Repose Angle: Why Doesn't Matter Float?

[Nirav Chavda]

shouldn't it float??

if one recalls the old classical physics terms namely repose angle, I've got a problem for them.
as it(repose angle) is meant for is a state when a matter lying on an inclined plane with a repose angle to ground ... then there will be equilibrium between the frictional and gravitational force... so in such case why does the mass slide down instead of floating? and that too with "SOME" CONSTANT speed?
as far as i think .. it should be floating..
any help there? thanks

 

[brewnog]

Could you elaborate on that please?

 

[Doc Al]

What do you mean by "floating"?

If the mass is initially at rest, and the static friction is sufficient to balance the component of the weight acting down the plane, then the mass will remain in place.

 

[Nirav Chavda]

What do you mean by "floating"?

If the mass is initially at rest, and the static friction is sufficient to balance the component of the weight acting down the plane, then the mass will remain in place.

my friend but then it is not expected to remain there
as observed it would start sliding down
but the question that kicks me the most is why does it slide down with CONSTANT SPEED?
point to be noted - even though the gravitaional and frictional force are supposed to be same mathematically in this state ... motion is observed along the gravitational direction ... why?

 

[Nirav Chavda]

what i simply mean by floating is that the mass in that state will have net zero force acting on it (air friction can be considered nil) so it should either simply remain there or start moving randomly on the plane.

 

[Doc Al]

A mass with zero net force does not "start moving randomly". If its initial speed is zero, it remains zero. If it's moving (in which case it's kinetic friction that matters) then it will remain moving at constant speed.

 

[HallsofIvy]

what i simply mean by floating is that the mass in that state will have net zero force acting on it (air friction can be considered nil) so it should either simply remain there or start moving randomly on the plane.

No, that's not correct. The object will have a force of gravity straight downward. The "supporting" force (without friction) is perpendicular to the inclined plane. They do not "cancel" and the net force is not zero.

 

[mukundpa]

The gravitational force and the frictional force are not balancing each other. The friction is tangential to the plane, while the gravity is vertical. Friend you have forgotten the normal reaction. Is it?

 

[Nirav Chavda]

A mass with zero net force does not "start moving randomly". If its initial speed is zero, it remains zero. If it's moving (in which case it's kinetic friction that matters) then it will remain moving at constant speed.

but then how will you explain the sliding down of that matter where the initial speed is zero.

 

[Nirav Chavda]

The gravitational force and the frictional force are not balancing each other. The friction is tangential to the plane, while the gravity is vertical. Friend you have forgotten the normal reaction. Is it?

i didn't get you when you said not balanced.
i'm talkin about the gravity acting along the plane.

 

[mukundpa]

that is the component of the weight tangential to the plane, what about the other component normal to the plane?

 

[Nirav Chavda]

No, that's not correct. The object will have a force of gravity straight downward. The "supporting" force (without friction) is perpendicular to the inclined plane. They do not "cancel" and the net force is not zero.

you are not getting my point.. I'm speaking of the active gravity ie- gravity acting along the plane (inclined downwards )
at repose angle they ARE equal and that's what repose angle is meant for.

 

[mukundpa]

The normal compnent is pushing the body towards the plane and thus the plane is reacting and appling equal and opposite reaction which is called the normal reaction.

 

[Doc Al]

but then how will you explain the sliding down of that matter where the initial speed is zero.

Please try to explain your question once again, clearly. Is there friction along the plane? Is the friction great enough to balance the component of gravity acting down the plane? If yes, then the mass is in equilibrium: it will NOT start moving down the plane.

Of course, if the friction is insufficient, there will be a net force on the mass acting down the plane. It will start moving. Where's the issue?

 

[Nirav Chavda]

that is the component of the weight tangential to the plane, what about the other component normal to the plane?

just forget those normal forces as we just want the mass to float meaning it should move on the plane randomly or remain still.
here normal aren't required as we are stuck with the plane.

 

[Doc Al]

just forget those normal forces as we just want the mass to float meaning it should move on the plane randomly or remain still.
here normal aren't required as we are stuck with the plane.

Understanding the role of normal force is crucial in understanding the behavior of the mass. All forces count. (It's the normal force that determines the maximum value of the friction force.)

 

[Nirav Chavda]

Please try to explain your question once again, clearly. Is there friction along the plane? Is the friction great enough to balance the component of gravity acting down the plane? If yes, then the mass is in equilibrium: it will NOT start moving down the plane.

Of course, if the friction is insufficient, there will be a net force on the mass acting down the plane. It will start moving. Where's the issue?

brother ... here is my question again-

a mass is placed on an rough inclined plane which has an angle = inverse tan(coefficient of linear frictional force)
in such case the gravity down the plane (inclined) and the limiting frictional force are balanced.

just tell me what will happen next?

 

[mukundpa]

Thanks, at least you say that we are stuck with the plane, and this is due to the nornal forces.
As far as tangential forces are concerned we say that in the limiting equlibrium the body is at the verge of sliding down. The forces are balanced and hence there is no acceleration.
A slight disterbunce(very little force) may disturb the equilibrium and the friction will change to kinetic friction less then the static one and the body start accelerating, but still normal componene of the weight keep the body pushing towards the plane and the body can not float.

 

[Nirav Chavda]

Understanding the role of normal force is crucial in understanding the behavior of the mass. All forces count. (It's the normal force that determines the maximum value of the friction force.)

i'm telling to neglect noraml force becoz here the mass is remaining constant and so remains the N.F
so N.F doesn't mean much when we talk of motion along the 2D inclined plane as it doen't change at all with time

 

[Doc Al]

brother ... here is my question again-

a mass is placed on an rough inclined plane which has an angle = inverse tan(coefficient of linear frictional force)
in such case the gravity down the plane (inclined) and the limiting frictional force are balanced.

just tell me what will happen next?

You are talking about an incline exactly at the angle at which the maximum static friction just balances the component of gravity down the plane. Since the net force is zero, and the mass starts at rest: Nothing will happen. Exceed that angle by just a bit and there will be a net force.

(Lot's of luck being exactly at that angle.)

 

[Doc Al]

i'm telling to neglect noraml force becoz here the mass is remaining constant and so remains the N.F
so N.F doesn't mean much when we talk of motion along the 2D inclined plane as it doen't change at all with time

I take it that you've never derived for yourself the formula for determining the angle at which the plane must be to have the mass just start to slide.

 

[Nirav Chavda]

Thanks, at least you say that we are stuck with the plane, and this is due to the nornal forces.
As far as tangential forces are concerned we say that in the limiting equlibrium the body is at the verge of sliding down. The forces are balanced and hence there is no acceleration.
A slight disterbunce(very little force) may disturb the equilibrium and the friction will change to kinetic friction less then the static one and the body start accelerating, but still normal componene of the weight keep the body pushing towards the plane and the body can not float.

great ! you got a point there!
so there is an infinitesimal (or so ) disturbance which changes the static friction to kinetic friction where K.F<S.F

but why has it to move only downwards?

 

[Nirav Chavda]

I take it that you've never derived for yourself the formula for determining the angle at which the plane must be to have the mass just start to slide.

why do you think so?

 

[Doc Al]

why do you think so?

Because of your statement about the unimportance of the normal force.

Please make whatever point you wanted to make.

 

[Nirav Chavda]

Because of your statement about the unimportance of the normal force.

Please make whatever point you wanted to make.

just tell me how will you use this N.F to prove that the body just can't move in such conditions ... here actually (as observed) the mass would slide down

 

[mukundpa]

If the external infinitesimal force is up the plane then it reduces the tangential downward force, hence reduces the static friction (not limiting), no question of sliding up, makes only downward sliding is possible.

 

[Doc Al]

What is your point?

If the force on the object is zero: what makes you think it will start moving?

If the force on the object is not zero: it will start moving. So what?

If you are exactly at the limiting angle, then what really will happen depends on the precise initial conditions. So what?

 

[Nirav Chavda]

If the external infinitesimal force is up the plane then it reduces the tangential downward force, hence reduces the static friction (not limiting), no question of sliding up, makes only downward sliding is possible.

then why has it to move with some constant speed? i see you're slowly getting to the point

 

[Nirav Chavda]

What is your point?

If the force on the object is zero: what makes you think it will start moving?

If the force on the object is not zero: it will start moving. So what?

If you are exactly at the limiting angle, then what really will happen depends on the precise initial conditions. So what?

let me make it clear for you... THE BODY IS OBSERVED TO MOVE DOWNWARDS WITH CONSTANT VELOCITY-- THATS A FACT not my THOUGHT .
infact I'm in favour of the object remaining there or moving randomly(less chance for latter)

 

[Doc Al]

then why has it to move with some constant speed? i see you're slowly getting to the point

Start with the mass resting on the incline at some angle less than the limiting angle. Slowly increase the angle, until it just starts to move. When it starts sliding, kinetic friction (which is generally less than the static friction) takes over and there is a net force downward.

 

[mukundpa]

Not with the constant velocity but with accleration. Youuuuuuuuu can calculate it.

 

[Nirav Chavda]

Start with the mass resting on the incline at some angle less than the limiting angle. Slowly increase the angle, until it just starts to move. When it starts sliding, kinetic friction (which is generally less than the static friction) takes over and there is a net force downward.

you say the body will have net force downward then it'll accelerate which contradicts the fact that it moves down with CONSTANT SPEED which cannot happen if net force ACTS.

 

[Nirav Chavda]

Not with the constant velocity but with accleration. Youuuuuuuuu can calculate it.

this case can be thought to be similar to the body on a horizontal plane.
there when force just equal to the static force is applied the body starts moving but with zero acceleration

 

[Doc Al]

let me make it clear for you... THE BODY IS OBSERVED TO MOVE DOWNWARDS WITH CONSTANT VELOCITY-- THATS A FACT not my THOUGHT .

Have you seen this "fact" with your own eyes? Do you have a reference?

I'm doing the "experiment" right now in my office, with an eraser and a clipboard. Sure looks like accelerated motion to me.

Of course, if you are able to keep the speed very small (with tiny adjustments of angle), it would not surprise me to see the friction changing back and forth from static to kinetic. (The typical models of friction are only approximate.)

 

[Doc Al]

this case can be thought to be similar to the body on a horizontal plane.
there when force just equal to the static force is applied the body starts moving but with zero acceleration

How do you start moving with zero acceleration?