Force on Table when Dropped: Find Out with Friends!

[mreznicek]

Friends:

Let's say a 1 kg. mass is droped a negligible distance above a table. What is the maximum force exerted on the table?

What would the force be if the object were dropped L meters above the table?

Thanks amigos! -MigsP.S. This is not a homework question! I finished M.E. a long time ago!

 

[Stevedye56]

F=ma?

 

[mreznicek]

a=~0, thus F=0, and this aint possible!

 

[UtterMess]

if a=~0 that means a is not = 0. so then F = 0 is not true.

There's always acceleration if you're dropping it. It just depends on how far its falling. You just need to find out how far "negligible" is and how long it takes to hit the table.

 

[mreznicek]

hmmmm... What about the impulse?

 

[Astronuc]

What is a negligible distance? 1 mil, 1 mm, 1 inch?

A mass M has a weight Mg. If the mass falls then it will hit the table and lose it's momentum, so figure the change in velocity and the time interval it takes to reach zero velocity.

If a mass falls from height L, then MgL = 1/2 Mv² so gL = v²/2, or

$$v = \sqrt{2gL}$$

 

[mreznicek]

OK Astronuk, I understand your thinking. What I don't understand is how you get to the force F if you don't know anything about the time. (Or is the time the time it takes from release above the table to stop? If so, the closer the the book is to the table then time tends towards zero... ...and the force is just the weight of the book?) I know that the impulse is an integral, but how, with the information at hand can we get to F? It's something that always puzzles me, and I hope that here we can dilucidate it. I do appreciate your educating me! -Migs

 

[HallsofIvy]

"~0" was "approximately 0", not "not 0"!

The table acts like a spring. You can't calculate the maximum force on the table without knowing how long it will take the table to bring the book to a stop- i.e. know the "spring constant" or "elasticity" of the table, book combination.

If you assume the table and book are rigid- that there is no compression of either and the book stops instantaneously, then there is infinite force.

 

[Astronuc]

If so, the closer the the book is to the table then time tends towards zero...

As the distance (and time) approaches zero, the the force approaches the weight.

One approximation to the time is to divide the length of the Mass or Table by the speed of sound in that Mass or Table, whichever is less resilient. Pressure waves travel at the speed of sound.

 

[mreznicek]

HallsofIvy and Astronuc:

Thanks again for the info. With your last two posts the question becomes again a problem for me since the elasticity of the table becomes an relatively unknown factor. Are there any "rules of thumb used in cases like this? (Sort of like Astronuc's approximation above). When the collision is inelastic does it usually have to be solved by some approximative or experimental manner? How do folks design stuff like highway barriers with collision in mind? Again thanks amigos! Migs

 

[arildno]

Well, you need to determine the particular table's "spring constant" experimentally, i.e, find out what compression occurs for a given force, utilizing a Hooke-like law to determine the spring constant.
Then you can model the table as an ideal spring and get some numerical answers to your problem.

 

[mreznicek]

Thanks arildno!-Migs

 

[ZapperZ]

Note that while it wasn't a homework question, it is still a homework-TYPE question, and should be in the HW/Coursework forum.

Zz.