Friction, Mass and Acceleration: Analyzing Block Motion

In summary, the conversation discusses the concept of friction and its role in causing a block to slide. The equation F=u*n and F=(m1+m2)a is used to calculate the force of friction, which is then set equal to Newton's Second Law (F=ma). The acceleration terms are not cancelled out, but rather replaced with their value found in a previous part of the problem. This leads to the final equation F=(u*m1g(m1+m2))/m2, which explains the force acting on object 2 when friction breaks and the two masses start sliding.
  • #1
as2528
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Homework Statement
Two blocks of mass m2 and m1 are put on a frictionless level surface as shown in the figure below. The static coefficient of friction between the two blocks is µ. A force F acts on the top block m2.

(c) Find the magnitude of the force F above which the block m1 starts to slide relative to the block m1.
Relevant Equations
F=ma
F=u*N
The block starts to slide if friction can no longer hold the block.

F=u*n and F=(m1+m2)a
so: (m1+m2)a=uN=>am1+am2=uN=>am2=(uN)/(am1)

So:am2=(uN)/(am1) is the force.

The answer is F=(u*m1g(m1+m2))/m2
I do not see how the acceleration terms are canceled. Is my answer equivalent to this?
 

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  • #2
There is no figure below. Please post it.
 
  • #3
kuruman said:
There is no figure below. Please post it.
Added it!
 
  • #4
Please use the "Attach files" link on the lower left to put the figure in your post. It is inconvenient for people to download pdf files just to look at a figure. You will have to do that because you need to post your free body diagram that resulted in your equation.
Can you identify what each "F" in your equation stands for and explain your reasoning?
F=u*n and F=(m1+m2)a

(Fill in the blanks)
The first F stands for _________________________

The second F stands for _________________________

I set the two equal because _____________________________
 
  • #5
kuruman said:
Please use the "Attach files" link on the lower left to put the figure in your post. It is inconvenient for people to download pdf files just to look at a figure. You will have to do that because you need to post your free body diagram that resulted in your equation.
Can you identify what each "F" in your equation stands for and explain your reasoning?
F=u*n and F=(m1+m2)a

(Fill in the blanks)
The first F stands for _________________________

The second F stands for _________________________

I set the two equal because _____________________________
I have now attached the pictures. The first F is for Newton's Second Law. The second F is for the force of friction. When the force of friction breaks, and I set it equal to Newton's Second Law, I can find the magnitude of the force acting on object 2 at that instant.
 
  • #6
Do you understand how the first equation in part (c) was put together? The acceleration does not "cancel out". It is replaced by its value found in part (b). Just before the two masses start sliding relative to each other, they have the common acceleration from part (b). In your expression you left the acceleration as ##a## which doesn't do much for you. The two masses have common acceleration ##a=\frac{F}{m_1+m_2}## until the top mass starts sliding on the bottom mass.
 
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  • #7
kuruman said:
Do you understand how the first equation in part (c) was put together? The acceleration does not "cancel out". It is replaced by its value found in part (b). Just before the two masses start sliding relative to each other, they have the common acceleration from part (b). In your expression you left the acceleration as ##a## which doesn't do much for you. The two masses have common acceleration ##a=\frac{F}{m_1+m_2}## until the top mass starts sliding on the bottom mass.
I see now. I did not realize that, I understand now. Thanks!
 
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FAQ: Friction, Mass and Acceleration: Analyzing Block Motion

What is the relationship between friction, mass, and acceleration in block motion?

The relationship between friction, mass, and acceleration in block motion is governed by Newton's second law of motion. The frictional force opposes the motion of the block and is proportional to the normal force, which is the weight of the block (mass times gravity). The net force acting on the block is the applied force minus the frictional force, and this net force determines the acceleration of the block according to the equation \( F = ma \), where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration.

How does increasing the mass of a block affect its acceleration if the same force is applied?

Increasing the mass of a block while applying the same force decreases its acceleration. According to Newton's second law, \( a = \frac{F}{m} \). If the applied force \( F \) remains constant and the mass \( m \) increases, the acceleration \( a \) must decrease. This inverse relationship means that heavier blocks accelerate less when the same force is applied compared to lighter blocks.

What role does the coefficient of friction play in block motion?

The coefficient of friction is a dimensionless number that represents the ratio of the frictional force between two surfaces to the normal force pressing them together. It plays a crucial role in block motion by determining the magnitude of the frictional force. There are two types of coefficients: static friction (when the block is at rest) and kinetic friction (when the block is in motion). The frictional force can be calculated using \( f = \mu N \), where \( \mu \) is the coefficient of friction and \( N \) is the normal force. Higher coefficients indicate greater frictional forces, which oppose the motion more strongly.

How can you calculate the acceleration of a block on an inclined plane?

To calculate the acceleration of a block on an inclined plane, you need to consider the components of gravitational force along and perpendicular to the plane. The component along the plane is \( mg \sin(\theta) \), and the component perpendicular to the plane is \( mg \cos(\theta) \), where \( m \) is the mass of the block, \( g \) is the acceleration due to gravity, and \( \theta \) is the angle of the incline. If friction is present, the frictional force is \( \mu mg \cos(\theta) \). The net force along the plane is \( mg \sin(\theta) - \mu mg \cos(\theta) \), and the acceleration \( a \) can be found using \( a = \frac{mg \sin(\theta) - \mu mg \cos(\theta)}{m} \),

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