Please someone explain where i am going wrong.

Thanks!

 

[Spinnor]

The rod has twice the mechanical advantage as the ball. If the rod moves down two inches the ball only moves up one inch. If the rod were half the mass as the ball the system would balance and there would be no movement. The movements of the rod and ball are correlated, the rod moves twice the distance as the ball.

Good luck!

 

[Saitama]

Hello Spinnor!
I don't understand what you mean by the term "mechanical advantage"? I understand when you said that the rod moves down two inches and the ball only moves up one inch but i can't see any relation of it with the ball's movement.

 

[Spinnor]

Suppose you hold the ball to keep it from moving. You can calculate what the tension is in the rope holding the ball. The tension in one rope is double the other. See below.

 

[Saitama]

Suppose you hold the ball to keep it from moving. You can calculate what the tension is in the rope holding the ball. The tension in one rope is double the other. See below.

Thanks a lot Spinnor, i understand it now!