# How Does Friction Affect Acceleration on an Incline?

• harambe
In summary: It should become obvious if you write out the equations. Let the force between them be Fnx. Write out the ΣF=ma equation for each block, then add them together so that the two Fnx terms cancel.Fnx=maFnx+ma=maThis is the equation for a system in equilibrium. If you take the total force on the system (Fnx+ma), it will equal the total mass (mg) of the system. So the force between the blocks becomes just the mass of material (2kg+4kg=6kg) pushing on the blocks.The force between the blocks becomes just the mass of material (2kg+4
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)

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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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harambe said:
inclination 30.
So we are to ignore the 35 in the diagram, right?
harambe said:
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

harambe said:
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.

Okay so would they act as a single system??

Also How will friction act now

harambe said:
Okay so would they act as a single system??
Yes.
harambe said:
How will friction act now
What do you think? Would the frictional forces change?

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

harambe said:
Maybe not because they are part of the reason they are acting as a system
What forces act between the blocks?

Normal force

harambe said:
Normal force
Right, so does that affect the normal forces between the blocks and the slope?

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

harambe said:
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

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

harambe said:
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 Fnx. Write out the ΣF=ma equation for each block, then add them together so that the two Fnx terms cancel.

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

harambe said:
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.

harambe
harambe said:
Not that one...I am talking about the force down the incline(mgsintheta)
So am I.

jbriggs444 said:
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

harambe said:
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.

## 1. What is the formula for calculating acceleration on an incline?

The formula for calculating acceleration on an incline is a = gsinθ, where a is the acceleration, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of incline.

## 2. How does the angle of incline affect the acceleration?

The acceleration on an incline is directly proportional to the angle of incline. This means that as the angle of incline increases, the acceleration also increases.

## 3. Does the mass of the object affect the acceleration on an incline?

Yes, the mass of the object does affect the acceleration on an incline. The higher the mass of the object, the greater the force of gravity acting on it, and therefore the greater the acceleration.

## 4. How does friction play a role in acceleration on an incline?

Friction acts in the opposite direction of the motion of the object on the incline, and therefore it can decrease the acceleration. The amount of friction present depends on the surface of the incline and the object.

## 5. What is the difference between acceleration on an incline and acceleration in free fall?

In free fall, the acceleration is solely due to the force of gravity, whereas on an incline, the acceleration is influenced by both gravity and the angle of incline. In free fall, the object accelerates at a constant rate, while on an incline, the acceleration can vary depending on the angle and other factors.

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