Wouldn't it momentarily weigh less as the first grain of sand fell, with a fluctuating lowering of weight between each grain falling, before ending up at the same weight as it started?
Struggling with this problem....
- Thread starter Fab Foodie
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roubaixtuesday
self serving virtue signaller
The impulse increases with height, but the time between impulses decreases. These cancel one another out, so the net effect is zero *but* there is a time dependence as the impulses start later but also finish later than the loss in weight as grains drop.
So there is an initial drop, then a period when the weight is net unchanged, then a final increase in weight recorded. The BBC explanation glosses over this.
The article linked upthread claims that there is also a net deceleration of change in height of the centre of mass of sand over time which results in a net increase in weight over the time of discharge of the sand, as I read it. Not sure I've understood that properly though.
nickyboy
Norven Mankey
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It's all about conversion of Potential Energy in to Kinetic Energy. PE is mgh where "h" is the height above the surface of the sand (so "h" gets smaller as sand drops through the timer). KE is 1.2mv2 where "v" is velocity. As the velocity when it hits the surface of the sand is proportional to the "h" it has dropped, the KE reduces at exactly the same rate as the PE (assuming it's a vacuum etc etc)
Stephenite
Membå
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I'm not sure if this is going to effect the answer but since E=mc squared doesn't the mass of the sand grains increase as they fall?
swee'pea99
Legendary Member
Top bet hedging there. Irreproachable.
Does the pile of sand not soften the impact - or even as it is a cone not deflect the impact from being directly down?
swee'pea99
Legendary Member
All?
roubaixtuesday
self serving virtue signaller
The softness of impact isn't relevant - it's the net change in velocity (momentum) which delivers the force. A hard stop and a soft stop, even a bouncing stop, all deliver the same net change in the end, averaged over time between grains impacting.
swee'pea99
Legendary Member
It seems intuitively obvious to me that you're right.
Rather than sand, think of a man holding a cannonball at the top of a structure, man, cannonball & structure all resting on super-sensitive scales. The moment he drops it from the top, it's no longer supported by the structure. The total weight, registered by the scales, will fall by a few kilos (from structure+man+cannonball to structure+man).
What happens afterwards doesn't change that t+1 'lighter' state of affairs, however transient.
Seems to me.
Globalti
Legendary Member
No change in the weight; the acceleration and freefall of the grains will be cancelled out by their energy as they hit the pile.
Immediately after you flip the glass there will be a tiny momentary loss of weight as the first grains go into freefall and as the hour ends a tiny gain in weight as the opposite happens.
Immediately after you flip the glass there will be a tiny momentary loss of weight as the first grains go into freefall and as the hour ends a tiny gain in weight as the opposite happens.
OP
OP
Fab Foodie
hanging-on in quiet desperation ...
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Oh, I don't know....AAAAAaaaaarrrrrrrggggggggggggggggggghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
If it was an hour timer, you'd have the same rate of sand hitting the bottom, but the velocity would be greater, so the impulse would be greater? The start and end points would be delayed because of a greater height, but the time interval when the sand would be descending would still be an hour?
