Physics-related disagreement with teacher

[1MileCrash]

It boils down to this:

Imagine you had a mattress for you and your significant other, who is lighter than you. You sleep on the right side. You are top heavy.

Is the most pressure on the top right quadrant of the surface of the mattress, or the top right quadrant of the bottom surface of the mattress?

Thank you.

 

[nasu]

I don't think the pressure is uniform on either quadrant so the comparison is not so relevant.
But assuming a single mattress spring (assuming a spring mattress) the pressure on top of the spring will be the same as the pressure on the bottom of the spring.

It may be that on the bottom the pressure is distributed more uniformly so it may be lower than the pressure on some areas of the top, where is less uniform.

 

[jbriggs444]

The weight of the mattress figures in. Averaged over the entire quadrant, I would expect higher pressure on the bottom.

 

[sophiecentaur]

You would need to know the area of contact with each body, if you wanted to know the pressure. That could raise a further set of embarrassing questions.

 

[berkeman]

If the springs inside the mattress are tied together sideways (a common practice), that will transfer some of the downward pressure to adjacent springs, thus dispersing the force (and pressure) a bit from the top of the mattress to the bottom. So if there is a high pressure point on the top of the mattress, it will be blurred a bit and dispersed some before reaching the bottom of the mattress. So the highest pressure is on the top of the mattress.

Think about it in an easier configuration to analyze -- put a bolwing ball in the center of the mattress. All of the pressure of the ball is below the ball on the top surface of the mattress. But that high pressure area is dispersed some to a wider area by the time it reaches the bottom surface of the mattress.

 

[Borek]

If it is an air inflatable mattress, pressure is identical everywhere.

 

[berkeman]

If it is an air inflatable mattress, pressure is identical everywhere.

 

[jbriggs444]

If it is an air inflatable mattress, pressure is identical everywhere.

That is not correct. The internal air pressure is uniform. But the external pressure on an air mattress does not match the internal air pressure.

 

[berkeman]

That is not correct. The internal air pressure is uniform. But the external pressure on an air mattress does not match the internal air pressure.

Would it not for the flat bottom surface?

 

[sophiecentaur]

The tension in the envelope also needs to be included, I seem to remember - as with tyres.

 

[jbriggs444]

Would it not for the flat bottom surface?

There is a significant amount of internal structure in, for instance, an air mattress intended for camping. In order to keep the mattress from going spherical, the top and the bottom surfaces are essentially tethered together. When you lie on the top you are easing tension in the tethers and thereby lowering the upward force that they would otherwise exert on the corresponding portion of the bottom of the mattress.

Or, look at it another way... An air mattress is light-weight. If the pressure on the bottom is even and the pressure on the top is uneven that amounts to an unbalanced torque. It is difficult to sleep on a mattress that immediately flips you onto the floor.

Contrast to a water bed. If you lie on one side, the water level rises on the other. Even pressure on the bottom and no unbalanced torques.

 

[sophiecentaur]

So we need 1MileCrash to tell us what sort of mattress we are supposed to be discussing. Otherwise it's a typical PF wild goose chase and a possible excuse for fisticuffs with quadrature arguments being fought over.

 

[Borek]

what sort of mattress

That's what I was aiming at.

 

[Andrew Mason]

It boils down to this:

Imagine you had a mattress for you and your significant other, who is lighter than you. You sleep on the right side. You are top heavy.

Is the most pressure on the top right quadrant of the surface of the mattress, or the top right quadrant of the bottom surface of the mattress?

Thank you.

The greatest pressure is on the top of the mattress regardless of the kind of mattress it is (assuming that the mattress is not extraordinarily heavy ie. it weighs less than the person). This is because the weight of the person is applied to the contact area between the person and top of the mattress which is much less than the area of contact between the mattress and the box spring .

AM

 

[sophiecentaur]

Imo, the bottom line is that the pressure could only be definitely uniform across the floor if the bed consisted of a piston (no friction with the sides) covering a box full of just fluids with no internal links, with rigid (massless) sides and a horizontal base (which could be flexible. In that case, whether the fluid were water or air, the pressure at the bottom would be uniform because the only forces involved would be due to fluid pressure.

(I am fascinated about this teacher's interest in what goes on in peoples' beds. . . .. )

 

[1MileCrash]

So we need 1MileCrash to tell us what sort of mattress we are supposed to be discussing. Otherwise it's a typical PF wild goose chase and a possible excuse for fisticuffs with quadrature arguments being fought over.

Unfortunately I have no such details.

The he said the least pressure was at the bottom-underneath, but I thought the fact that it was also supporting the weight of the mattress meant it had more pressure than the bottom-top.

It was just a geometric exercise to show that we can't actually orient the bed to that the top right top of the mattress is put where the bottom right underneath is.

 

[sophiecentaur]

Unfortunately I have no such details.

The he said the least pressure was at the bottom-underneath, but I thought the fact that it was also supporting the weight of the mattress meant it had more pressure than the bottom-top.

It was just a geometric exercise to show that we can't actually orient the bed to that the top right top of the mattress is put where the bottom right underneath is.

I would agree with that because the moments must all sum to zero in equilibrium - however you try to share the pressures out. It's only when there is no rigidity that you can avoid moments.

It seems to me like a bit of daft question, in any case. (The teacher's and not yours.) We teachers are all guilty of having posed questions which don't have satisfactory answers from a student's point of view.

 

[Andrew Mason]

Unfortunately I have no such details.

The he said the least pressure was at the bottom-underneath, but I thought the fact that it was also supporting the weight of the mattress meant it had more pressure than the bottom-top.

It was just a geometric exercise to show that we can't actually orient the bed to that the top right top of the mattress is put where the bottom right underneath is.

Pressure is force per unit area. The area that your body presses on is much less than the area of the mattress. Since the mattress distributes force over the area of the mattress, the pressure variation on the top surface is much greater than the pressure on the bottom of the mattress.

Think of it this way: would you rather have a guy run into you with 1. a mattress between you and him or 2. a few layers of clothes between you and him so you can feel with his pointy shoulders, elbows, knees? Pressure = pain.

AM

 

[A.T.]

Pressure is force per unit area. The area that your body presses on is much less than the area of the mattress. Since the mattress distributes force over the area of the mattress, the pressure variation on the top surface is much greater than the pressure on the bottom of the mattress.

The pressure variation, and hence the deformation is usually greater on top. On which side the highest pressure occurs depends on the ratio of mattress' mass to person's mass. But for most adults on normal mattress it should be on top too.