That requires the table to generate a force of 6 ounces whether or not the glass is present. The table is rigid and just passes forces that are applied to it. Unless you want to take it’s modulus of elasticity into account.
Nothing is perfectly rigid. The table deforms a tiny bit. Even things that are very rigid have a tiny deformation at the molecular level.
Came in here to say this. Even “incompressible” liquids like water and oil are actually compressible. The degree to which they are compressible is so small as to go unnoticed by the average person in their daily lives, but there are some applications where it matters. Industrial water jet cutters use a high-speed jet of abrasive-laden water to cut metal parts, and common-rail diesel pumps supply high-pressure fuel to the injectors of a diesel engine. Both operate at tens of thousands of psi, and at those kinds of pressures the density of the water (or diesel fuel) is several percent higher than at ambient pressure.
That’s why it has a modulus of elasticity. Beyond the MOE it is rigid. Otherwise it would compress to nothing.
It could break. But then that would be a dynamics problem until it again reached equilibrium.
No it doesn’t. Does the spring generate a force of 6 ounces whether or not it is compressed? Compressing the spring creates the force, just as compressing the table.
“Beyond the MOE” only occurs when an object has been loaded beyond it’s yield strength, beyond which permanent deformation occurs.
This does not happen when you set a glass down on the table. The table, legs, and floor all elastically deform until the spring force exactly balances out the glass. The spring behavior for each component is all governed by the MOE (Young’s Modulus) of each material.
As you take hold of the glass again, applying force to pull the glass upward, the table, legs, and floor all reduce their elastic deformation, exactly matching the force reduction on the bottom of the glass, right up to until the instant at which you’ve completely lifted the glass off the table, when the deformation and force on the top of the table return to zero.
If they were equivalent, then if I quickly lifted the glass from the table, the coaster under it would be catapulted into the room.
Excellent explanation!
I recall a factoid that if water was totally incompressible sea level would be about 200-ft higher.
They’re not equivalent, they’re analogous.
The coaster does not contain much potential energy, because the displacement is not much (recall that work=force*distance). That’s unlike a conventional spring, which stores significant energy because the force is applied over a long distance. The spring will fly into the air but the coaster doesn’t have the energy for it, even though the force is the same.
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not necessarily, because no matter how quickly you lift the glass the total potential energy being released is dependant on how much energy was being stored as compression in the first place. It may not be enough to overcome gravity.
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we are talking about objects compressed very slightly at the molecular level, “quickly” in this context could be a significant fraction of the speed of light. If you lifted a cup off a coaster at 0.8c, some weird forces would probably come into play.
I just went through the math, and you’re right. The ocean is about 3700 meters deep, and the water at the bottom is more dense than the water at the top because it’s being squeezed by all the water above it: 1025 kg/m^3 at sea level, 1044 kg/m^3 at depth. If you took that 3700-meter-tall column of compressed water and stretched it until it was all at a consistent 1025 kg/m^3 from top to bottom it would be 3743.6 meters tall. That’s an extra 43.6 meters, or 143 feet.
Yay! It was in one of those strange but true pieces – you swallow eight spiders a year was another in the list – and I was too lazy busy to actually research and do the math which is why I termed it as a factoid.
If Left_Hand’s students have previously worked with magnets, specifically the donut shaped magents, they have probably stacked them up on a pencil, where you can see how adding more magnets pushes them all down closer to each other. I think this will be helpful in the lesson.
This might not help, but consider a set of bathroom scales - they register weight because of the two halves of the device (the bit contacting the floor and the bit contacting your feet) are compressed together by the force caused by gravity accelerating you toward the earth, when you stand on them.
But they can also be made to register something by picking them up and squeezing the top and bottom together between your hands. But if you hang the scales on a piece of string and only press on one side, they will not register anything (well, not much, and not for long) - because there’s nothing resisting the push. You have to push on both halves in opposite directions to measure anything happening.
Finally, if you place the scales against a wall and push, they will register something. The wall must be pushing back. If in doubt, place the scales against a window - with the display facing the window and push on the part of the scales that is normally the bottom. Get someone outside to read the display through the window. The window is resisting by pushing back when you push on it, as evidenced by the numbers on the display.
I’ve always seen examples with boats. How the boat moves away from the dock when you step out of the boat towards the dock. Or rowing, where you push against the water and the water pushes back thereby propelling the boat.
So if I put an apple on a table, the table is a spring and is pushing back up onto the apple? I can buy that. But I could have sworn my college physics prof said the Earth was pushing back up onto the apple.
When you’re standing barefoot on the Earth, isn’t the Earth pushing up on you with the same force?
The table pushes on the apple, and the ground pushes on the table. Slice the objects however you wish, and you’ll find the bottom one pushing up to counteract the force of gravity from everything above.