Find Lowest Speed to Yank Tablecloth - F/dt=0

[meowts]

Homework Statement

Greetings. Everyone is familiar with the experience of yanking the tablecloth at such a speed that objects don't move. Help me find the lowest speed at which to yank the tablecloth so that the objects on the table don't move at all.

Relevant Equations

dx/dt = v

mdx/dt = F, dx → 0

 

[berkeman]

Is this for schoolwork, or just for your personal curiosity?

 

[meowts]

Is this for schoolwork, or just for your personal curiosity?

homework at university

 

[berkeman]

Okay, then you need to show lots of effort on the problem before we can be of tutorial help. Try to simplify it a bit, and think about how to draw free body diagrams (FBDs) of the table, the tablecloth, and a typical thing that might be sitting on the tablecloth (like a drinking glass and maybe a plate). Then try to calculate what speed the tablecloth needs to move to give you a reasonably small displacement of the plate (say 1cm), and to avoid tipping over the drinking glass.

Please show your work. Thank you.

 

[berkeman]

BTW, if you haven't already done it, you might do a Google search on videos of this being done. Watching a couple of them should help you to see how little displacement can be achieved. Also, think about what kind of friction coefficients are best between the tablecloth and the table, and the tablecloth and the dish/glass.

 

[kuruman]

In addition to what @berkeman noted, I will add this question that you should seriously consider. Is it about speed, as the question seems to imply, or is it about something else? People who travel (first class) in airplanes at 600 mph don't see their champagne glasses move on their tablecloth-covered personal trays. Should your answer be a speed greater than 600 mph or should you reconsider what is really being asked?

 

[jbriggs444]

Help me find the lowest speed at which to yank the tablecloth so that the objects on the table don't move at all.

The desired condition "don't move at all". Is that how it is expressed in the problem assignment? Would such a condition be achievable at any speed?

@berkeman has provided two reasonable alternative criteria. Move a plate by no more than 1 cm. Or avoid tipping over a goblet of some particular dimensions.

What do we know about the setup? What do we need to know about the setup?

 

[kuruman]

The desired condition "don't move at all". Is that how it is expressed in the problem assignment? Would such a condition be achievable at any speed?

This condition is apparently achieved in the following video demonstration that clearly shows what's relevant. It's not the speed, it's the "speed of the speed", a.k.a. $\dots$?

 

[jbriggs444]

This condition is apparently achieved in the following video demonstration that clearly shows what's relevant. It's not the speed, it's the "speed of the speed", a.k.a. $\dots$?

Both videos (the first one and the better one you replaced it with) show that the experimenter is grabbing the hoop on the right, causing it to compress downward and out of the way. Both experimenters get their hand going first and grab with a moving hand, this mitigates the need for a high hand acceleration.

But yes, it is how rapidly the support can be removed from beneath the object of interest. Which requires a large hoop acceleration.

If you try this with a real tablecloth, avoid ones with a seam around the edge. Practice with plastic cups.

 

[Bystander]

Practice with plastic cups.

..., or Corel(where'd the copyright symbol go?).

 

[berkeman]

..., or Corel(where'd the copyright symbol go?).

Maybe in LaTeX? $\copyright$ or $\textcopyright$

Oops, I guess not...

 

[jbriggs444]

Maybe in LaTeX? $\copyright$ or $\textcopyright$

Googled up this:
$\enclose{circle}{\text{c}}$
$\enclose{circle}{\text{c}}$

Search for "latex circled text" failed. But search for "mathjax circled text" worked like a champ.

 

[pbuk]

..., or Corel(where'd the copyright symbol go?).

What, this one? ©

Copy and paste from above.