[Physics] Is ordering players by height beneficial in a game of tug of war

newtonian-mechanics

This can be considered a follow-up turn-around question for this similar question.

I recently came across this interesting analysis of the game of tug of war.
One of the closing discussions is the following image:

Sample image

However, the writer follows up that:

[Given there are multiple people on both teams,] the drawing above
shows that the shorter players on the left team also experience an
upward component of force, and therefore the friction on their feet is
reduced. The shorter player on the right team certainly experiences
decreased friction, but the other players on the right team have
increased friction at their feet.

How do all the forces add up? Is it beneficial to put taller people first in a game of tug of war as shown in the diagram above, or do the forces cancel each other out?

Best Answer

For calculating the total force a team can generate, it is useful to consider one team as a single system. Note that the total normal force of a team acting on ground only depends on the total mass of the team and the vertical component of tension force of the rope between the teams. You can't do much to increase the team's mass, however you indeed can generate downforce (and upforce for the other team) by putting the tallest closest to the other team (perhaps also the tallest could try to lift the rope even higher, though I'm not sure it will help in practice. The friction force generated by real people is not purely proportional to the normal force).

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