A small object is at rest on the edge of a horizontal table. It is pushed in such a way that it falls off the other side of the table, which is 1 m wide, after 2 s. Does the object have wheels?
Spoiler:ShowA hint is given, not sure how it helps.
What is the maximum possible value of the coefficient of friction if the object is not to stop on the table?
This problem drove me crazy.
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 05072016 21:27

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 05072016 22:05
(Original post by tangotangopapa2)
A small object is at rest on the edge of a horizontal table. It is pushed in such a way that it falls off the other side of the table, which is 1 m wide, after 2 s. Does the object have wheels?
Spoiler:ShowA hint is given, not sure how it helps.
What is the maximum possible value of the coefficient of friction if the object is not to stop on the table?
2 seconds seems like a long time for something to spend slowing down over 1m otherwise. 
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 05072016 22:11
(Original post by Joinedup)
might be on an air hockey table
2 seconds seems like a long time for something to spend slowing down over 1m otherwise.
Can you please prove mathematically that it is on an air hockey table? What about wheels? 
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 05072016 22:37
Alright, first time I'm answering a physics question on this forum, so bare with me (Oh, an I don't know if you have a formula editor built into this page, sry for not using it now if there is one.)
Start with the basing GCSE formula for distance cover while having constant acceleration:
s=(at^2)/2
We already have s and t given, what is a? Well, you have friction acting upon the body, which, in this case, is simply weight times the friction coefficient.
a = F/m = fmg/m = fg
Therefore:
s = (fgt^2)/2
Rearranging and plugging in the numbers will give you f = 0.05 [dimensionless]. Now ask yourself what actually happened. The object travelled exactly 1m and stopped, therefore if f = 0.05 then it will stop at the opposite side of the table, not fall. You can also find that the initial velocity of the object must have been exactly 1 m/s (you can calculated this yourself). So, if you want the object to fall, you have to decrease the coefficient of friction below 0.05 AND decrease the initial velocity to meet your conditions. The other extreme situation is when f=0 and v_0 = 0.5m/s. You could probably figure out the relationship between f and v_0, but I'll leave that to you.
Dunno, how this proves/disproves whether the object has wheels, but I hope this helpsPost rating:1 
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 05072016 22:48
assuming constant accelleration
s=0.5 (u+v) t
gives us initial speed of 1 m/s and therefore acceleration of 0.5 ms^{2}
since for the accelerating force on a horizontally sliding object F=ma and F=μmg
you can estimate the coefficient of friction
μ=a/g
which can be compared to a table of common materials http://www.engineersedge.com/coeffients_of_friction.htm 
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 05072016 22:56
(Original post by Joinedup)
assuming constant accelleration
s=0.5 (u+v) t
gives us initial speed of 1 m/s and therefore acceleration of 0.5 ms^{2}
since for the accelerating force on a horizontally sliding object F=ma and F=μmg
you can estimate the coefficient of friction
μ=a/g
which can be compared to a table of common materials http://www.engineersedge.com/coeffients_of_friction.htm 
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 05072016 23:02
(Original post by Blank_Planet)
Alright, first time I'm answering a physics question on this forum, so bare with me (Oh, an I don't know if you have a formula editor built into this page, sry for not using it now if there is one.)
Start with the basing GCSE formula for distance cover while having constant acceleration:
s=(at^2)/2
We already have s and t given, what is a? Well, you have friction acting upon the body, which, in this case, is simply weight times the friction coefficient.
a = F/m = fmg/m = fg
Therefore:
s = (fgt^2)/2
Rearranging and plugging in the numbers will give you f = 0.05 [dimensionless]. Now ask yourself what actually happened. The object travelled exactly 1m and stopped, therefore if f = 0.05 then it will stop at the opposite side of the table, not fall. You can also find that the initial velocity of the object must have been exactly 1 m/s (you can calculated this yourself). So, if you want the object to fall, you have to decrease the coefficient of friction below 0.05 AND decrease the initial velocity to meet your conditions. The other extreme situation is when f=0 and v_0 = 0.5m/s. You could probably figure out the relationship between f and v_0, but I'll leave that to you.
Dunno, how this proves/disproves whether the object has wheels, but I hope this helps 
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 05072016 23:04
(Original post by tangotangopapa2)
Thanks alot. So u cant be greater than 1ms1 , can it? So coeff of friction < g/20. 
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 05072016 23:09
(Original post by Blank_Planet)
Alright, first time I'm answering a physics question on this forum, so bare with me (Oh, an I don't know if you have a formula editor built into this page, sry for not using it now if there is one.)
Start with the basing GCSE formula for distance cover while having constant acceleration:
s=(at^2)/2
We already have s and t given, what is a? Well, you have friction acting upon the body, which, in this case, is simply weight times the friction coefficient.
a = F/m = fmg/m = fg
Therefore:
s = (fgt^2)/2
Rearranging and plugging in the numbers will give you f = 0.05 [dimensionless]. Now ask yourself what actually happened. The object travelled exactly 1m and stopped, therefore if f = 0.05 then it will stop at the opposite side of the table, not fall. You can also find that the initial velocity of the object must have been exactly 1 m/s (you can calculated this yourself). So, if you want the object to fall, you have to decrease the coefficient of friction below 0.05 AND decrease the initial velocity to meet your conditions. The other extreme situation is when f=0 and v_0 = 0.5m/s. You could probably figure out the relationship between f and v_0, but I'll leave that to you.
Dunno, how this proves/disproves whether the object has wheels, but I hope this helps 
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 10
 05072016 23:12
(Original post by Joinedup)
assuming constant accelleration
s=0.5 (u+v) t
gives us initial speed of 1 m/s and therefore acceleration of 0.5 ms^{2}
since for the accelerating force on a horizontally sliding object F=ma and F=μmg
you can estimate the coefficient of friction
μ=a/g
which can be compared to a table of common materials http://www.engineersedge.com/coeffients_of_friction.htmLast edited by B_9710; 05072016 at 23:16. 
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 05072016 23:29
Find the coefficient of friction assuming constant deceleration, as it is shown above it is 0.05. From experience you should know that this is too small, hence why it's probably using wheels.
Post rating:1 
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 06072016 00:10
(Original post by B_9710)
What the final speed? I don't think you have done this correctly.

Fwiw
Suppose other explanations could be that you're on the Moon or in a lift that's accelerating downwards. 
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 06072016 00:44
(Original post by Joinedup)
Stops at the edge of a 1m table if I read it properly, so final speed is zero... In this case we really only care about the magnitude of the accn.

Fwiw
Suppose other explanations could be that you're on the Moon or in a lift that's accelerating downwards.
You still cannot tell if it's on wheels though, there was no indication that the table is rough, and even if it is rough the coefficient of friction could infact be a small value. Plus how do wheels even affect the motion anyway?Last edited by B_9710; 06072016 at 00:48. 
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 06072016 08:39
(Original post by B_9710)
Oh I see what you're saying, I misinterpreted it when I first read it.
You still cannot tell if it's on wheels though, there was no indication that the table is rough, and even if it is rough the coefficient of friction could infact be a small value. Plus how do wheels even affect the motion anyway?
Note that 1 m/s is the maximum possible initial speed which gives c.o.f g/20. It could have been less. For instance, 0.5 m/s gives value of cof very very close to zero. Note that in all these calculations, final velocity is assumed to be zero, which may not be the case. It should have some speed in order to fall off the table. In that case, cof for each initial speed should be lower.
The way wheel works is by reducing friction. Only friction between wheel's bottom & ground and friction within internal system comes into account. 
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 06072016 08:50
(Original post by B_9710)
Oh I see what you're saying, I misinterpreted it when I first read it.
You still cannot tell if it's on wheels though, there was no indication that the table is rough, and even if it is rough the coefficient of friction could infact be a small value. Plus how do wheels even affect the motion anyway?
wheels should reduce the resistance and therefore the acceleration though. 
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 06072016 09:54
(Original post by tangotangopapa2)
Now that the coefficient of friction must be less than g/20. Though it does not prove that the object has wheel but highly indicates so. No known material used to make table has that small c.o.f. Had it stopped at the edge, then equality would have holded.
Note that 1 m/s is the maximum possible initial speed which gives c.o.f g/20. It could have been less. For instance, 0.5 m/s gives value of cof very very close to zero. Note that in all these calculations, final velocity is assumed to be zero, which may not be the case. It should have some speed in order to fall off the table. In that case, cof for each initial speed should be lower.
The way wheel works is by reducing friction. Only friction between wheel's bottom & ground and friction within internal system comes into account. 
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 06072016 09:59
(Original post by B_9710)
But we are actually modelling the object as a particle, so it's not like the object has any surface area so actually wheels make no difference to a particle in terms of the resistance acting on it as the only resistive force is friction. No obviously friction does increase as surface area in contact with the tbe increases, but as we are modelling it as a particle, it has no surface area and so you can really not say whether it has wheels or not. It's really a false question. 
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 06072016 10:02
(Original post by tangotangopapa2)
Yes, you are right. As it has been mentioned earlier, it is not a fair question to meet in an exam. Do you think it makes sense to ask this question stating 'Is the object sliding or rolling?' 
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 07072016 10:36
(Original post by tangotangopapa2)
Now that the coefficient of friction must be less than g/20. 
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 07072016 10:41
(Original post by Blank_Planet)
I actually made a tiny mistake: the coefficient of friction must be <1/20 not <g/20. The later is the max acceleration of the object. Coef. of friction is a dimensionless quantity. Small difference, but I thought its better to make things clear.
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Updated: July 7, 2016
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