Mechanical advantage of a mountain climber (pulley)

[christian0710]

Hi I have a hard time undersanding the mechanical advantage of this pulley system (in the video below): I understand that when a person is holding you, then the mechanical advantage is 2, because 50% of the weight or Load is on the rope going from the harness to the top left anchor point, and the other 50% is transmitted to the person holding the rope. BUT If you hold the rope, then you only carry 1/3 or the weight. Does this mean that 2/3 of your weight is transmitted from the rope to the Top left anchor point and 1/3 of your weight is transmitted to your hands pulling the rope? I can't really visualize it and would appreciate some help.

 

[sophiecentaur]

It could help if you consider that the work done on the rope by your pulling arm in pulling yourself up is less, per unit gain in height because your shoulder moves up the mountain by 10cm for every 20cm of rope pulled through the top pulley - which means that your arm goes through 30cm of distance, relative to your body. So the Velocity ratio for the climber is 3 where the VR for the other guy is 2.
PS I use the term Velocity Ratio because that is just down to geometry. MA is the ratio between actual Load and Effort, which will be affected by friction and any 'dead weight' in a system. MA needs to be measured for each case. (Strictly) As the lovely Mr Scales taught us: Efficiency = MA/VR and, of course, is always less than unity. But climbers know how to climb mountains and why should they know the intricacies of Mechanics - except if they really want to know the forces likely to involved in a real situation?