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Question
I have a box on the floor (80kg) and i want move it for example 5 meters .
I use a rope that is linked on the box to pull.
Which is the best way to minimize my effort ?
I mean : i can pull the box with the rope parallel to floor or i can choose to arrange the rope such as to have an angle 10-20-30 ecc. between the rope and the floor...
There is a specific angle that is the best to minimize ?
I know that for this kind of calculation is important to know the friction coefficien between box and floor...
But if we suppose that we don't know the value of this coefficient, the physic is able to suggest me ?

Answer
You're right, that's important.  For a slick surface you would definitely want to pull at a minimal angle.  For a sticky surface you would definitely want to lift and even perhaps swing more than pull at zero angle.  The length of your rope is even important, if you were to lift it and swing then a long rope would require the least lifting because that would minimize the distance down it would swing compared to a short rope.  

If you want to drag it, if you pull horizontally you will exert a certain force over a certain distance which depends on the coefficient of friction linearly.  That means that you will expend (mu)*m*g*d of energy, and I assume you're speaking of energy when you type "effort," rather than meaning force.  You want to minimize the force along the distance that you pull, but not at the cost of exerting a higher force or over a longer distance to move the object.  If it slides easily, then slide it and don't try to lift and swing it.  That would take almost zero force and zero work.  If it's a sticky surface, like rubber, you would need to minimize the force used to move it.  In the extreme cases, you would do the lift-and-swing thing, rather than trying to slide it.

Physics can't help you without that number.

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Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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