How Does Friction Affect Acceleration on an Incline?

[harambe]

Homework Statement

Figure shows two blocks in contact sliding down an inclined surface of inclination 30.The friction coeffecient between the block of mass 2kg and the incline is μ=0.20 and that between block of mass 4kg and the incline is μ=0.30.Find the acceleration of 4 kg block (g=10m/s2) (Angle of the incline is 30) (Coeffecient of friction as per the question,not by the diagram)

Homework Equations

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The Attempt at a Solution

I thought that since there is friction acting therefore the accelerations will be different in these masses

For 4 kg

Force down the plane - Mgsinθ=40sin30=20N

Friction- μN=0.3X40cos30=10.32

a= Force-friction/mass
=20-10.32/4
=9.88/4
=2.47m/s2

But the answer is 2.7m/s2 so can anybody tell me what I did wrong

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[haruspex]

inclination 30.

So we are to ignore the 35 in the diagram, right?

the accelerations will be different in these masses

Can the upper mass accelerate faster than the lower mass?

 

[harambe]

Yeah we have to ignore the angle of incline in the figure.

Since coeffecient of friction for 2kg<coeffecient of friction of 4kg ,acceleration of 2kg block down the plane will be more than the acceleration of 4kg block,if allowed seperately. .But as 2kg block is behind the 4kg block both of them will move with same acceleration a.This is what my book gives in the solution tho I didn't understand this

 

[haruspex]

Yeah we have to ignore the angle of incline in the figure.

Since coeffecient of friction for 2kg<coeffecient of friction of 4kg ,acceleration of 2kg block down the plane will be more than the acceleration of 4kg block,if allowed seperately. .But as 2kg block is behind the 4kg block both of them will move with same acceleration a.This is what my book gives in the solution tho I didn't understand this

Are you saying that you still do not understand?
Suppose the blocks start a little apart. The upper block will slide down faster and meet the lower block. There will now be a force between them. This will reduce the acceleration of the upper block and increase that of the lower block, bringing them equal.

 

[harambe]

Okay so would they act as a single system??

Also How will friction act now

 

[haruspex]

Okay so would they act as a single system??

Yes.

How will friction act now

What do you think? Would the frictional forces change?

 

[harambe]

Maybe not because they are part of the reason they are acting as a system

 

[haruspex]

Maybe not because they are part of the reason they are acting as a system

What forces act between the blocks?

 

[harambe]

Normal force

 

[haruspex]

Normal force

Right, so does that affect the normal forces between the blocks and the slope?

 

[harambe]

You mean the motion of this system...I think the normal forces would remain the same as if they had during separate motion

 

[haruspex]

You mean the motion of this system...I think the normal forces would remain the same as if they had during separate motion

Right, so do the frictional forces change?

 

[harambe]

No.I got this now

Thanks

 

[harambe]

I got the answer but I have one last doubt...why do the forces down the plane get added for this case.When they collide then the normal forces between them will slow down the upper block and accelerate the lower block till they become equal in acceleration but I don't know how the force down the plane plays during this motion

 

[haruspex]

I got the answer but I have one last doubt...why do the forces down the plane get added for this case.When they collide then the normal forces between them will slow down the upper block and accelerate the lower block till they become equal in acceleration but I don't know how the force down the plane plays during this motion

It should become obvious if you write out the equations. Let the force between them be F_nx. Write out the ΣF=ma equation for each block, then add them together so that the two F_nx terms cancel.

 

[harambe]

Not that one...I am talking about the force down the incline(mgsintheta)

 

[jbriggs444]

Not that one...I am talking about the force down the incline(mgsintheta)

If I understand the question it is about the "constraint force" that prevents the upper (2 kg) block from sliding right on down and through the lower (4 kg) block. This force is essentially the same as that of a table supporting a book, the floor supporting your feet or of one brick holding up another.

The way I like to think of these forces is that they reflect an equilibrium. When the blocks come together, they cannot interpenetrate. Instead, they will each compress slightly. If the blocks are fairly rigid, there will be a large force for only a small amount of compression. If the block material is elastic there will be a recoil. The material of both blocks will return to its unstressed shape and the blocks will bounce away from one another. And fall back together. And bounce away. Typical blocks are not very elastic. There will be little or no rebound. Any bounces will quickly disappear. The associated impact energy will dissipate into vibrations, heat and sound. The details of the dissipation do not matter. All that matters is that it occurs. The two blocks will end up in a stable configuration, in contact with each other, moving at the same speed and compressed by just the right amount to account for the force that each exerts on the other. That is, an equilibrium is attained.

In practice, the amount of compression is often negligible. We can pretend that the blocks are ideally rigid and end up in contact with one another with exactly the right amount of force. We can ignore the microscopic manner in which this state is achieved.

 

[haruspex]

Not that one...I am talking about the force down the incline(mgsintheta)

So am I.

 

[harambe]

If I understand the question it is about the "constraint force" that prevents the upper (2 kg) block from sliding right on down and through the lower (4 kg) block. This force is essentially the same as that of a table supporting a book, the floor supporting your feet or of one brick holding up another.

The way I like to think of these forces is that they reflect an equilibrium. When the blocks come together, they cannot interpenetrate. Instead, they will each compress slightly. If the blocks are fairly rigid, there will be a large force for only a small amount of compression. If the block material is elastic there will be a recoil. The material of both blocks will return to its unstressed shape and the blocks will bounce away from one another. And fall back together. And bounce away. Typical blocks are not very elastic. There will be little or no rebound. Any bounces will quickly disappear. The associated impact energy will dissipate into vibrations, heat and sound. The details of the dissipation do not matter. All that matters is that it occurs. The two blocks will end up in a stable configuration, in contact with each other, moving at the same speed and compressed by just the right amount to account for the force that each exerts on the other. That is, an equilibrium is attained.

In practice, the amount of compression is often negligible. We can pretend that the blocks are ideally rigid and end up in contact with one another with exactly the right amount of force. We can ignore the microscopic manner in which this state is achieved.

That was an excellent explanation .Correct me if I am wrong.So basically the blocks will get compressed and recoil repeatedly and eventually fall into equilibrium

 

[jbriggs444]

That was an excellent explanation .Correct me if I am wrong.So basically the blocks will get compressed and recoil repeatedly and eventually fall into equilibrium

Right.