What is the Coefficient of Friction Between Two Blocks on a Horizontal Surface?

In summary, the problem involves two blocks, one with a mass of M and the other with a mass of 2M, being accelerated across a horizontal frictionless surface. The frictional forces between the blocks keep them from sliding relative to each other, causing them to move with the same acceleration. The question asks for the magnitude of the horizontal component of the force exerted on the small block by the large block. Through analysis of the forces acting on each block, it is determined that the frictional force is equal to one-third of the applied force, or P/3.
  • #1
PinkDaisy
9
0
The question is:

"Two blocks are accelerated across a horizontal frictionless surface as shown. Frictional forces keep the two blocks from sliding relative to each other, and the two move with the same acceleration. What is the magnitude of the horizontal component (frictional force) of the force exerted on the small block by the large block?"

The mass of the small block on top is: M ,the mass of the bottom block is: 2M , and the force, P is: 3 N.

I drew the FBD's, block M has three forces: n1 (up), Mg (down), and f (right). Block 2M has 5 forces? P (right), 2Mg (down), n1 (down), n2 (up), and f (left).

I can't seem to get it, there appears to be too many unknowns to me.

I appreciate any help. Thanks!
 
Physics news on Phys.org
  • #2
No picture for us to see?

[itex]\sum \vec F=m\vec a[/itex]

You know the acceleration. Without a picture its hard to determin if your assessments are correct. The force of friction will act in the same direction as the motion of the lower block. You know the masses of the blocke. you can form two equation--one f=ma for each block and you have two unknowns. You should be able to get an answer.

Of those 5 forces can't you relate them so that they are all in terms of M and f? Give it a try and see. Remember the top block's M is the same as the bottom block M--there's just two of them on the bottom though. The frictional force on the top block is the same as on the bottom block too.

Anyway, hope this helped. Show what you've done if you need more help. From what I can see your assessment of the forces is correct but without a picture I can't be 100% sure.
 
  • #3
Sorry about no picture. It is a surface with two boxes stacked on each other with the smaller one on top. The force P pulls the bottom box to the right.

These are my equations but then I don't know where to go.
\sum Fy (M) = n1 - mg so n1=mg
\sum Fx (M) = f1 = ma so \mu mg = ma

\sum Fy (2M) = n2 - n1 - 2Mg = 0 so n2=3Mg
\sum Fx (2M) = P - f2 = 2Ma so P-\mu(3Mg)=2Ma
 
  • #4
OHH! I think I finally got it!

I took both of the \sum Fx equations and solved them for ma then set them equal to each other and then solved for f.

f=ma and (P-f)/2=ma

f=(P-f)/2
P=f/3

I was confused by the question, I thought that it wanted me to solve for \mu, but it was really asking about f.

Right?
 
  • #5
PinkDaisy said:
f=ma and (P-f)/2=ma

f=(P-f)/2
P=f/3
That last equation should be P = 3f so f = P/3.
 
  • #6
Oops, you are exactly right. The excitement from finally conquering the problem caused my fingers to malfunction! Thanks for the help!
 

FAQ: What is the Coefficient of Friction Between Two Blocks on a Horizontal Surface?

What is the coefficient of friction?

The coefficient of friction is a dimensionless quantity that measures the resistance of two surfaces to sliding against each other. It is typically denoted by the Greek letter μ (mu) and can range from 0 to 1, with lower values indicating less friction and higher values indicating more friction.

How is the coefficient of friction calculated?

The coefficient of friction can be calculated by dividing the force of friction between two surfaces by the normal force pressing the surfaces together. This can be done experimentally by measuring the force required to move an object across a surface at a constant speed, or it can be calculated using the material properties and surface characteristics of the two surfaces.

What factors affect the coefficient of friction?

The coefficient of friction can be affected by several factors, including the type of surfaces in contact, the roughness or smoothness of the surfaces, the amount of force pressing the surfaces together, and the presence of any lubricants or contaminants on the surfaces.

Why is the coefficient of friction important?

The coefficient of friction is important in many scientific and engineering applications because it can affect the performance and efficiency of systems that involve sliding or rolling surfaces. It is also an important factor to consider in safety and design considerations, such as when determining the stopping distance of a vehicle or the grip of a shoe on a surface.

Can the coefficient of friction be changed?

Yes, the coefficient of friction can be changed by altering the factors that affect it, such as changing the surface properties or using lubricants. It can also be affected by external factors, such as temperature or humidity. However, the coefficient of friction is an inherent property of the materials and surfaces in contact, so it cannot be completely eliminated.

Back
Top