Force&Friction- Two blocks stacked on top

In summary, the conversation discussed a physics problem involving a slab and block with given masses and coefficients of friction. The resulting accelerations of the block and slab were calculated using relevant data and the attempt at a solution. A question was raised about the denominator in part B, but it was clarified that the solution manual was incorrect as the forces cannot be combined and the bodies are in relative motion.
  • #1
physStudent_3
1
0
Hello, I have worked out this physics problem. I then checked my answer, it was correct. However, I have a question about Part B which I will address once all of my information is given;

Homework Statement


A slab of mass m2 = 40kg, rests on a frictionless floor, and a block of mass m1 = 10kg rests on top of the slab. Between the block and the slab the coefficient of static friction is 0.60 and the coefficient of kinetic friction is 0.40. The block is pulled by a horizontal force F of magnitude 100N. What are the resulting accelerations of (a) the block and (b) the slab?

2. Relevant data
m1 = mass of block
m2 = mass of slab
f1 = force of friction between block and slab
a1 = acceleration of block
a2 = acceleration of slab

The Attempt at a Solution



A) a1 = [ F - (u)(m1)(g) ] / (m1)

a1 = [ 100 - (0.4)(10)(9.8) ] / (10)

a1 = 6.08 m/s^2

B) a2 = f1 / m2

a2 = 39.2 / 40

a2 = 0.98 m/s^2

My question is; Since the block (m1) is resting on top of the slab (m2) then shouldn't the two be added together in the denominator of the equation in part B?

Is my solution manual wrong?

Thank you for your insight.
 
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  • #2
Is the answer given under "attempt at solution" solution manual's or yours?
That part seems correct.
 
  • #3
physStudent_3 said:
My question is; Since the block (m1) is resting on top of the slab (m2) then shouldn't the two be added together in the denominator of the equation in part B?

Is my solution manual wrong?

no, that is wrong:
firstly because in part B the force is friction force which will become internal force and hence cannot be used.
secondly, you cannot club the bodies because they are moving with respect to each other and hence on clubbing it would not remain a translational motion
 

What is force?

Force is a physical quantity that causes an object to accelerate, change direction, or deform. It is measured in Newtons (N) and is represented by the symbol F.

What is friction?

Friction is a force that opposes the motion of an object. It is caused by the interaction between two surfaces and can be affected by factors such as surface roughness and the weight of the objects.

How does friction affect two blocks stacked on top of each other?

Friction between the two blocks will cause them to resist sliding against each other. This means that more force will be required to move the top block compared to if it was on a smooth surface.

What factors affect the amount of friction between the two blocks?

The amount of friction between the two blocks can be affected by factors such as the weight of the blocks, the surface roughness of the blocks, and the type of material the blocks are made of.

How can friction be reduced between the two blocks?

To reduce friction between the two blocks, you can use a lubricant, such as oil or grease, between the surfaces. Additionally, reducing the weight of the blocks or using smoother surfaces can also decrease friction.

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