Two people carrying an object up stairs

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In summary, the question is whether it is advantageous to be at the top or bottom when carrying a uniform object. The tension in the ropes supporting the object is equal, regardless of orientation, and the person on the bottom may end up carrying more weight due to the difficulty of getting a good grip. However, at extreme angles, the person on the bottom always carries more weight. A force diagram can be used to show that the force at the bottom is always greater than the force at the top, except at a 0 degree angle. In practice, it is better to be at the top as the person on the bottom is at risk of being crushed if the object is dropped.
  • #1
jschwalbe
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Hi all--

First time poster, long time physics lover. ;)

My dad and I got into a discussion the other day since we are about to start moving out of one house and into another. When carrying a uniform object (such as a couch, or large slab of granite), is it advantageous to be at the top vs. the bottom, or does each carrier support the same amount of weight?

My approach to the problem was to envision a uniform wooden board supported by rope at the ends.. tilting the object would have no effect on the tension in either rope.. they would be equal. Drawing out a force diagram with the CoM at the middle and at various angles, each rope would indeed seem to have the same amount of tension. Thus my argument is that it doesn't matter realistically which side of the (uniform) couch you're on, it's still heavy. ;)

My dad's approach was to go to the extremes and say, what if it was straight up and down (instead of the 30-45 deg incline of most stairs); in which case the person on the bottom would be carrying 100% of the burden. He then theorized that it would be better to be on the top because you would be supporting less. I do not think that this question can be answered by looking at the extremes, and disagree with his reasoning.

Thoughts, physics lovers?
 
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  • #2
If getting a good grip on the object wasn't an issue, then orientation wouldn't be much of an issue. In the vertical case, the person above could be supporting all the weight, or the person below, or some combination. In the real world, it's probably difficult to get a good pulling grip on most objects, so the person on the bottom is usually lifting more of the weight.
 
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  • #3
Instinctively someone carrying a weight is trying to make the less effort.
If a weight is carried by two, none really is able to feel the effort of the other, so each one is honestly trying to make the less effort as possible.
If two people are carrying a long object (say a ladder) up on a stair (which is usually at 45°), easily the one on the top will finally push 1/4 of the weight, and the one on the bottom the 3/4 of the weight.

This is because the one on the top is just required to counterbalance the torque given by mg in the center of mass, so he pushes:
[tex]mg/2\sqrt2[/tex]
He's not really cheating, but he has no exact means to tell how much he should push. The ladder doesn't fall, he did his job.
As it is clear in the drawing what happens is that the man on the bottom can carry up to 3 time that weight carried by the man on the top.
That is why if you're a man and a woman, let always the woman be on top :).

If you and you dad want to be sure you carry each half of the weight, you should support the weight with a short piece of rope, so the tension of the rope is always upward. But like this is more uncomfortable.
 
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  • #4
Thanks for the replies.. however they seem to differ! Would anyone be willing to help me understand with a force diagram? (Esp with the 2nd post from Quinzio.)

Thanks!
 
  • #5
jschwalbe said:
Thanks for the replies.. however they seem to differ! Would anyone be willing to help me understand with a force diagram? (Esp with the 2nd post from Quinzio.)

Thanks!

Your dad is completely right.

Yes, looking at the extremes is the best way to understand it. At 0 degrees, the two support the same weight (mg/2) whereas at 90 degrees, the person at the bottom supports all the weight whereas the person at the top supports nothing.

To find the two forces at an arbitrary angle, one must use torque in addition to force.
At any angle, we have F1 + F2 = mg (where F1 and F2 are the upward forces exerted by the two persons). For an arbitarty angle theta, we can use that the net torque must be zero to get a relation between F1 and F2. That will show that the force at the bottom is always larger than the force at the top, for theta different than zero.
 
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  • #6
This is an example, I believe it's correct:http://imageshack.us/m/38/1089/stairss.jpg
 
  • #7
I'm wondering the same thing. Can anyone else please confirm this solution? Thank you very much!
 
  • #8
It's always better to be at the top. If the top guy drops his load, the bottom guy gets run over by it. Same result if the bottom guy drops the load. Either way, the bottom guy gets screwed.
 
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  • #9
SteamKing said:
It's always better to be at the top. If the top guy drops his load, the bottom guy gets run over by it. Same result if the bottom guy drops the load. Either way, the bottom guy gets screwed.

:biggrin:

Back to physics, in the rare case the thing has center of mass beneath the plane of grip, i.e. if you move a bathtub and hold it on the top, it is easier for the lower guy. If it is ladder, both exert the same force, and the most usual case, if it is wardrobe hold from below, it is easier for the guy on the top.
 
  • #10
Quinzio said:
This is an example, I believe it's correct:http://imageshack.us/m/38/1089/stairss.jpg

That picture is ok if you are saying that the top guy is supporting the object on a smooth tray - or on the flat of his hand.
In practice, the top guy will (or should) be pulling up the slope. He could actually cancel the force acting down the slope completely and leave the bottom guy with no more than (his share of ) the normal force to deal with. The force along the slope can be shared in any way the two guys arrange it. If the top corner is smooth and you can't get a grip on it. a loop of rope around the object will allow the top guy to do his fair share.
 
  • #11
I'm not a physics guy, but like questions like this. The center of gravity of the object would be one factor, and the other factor would be the angle of the object. If you were to hold either end of a rectangular wooden block in your hands, and move one hand up and the other down, you'd see that the weight would shift to the lower hand. So the guy at the bottom is bearing more weight.

Though I always like to be at the bottom because I can get a better grip on it.
 
  • #12
I recommended reading post #2 carefully. Its not possible to know who is carrying the most weight even if the stairs are vertical.

For example consider what happens if the person at the bottom picked up a chair on his own and passed it up to the man at the top. At various times they both carry the weight of the chair on their own or in some variable proportion that ranges from 0 to 100% of the load.
 
  • #13
CWatters said:
I recommended reading post #2 carefully. Its not possible to know who is carrying the most weight even if the stairs are vertical.

For example consider what happens if the person at the bottom picked up a chair on his own and passed it up to the man at the top. At various times they both carry the weight of the chair on their own or in some variable proportion that ranges from 0 to 100% of the load.

Well yeah, but the real question here is, how is the weight distributed between the two carriers. Now how much force each one is going to apply.
 
  • #14
RiverM said:
Well yeah, but the real question here is, how is the weight distributed between the two carriers.

Yeah ok if neither is allowed to apply torque. One man can carry a rod (eg a fishing rod) without needing anyone at the other end. All of the weight is at his end whichever end he chooses to be at.
 
  • #15
CWatters said:
Yeah ok if neither is allowed to apply torque. One man can carry a rod (eg a fishing rod) without needing anyone at the other end. All of the weight is at his end whichever end he chooses to be at.
If neither is allowed to apply a torque, you still have a concern that the force that each applies may not be purely vertical. Without resolving that, no definite answer is possible. If both apply purely vertical forces then the principles in #5 and #9 apply.
 
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  • #16
RiverM said:
Well yeah, but the real question here is, how is the weight distributed between the two carriers. Now how much force each one is going to apply.
I think you must mean a special (the simplest) case, in which they are just applying a force vertically. The share of the weight that each one gets will depend upon the position of the Centre of mass of the load. If you take moments about the CM, the clockwise moment for the guy at one end will be equal and opposite to the anticlockwise moment from the other guy. That will give you one equation.
Force1X(horizontal distance from CM to man1) = Force2X(horizontal distance from CM to man1)
You will need another equation and that is that the sum of the Forces is the total weight.
Two simultaneous equations will give you the two force values.
If the CM is half way along then the forces will be equal. (most trivial case)
But this is not a realistic situation and could be very hard for the two carriers to achieve unless they actually were holding the load with force meters and could make sure they were supporting half the weight and only lifting vertically. In practice, one of them will be applying more force by pulling / pushing in the horizontal plane and also applying some torque by multiple contact with the load.
 
  • #17
If you lift one end of a barbell off the ground, and stand it vertically, it gets very easy when it's almost vertical.

If the barbell weighs 50 pounds, and you lift one end, you'd initially be lifting about 25 pounds right? And the ground would be holding the other 25 pounds. But when the bar is almost upright, you'd barely be holding any weight, just a slight push is all that's needed and the ground would be holding all 50 pounds when the bar is upright.

For this example, I think you can think of the lower person as being like the ground. Both ends always stay equal distance from the center of gravity, but the closer the higher end gets to being verticle, the more the weight is transferred to the lower end.
 
  • #18
RiverM said:
But when the bar is almost upright, you'd barely be holding any weight, just a slight push is all that's needed and the ground would be holding all 50 pounds when the bar is upright.
.

That's correct if you allow all the weight to be transferred to the ground. If you were to hang the top end from a metal stand with the bottom end touching the ground you wouldn't be able to calculate what percentage is carried by the stand or the ground.
 
  • #19
RiverM said:
If you lift one end of a barbell off the ground, and stand it vertically, it gets very easy when it's almost vertical.

If the barbell weighs 50 pounds, and you lift one end, you'd initially be lifting about 25 pounds right? And the ground would be holding the other 25 pounds. But when the bar is almost upright, you'd barely be holding any weight, just a slight push is all that's needed and the ground would be holding all 50 pounds when the bar is upright.

For this example, I think you can think of the lower person as being like the ground. Both ends always stay equal distance from the center of gravity, but the closer the higher end gets to being verticle, the more the weight is transferred to the lower end.

I would disagree with this. IMO, you are ignoring the horizontal forces involved in your situation of lifting the top of the barbell. If the barbell were resting on ice then there could be no horizontal forces, until the CM is directly below the upper lifting force, there will be equal shares (principle of moments). If you actually try the experiment, you will be pulling slightly sideways if you want to make the force you are applying greater than half the weight (assuming the CM is halfway along)
The situation of two guys carrying an object up stairs is far more complicated than the simple model that is being assumed on this thread.
 
  • #20
CWatters said:
.

That's correct if you allow all the weight to be transferred to the ground. If you were to hang the top end from a metal stand with the bottom end touching the ground you wouldn't be able to calculate what percentage is carried by the stand or the ground.

Why couldn't you measure it? You could put a little scale between the bar and the stand, that would tell you the weight that is being bore by each end.

I think the question the original poster was driving at is, when you have an unlevel, symetrical object (like a cylinder or recangle), would it naturally place more load on the lower end?

If you lay one end of a bar on a scale, and lift the other end up till it's horizontal, you'll see that the weight on the scale will increase. It would start out roughly half and half at the bottom, then gradually increase till there was nothing in your hand and all the weight would be on the scale. So in this example, the scale could be a person's hands, holding the couch. The force they actually apply doesn't chance the amount of weight that the object is applying.
 
  • #21
sophiecentaur said:
I would disagree with this. IMO, you are ignoring the horizontal forces involved in your situation of lifting the top of the barbell. If the barbell were resting on ice then there could be no horizontal forces, until the CM is directly below the upper lifting force, there will be equal shares (principle of moments). If you actually try the experiment, you will be pulling slightly sideways if you want to make the force you are applying greater than half the weight (assuming the CM is halfway along)
The situation of two guys carrying an object up stairs is far more complicated than the simple model that is being assumed on this thread.

But horizontal forces don't conflict with gravity. And we're talking about bearing weight here. It's much easier to move an object horizontally than vertically unless there is a lot of friction involved.
 
  • #22
CWatters said:
That's correct if you allow all the weight to be transferred to the ground.
But how would you arrange this is there were no horizontal forces allowed?
Even lifting and swinging the object could be a problem - probably impossible, I think, if no horizontal impressed forces were allowed.
If horizontal forces are allowed, initially, then the problem is easy and, whatever angle the object ends up at, the weight will be shared equally. In a real situation, it is possible to introduce torque at one end (what anyone would do naturally, aamof) and get any result you want - either taking from or adding load to the other guy. It could end up as a competition, of course.
 
  • #23
RiverM said:
Why couldn't you measure it?
No reason. If the measured force is only vertical then the 'other' force just has to be half of the total, the vector equation has to be obeyed.
 

1. How does the weight of the object affect the effort required to carry it up stairs?

The weight of the object directly affects the amount of effort required to carry it up stairs. The heavier the object, the more force is needed to lift it against gravity. This can result in increased strain on the muscles and joints of the individuals carrying the object.

2. Is it more efficient to have two people carry an object up stairs rather than one?

In general, yes. When two people are carrying an object up stairs, the weight is evenly distributed between them, making it easier for both individuals to lift and move the object. It also reduces the risk of injury from overexertion.

3. What factors determine the amount of energy expended when carrying an object up stairs?

The amount of energy expended when carrying an object up stairs is determined by several factors, including the weight of the object, the height and number of stairs, the speed at which the object is being carried, and the physical fitness of the individuals carrying the object.

4. How does the angle of the stairs affect the difficulty of carrying an object up?

The angle of the stairs can significantly impact the difficulty of carrying an object up. Steeper stairs require more effort to lift the object against gravity, while shallower stairs may allow for easier movement. The angle of the stairs can also affect the balance and stability of the individuals carrying the object.

5. Are there any techniques or strategies that can make carrying an object up stairs easier?

Yes, there are several techniques that can make carrying an object up stairs easier. These include using proper lifting and carrying techniques, such as keeping the object close to the body and using the legs to lift rather than the back. Additionally, taking breaks and alternating which side of the body is carrying the object can help reduce strain and fatigue.

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