Investigating the Weight of an Hourglass with Sand

[bjon-07]

My proffesor assigned the question to the class.

Will an hourglass filled with sand weigh any different if you tip over (i.e. the sand is on the top falling down vs. the sand is on the bottom not moving)


If the sand is on the top. a few grains of sand will be in free fall (these would be weightless) however when those grains of sand it the bottom of the glass they will have KE which should in theory increase the doward force the hour glass itself is pushing on the scale.

In class we calculated the normal force a failing chaing of height L to be N=3mgs/l.

I am having a really hard time with this problem. Can some one please help me. I will be forever greatfull.


I need to mathmatically prove what will happen in this experiment.


btw I did this in this experiment on a scale in the chem lab of my school. The two weighted the same. (not that the scale I used was not very accurate)

 

[Danger]

Will an hourglass filled with sand weigh any different if you tip over (i.e. the sand is on the top falling down vs. the sand is on the bottom not moving)

An hourglass is a closed system, so it can't gain or lose mass. The individual grains of sand that fall gain relative kinetic energy, but the overall system doesn't. Can't help with the math. Sorry.

 

[SpaceTiger]

An hourglass is a closed system, so it can't gain or lose mass. The individual grains of sand that fall gain relative kinetic energy, but the overall system doesn't.

This was already discussed in the homework section, but remember that there's a difference between weight and mass. Weight has units of force, so it depends on the internal motion as well as the mass. To see that something weighs a different amount while its content are in free fall, just imagine a large sealed bag of groceries. What happens when you turn it over? Does the weight change when the groceries hit the bottom?

 

[Danger]

Weight has units of force, so it depends on the internal motion as well as the mass. To see that something weighs a different amount while its content are in free fall, just imagine a large sealed bag of groceries. What happens when you turn it over? Does the weight change when the groceries hit the bottom?

I see your point, but disagree. Perhaps it's because I'm using improper definitions. Bear in mind that I have no formal education. To me, weight has always meant the measured quantity of mass within a gravitational or accelerating environment, and therefore doesn't have units of energy attached. What you describe would be impact energy in my understanding. If that's the case, then the weight would change every picosecond as new grains of sand intermittently hit bottom. You wouldn't be able to get an accurate measurement. If this is an incorrect assessment, please explain further. I hate having my facts wrong; it's worse than not having any at all.

edit: If that is also explained in the homework section, can you tell me where or provide a link? I have a lot of trouble trying to find things around here.

 

[Doc Al]

There seems to be some confusion about the meaning of "weight". There are two useful meanings:

(1) "true" weight: this is a measure of the gravitational force exerted on an object. The weight of an object of mass m at the Earth's surface is mg.
(2) "apparent" weight: this is a measure of the supporting force an object experiences.​

It is apparent weight that changes when an object accelerates; it is apparent weight equalling zero that is called "weightlessness".

In this problem, the hour glass is presumed to rest on a scale; that scale reads the apparent weight of the hour glass. (Its true weight will not change.)


https://www.physicsforums.com/showthread.php?t=70670

 

[Meir Achuz]

The hourglass with the falling sand will register a smaller reading on a scale.
This is because the center of mass of the closed system of the glass and the sand is accelerating downward due to the downward acceleration of the falling sand.
Therefor the upward normal force on the system (which is what the scale interprets as "weight") will be less than Mg, where M is the mass of the sand plus glass.
To give a numerical answer, you would have to know the mass of the sand in the air, acelerating down.

 

[ramollari]

This is because the center of mass of the closed system of the glass and the sand is accelerating downward due to the downward acceleration of the falling sand.

The center of mass is moving downward, but it is not necessarily accelerating. You should envision the falling sand as a standing vertical column, and not as a falling piece of mass.

 

[Danger]

There seems to be some confusion about the meaning of "weight".

Thanks a million, Doc. The link only confused the hell out of me, but I like your explanation preceding it. It makes sense now. I've never heard of 'apparent weight' as an actual entity. Obviously, Space Tiger and I were referring to different things, and his explanation is the one that would be appropriate under the given circumstances. My apologies to Bjon-07 for misleading you, and to Tiger for contradicting you.
I'm going back to GD; I only have to be funny there, not smart.

 

[SpaceTiger]

My apologies to Bjon-07 for misleading you, and to Tiger for contradicting you.

You don't need to apologize. If you ask me, people shouldn't be afraid to speak up just because they think they might be wrong. That's part of how we learn. I didn't know that there were two kinds of "weight", so I learned something as well.

 

[Danger]

You don't need to apologize. If you ask me, people shouldn't be afraid to speak up just because they think they might be wrong. That's part of how we learn. I didn't know that there were two kinds of "weight", so I learned something as well.

I think that this might be the beginning of a beautiful friendship, if you don't mind me quoting the Bogieman. I wasn't kidding about the 'no formal education' thing (as mentioned elsewhere, I never graduated high school). In instances like this where HS or university learning is in advance of my own, I will always defer to the more educated combatent. (Unless, of course, he says something really stupid... but that seems to be restricted to GD.)