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What's the optimum angle to pull a wide object over a horizontal plainplane

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I have a real life question (not homework so I'm struggling to find an answer online) that I'm hoping someone can assist me with out of curiosity.

So basically I have a wide object (pole in this case) that I want to pull a certain distance towards myself over the ground (so we can ignore any vertical-ness with the angles).

What's the optimum places to attach ropes and pull the object to myself and why?

Some illustrations of what I'm wondering (top down):

Scenario 1

Attaching the ropes in the middle of the object, in line with where I'm standing: One rope in the middle of the object

Scenario 2

2 Ropes attached at each point of the object 2 Ropes attached at each point of the object

Scenario 3

1 Rope attached to each point, and pulled with another rope in the middle of the first rope: 1 Rope attached to each point, and pulled with another rope in the middle of the first rope

Gut feeling

My gut's telling me that scenario 2 or 3 would be best, and most likely the most stable while pulling, but I'm wonder what the math behind this says

Edit 1

Definition of the optimal condition: At which angle or attachment point would the least amount of force be required to move the object

Thanks for pointing this out @basics

I have a real life question (not homework so I'm struggling to find an answer online) that I'm hoping someone can assist me with out of curiosity.

So basically I have a wide object (pole in this case) that I want to pull a certain distance towards myself over the ground (so we can ignore any vertical-ness with the angles).

What's the optimum places to attach ropes and pull the object to myself and why?

Some illustrations of what I'm wondering (top down):

Scenario 1

Attaching the ropes in the middle of the object, in line with where I'm standing: One rope in the middle of the object

Scenario 2

2 Ropes attached at each point of the object 2 Ropes attached at each point of the object

Scenario 3

1 Rope attached to each point, and pulled with another rope in the middle of the first rope: 1 Rope attached to each point, and pulled with another rope in the middle of the first rope

Gut feeling

My gut's telling me that scenario 2 or 3 would be best, and most likely the most stable while pulling, but I'm wonder what the math behind this says

I have a real life question (not homework so I'm struggling to find an answer online) that I'm hoping someone can assist me with out of curiosity.

So basically I have a wide object (pole in this case) that I want to pull a certain distance towards myself over the ground (so we can ignore any vertical-ness with the angles).

What's the optimum places to attach ropes and pull the object to myself and why?

Some illustrations of what I'm wondering (top down):

Scenario 1

Attaching the ropes in the middle of the object, in line with where I'm standing: One rope in the middle of the object

Scenario 2

2 Ropes attached at each point of the object 2 Ropes attached at each point of the object

Scenario 3

1 Rope attached to each point, and pulled with another rope in the middle of the first rope: 1 Rope attached to each point, and pulled with another rope in the middle of the first rope

Gut feeling

My gut's telling me that scenario 2 or 3 would be best, and most likely the most stable while pulling, but I'm wonder what the math behind this says

Edit 1

Definition of the optimal condition: At which angle or attachment point would the least amount of force be required to move the object

Thanks for pointing this out @basics

Source Link

What's the optimum angle to pull a wide object over a horizontal plain

I have a real life question (not homework so I'm struggling to find an answer online) that I'm hoping someone can assist me with out of curiosity.

So basically I have a wide object (pole in this case) that I want to pull a certain distance towards myself over the ground (so we can ignore any vertical-ness with the angles).

What's the optimum places to attach ropes and pull the object to myself and why?

Some illustrations of what I'm wondering (top down):

Scenario 1

Attaching the ropes in the middle of the object, in line with where I'm standing: One rope in the middle of the object

Scenario 2

2 Ropes attached at each point of the object 2 Ropes attached at each point of the object

Scenario 3

1 Rope attached to each point, and pulled with another rope in the middle of the first rope: 1 Rope attached to each point, and pulled with another rope in the middle of the first rope

Gut feeling

My gut's telling me that scenario 2 or 3 would be best, and most likely the most stable while pulling, but I'm wonder what the math behind this says