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cool_dude · Feb 17, 2007, 08:56 AM

Can somebody please explain to me if it is easier for a short person or a tall person to push a box across a floor? Please don't just say "short or tall person" explain why?

Capuchin · Feb 17, 2007, 09:42 AM

The short person will be able to push the box lower down, so the box will slide mor easily. The tall person will have to push the box near the top, and so he will apply a torque which will rotate the box about the pivot (the far bottom edge) and this will dig into the floor, making it harder to push.

It depends on the type of surface and how heavy the box is, if the box is really heavy and it's a carpet floor, it's probably easier to rotate it and so that tall person will be better suited. The short person has to rely on sliding the box, and so a smooth floor will be better for him. If the floor is slippery (ie the person's shoes have less grip), the taller person is probably better off, because he is pushing his side of the box upwards to rotate it rather than across, the short guy will just slide.

Hope this helps.

cool_dude · Feb 17, 2007, 10:43 AM

Thanks for the reply capuchin. My question is general. I guess I wasn't specific enough. Lets assums the floor is normal not slippery, the box isn't too heavy. In general who will it be easier for? Ignoring all the factors. Also can this be proven with math?

Capuchin · Feb 17, 2007, 11:46 AM

I think your teacher wants the case where pushing the box by rolling it isn't taken into account. So there is only sliding. In this case it's easier for the short guy because he lower compared to the box's center of gravity

Think of it this way, in order to slide a box, you need to push toward it's center of gravity. For a tall person to do this, he has to push downwards (diagonally) on the box, this makes the friction larger as there is more of a force on the ground. The smaller guy pushes upwards or straight into the box, making the friction less.

cool_dude · Feb 17, 2007, 12:05 PM

I totally agree with you. However this is not my physics class its my math geometry and discreete class. Thus my teacher does not want us explaining it by talking about friction. She wants us to use math. I have no idea how to apply math to a question like this. The way I see it is that your explanation is very suitable and that's exactly whata I would have done in a physics class. Any ideas on how I can use math to explain the problem?

Capuchin · Feb 17, 2007, 12:11 PM

Well you have to talk about friction. You should be able to do math on it, but it will be much more physicsy than mathsy.

I'll draw something up for you today or tomorrow.

asterisk_man · Feb 17, 2007, 07:48 PM

I'm guessing dot product comes into play in the expected answer. When the short person pushes, his push is more straight and less down and therefore more of it is useful. The dot product of two vectors show how much of the first vector is in the direction of the second vector. Dot product - Wikipedia, the free encyclopedia

The second vector will be the unit vector parallel to the floor in both cases. Assume both people push with a force equal to 1 unit. The dot product for the tall person is $\cos \theta_{tall}$ and the dot product for the short person is $\cos \theta_{short}$ . We'll assume that the box is shorter than both people's shoulders. $\theta$ will be in the range $\left[-\frac\pi 2 ,0\right)$ and $\theta_{tall} < \theta_{short}$ so cos in that range will always be less for the tall person and therefore their dot product will always be less. If you want to add friction you can show that the dot product of the tall person's vector with the unit vector pointing down will be greater and therefore the force of friction will be greater.

Does that sound like something more suitable to your math class?