What is the minimum force needed to move a block with friction present?

In summary: If you had to tug a heavy mass across a floor, how would you do...assuming you didn't want to pull it directly towards you?You would use an angle to determine how much force to apply. You would use an angle to determine how much force to apply.
  • #1
rudransh verma
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Homework Statement
A body of mass m results on horizontal floor with which it has coefficient of static friction ##\mu##. It is desired to move the block with minimum possible force. Find the applied force F.
Relevant Equations
##F_n=ma##
##F_s=\mu F_N##
We know the minimum force to move the body in presence of friction will be ##F>\mu F_N##
But it’s not right.
 
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  • #2
rudransh verma said:
We know the minimum force to move the body in presence of friction will be ##F>\mu F_N##
But it’s not right.
Why not? (What does ##F_N## equal?)
 
  • #3
Where is the effort here?
 
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  • #4
I am intrigued, what is the answer key @rudransh verma . Why you say its not correct? According to my opinion the minimum force is ##\mu mg##.
 
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  • #5
Doc Al said:
Why not? (What does ##F_N## equal?)
Delta2 said:
I am intrigued, what is the answer key @rudransh verma . Why you say its not correct? According to my opinion the minimum force is ##\mu mg##.
Yes ##\mu mg##. But the answer in my book says ##F=\frac{\mu mg}{\sqrt{1+\mu^2}}##
 
  • #6
rudransh verma said:
Yes ##\mu mg##. But the answer in my book says ##F=\frac{\mu mg}{\sqrt{1+\mu^2}}##
Something is fishy here, can you post some sort of figure that perhaps exists in the book for this problem?
 
  • #7
rudransh verma said:
But the answer in my book says ##F=\frac{\mu mg}{\sqrt{1+\mu^2}}##
Did you provide the complete problem statement?
 
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  • #8
Delta2 said:
Something is fishy here, can you post some sort of figure that perhaps exists in the book for this problem?
 

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  • #9
Seriously? You only now thought it relevant to tell us that the applied force F is at an angle?
 
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  • #10
Doc Al said:
Seriously? You only now thought it relevant to tell us that the applied force F is at an angle?
No. This is the complete question. There is no mentioning of any angle as you can see.I don’t know why they are applying force at an angle.
 
  • #11
rudransh verma said:
No. This is the complete question. There is no mentioning of any angle as you can see.I don’t know why they are applying force at an angle.
So you are saying that the diagram you just posted has nothing to do with this problem?
 
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  • #12
Doc Al said:
So you are saying that the diagram you just posted has nothing to do with this problem?
I am saying they have solved the problem assuming force at an angle. That diagram is not the part of question but of the answer.
 
  • #13
rudransh verma said:
I am saying they have solved the problem assuming force at an angle. That diagram is not the part of question but of the answer.
That's a bit hard to believe.

(1) Post the complete problem statement
(2) Post the complete solution provided.
 
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  • #14
Ah, I see the issue now. You were not told anything about the direction of the applied force, so you are free to apply it in any direction to solve for the minimum force needed. Assuming that the applied force must be horizontal was a mistake.
 
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  • #15
Doc Al said:
1) Post the complete problem statement

Doc Al said:
Post the complete solution provided.
 

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  • #16
See my last post. Do you see how being allowed to apply the force at an angle can affect the answer?
 
  • #17
rudransh verma said:
I don’t know why they are applying force at an angle.
Because that lowers the normal force and therefore the horizontal force required to move the block. Since the problem did not say anything about the direction, in order to find the minimal force, you need to find an expression for the required force as a function of the angle and then minimise with respect to the angle.
 
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  • #18
Is this more readable?

Versa Picture1.png
 
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  • #19
OK , well I am not sure if that "the force applied must be at an angle " should be part of the problem statement or the student would have to think it. I was not smart enough to think it, and I am deeply sorry for myself o:).
 
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  • #20
Delta2 said:
OK , well I am not sure if that "the force applied must be at an angle " should be part of the problem statement or the student would have to think it. I was not smart enough to think it, and I am deeply sorry for myself o:).
Everybody makes bloopers or misread problems sometimes. Obviously, stating explicitly that the force could be at an angle would make it more obvious, but technically it is also fair game with the problem just stating to find the minimal force.
 
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  • #21
Orodruin said:
Obviously, stating explicitly that the force could be at an angle would make it more obvious, but technically it is also fair game with the problem just stating to find the minimal force.
The problem asks specifically for the magnitude of the force. That's a very broad hint here.
 
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  • #22
Delta2 said:
OK , well I am not sure if that "the force applied must be at an angle " should be part of the problem statement or the student would have to think it. I was not smart enough to think it, and I am deeply sorry for myself o:).
It can help to put yourself into the problem. If you had to tug a heavy mass across a floor, how would you do it?
 
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  • #23
haruspex said:
It can help to put yourself into the problem. If you had to tug a heavy mass across a floor, how would you do it?
I don't know how you think but according to my thinking and intuition I would push it with horizontal force.
 
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  • #24
Delta2 said:
I don't know how you think but according to my thinking and intuition I would push it with horizontal force.
So you just learned something practically useful! 😉

In addition, pulling at an angle will also mean helping to overcome issues of bad grip on the ground on your part as you also increase your own normal force.
 
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  • #25
Delta2 said:
I don't know how you think but according to my thinking and intuition I would push it with horizontal force.
Maybe you need to do more manual labour!

Two physicists were watching workmen on a building site. "See how he pulls the wheelbarrow behind himself instead of pushing it in front. He has obviously worked out that because he is pulling up at a slight angle it reduces the rolling resistance", observed one.
The other physicist asked the workman why he did it. "I've pushed wheelbarrows for thirty years," he replied, "and I'm fed up with the sight of 'em."
 
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  • #26
Orodruin said:
Because that lowers the normal force and therefore the horizontal force required to move the block.
To apply minimum force the force of friction has to be less and will become less when we decrease the normal force and that would mean a tilted block.
But the eqns are ##F_N+F\sin \theta =mg##
##F\cos \theta=\mu F_N## which I don’t think is consistent with the tilted block.
 
  • #27
rudransh verma said:
and that would mean a tilted block.
No, it would not necessarily tilt the block. Why do you think so? There is a separate set of equations (based on torque balance) that would tell you whether the block tilts or not.

rudransh verma said:
which I don’t think is consistent with the tilted block.
Why not? They are valid as long as the coefficient of friction remains the same.
 
  • #28
Orodruin said:
No, it would not necessarily tilt the block. Why do you think so?
If it will not leave the ground at least from one side how the friction will decrease ?
 
  • #29
rudransh verma said:
If it will not leave the ground at least from one side how the friction will decrease ?
By decreasing the normal force. Maximal friction is proportional to normal force.
 
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  • #30
Orodruin said:
By decreasing the normal force. Maximal friction is proportional to normal force.
Are you saying applying a force at an angle can decrease the friction without actually lifting it. That there is some ##0<F_N<mg##
 
  • #31
rudransh verma said:
Are you saying applying a force at an angle can decrease the friction without actually lifting it. That there is some ##0<F_N<mg##
You should be able to figure out the answer to this. What does force and torque balance on the block tell you? For simplicity, consider a homogeneous block with mass ##m## with a vertical string being pulled up attached to one of its sides. Will the block start tilting at the first minimal application of force? If not, how hard can you pull before it does?
 
  • #32
Orodruin said:
Will the block start tilting at the first minimal application of force? If not, how hard can you pull before it does?
No. I think if we apply some upward force block will not move because ##F_N+ F_a=mg##. We need to increase the ##F_a=mg##. Then block will move. So we can apply a force to decrease the normal without actually lifting it up.
##F_a## is applied force.
 
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  • #33
rudransh verma said:
No. I think if we apply some upward force block will not move because ##F_N+ F_a=mg##. We need to increase the ##F_a=mg##. Then block will move. So we can apply a force to decrease the normal without actually lifting it up.
##F_a## is applied force.
Not be lifted up, when does it start tilting? Did you draw a free body diagram and do the torque analysis?
 
  • #34
Orodruin said:
Not be lifted up, when does it start tilting? Did you draw a free body diagram and do the torque analysis?
I have not studied about torque. Sorry. It’s in future chapters.
But I get it. Force at an angle will have its component in the direction of normal and that will decrease the normal force and thus friction. It will be enough to move the block forward.
 
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  • #35
rudransh verma said:
I have not studied about torque. Sorry. It’s in future chapters.
That is fine. Just as long as you are aware that until you reach and have learned those chapters, you will not really be able to tell when things tip over etc.
 
<h2>1. What is friction?</h2><p>Friction is a force that occurs when two surfaces come into contact and resist each other's motion. It is caused by the microscopic irregularities on the surfaces and can be affected by factors such as surface roughness and the type of materials involved.</p><h2>2. How does friction affect the movement of a block?</h2><p>Friction can act in two ways on a block: it can either help or hinder its movement. If the force applied to the block is greater than the force of friction, the block will move. However, if the force of friction is greater, the block will not move or will move at a slower rate.</p><h2>3. What factors affect the force of friction?</h2><p>The force of friction can be affected by several factors, including the type of surfaces in contact, the force pushing the surfaces together, and the presence of lubricants or other substances between the surfaces. The force of friction also increases with the weight of the object.</p><h2>4. How can we calculate the minimum force needed to move a block with friction present?</h2><p>The minimum force needed to move a block with friction present can be calculated using the formula F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force exerted by the surface on the block. The coefficient of friction is a value that depends on the type of surfaces in contact and can be determined through experiments.</p><h2>5. How can we reduce the force of friction to make it easier to move a block?</h2><p>There are several ways to reduce the force of friction, including using lubricants such as oil or grease between the surfaces, using smoother surfaces, or reducing the weight of the object. Additionally, reducing the surface area in contact can also decrease the force of friction. However, it is important to note that completely eliminating friction is not possible as it is a natural force that occurs whenever two surfaces are in contact.</p>

1. What is friction?

Friction is a force that occurs when two surfaces come into contact and resist each other's motion. It is caused by the microscopic irregularities on the surfaces and can be affected by factors such as surface roughness and the type of materials involved.

2. How does friction affect the movement of a block?

Friction can act in two ways on a block: it can either help or hinder its movement. If the force applied to the block is greater than the force of friction, the block will move. However, if the force of friction is greater, the block will not move or will move at a slower rate.

3. What factors affect the force of friction?

The force of friction can be affected by several factors, including the type of surfaces in contact, the force pushing the surfaces together, and the presence of lubricants or other substances between the surfaces. The force of friction also increases with the weight of the object.

4. How can we calculate the minimum force needed to move a block with friction present?

The minimum force needed to move a block with friction present can be calculated using the formula F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force exerted by the surface on the block. The coefficient of friction is a value that depends on the type of surfaces in contact and can be determined through experiments.

5. How can we reduce the force of friction to make it easier to move a block?

There are several ways to reduce the force of friction, including using lubricants such as oil or grease between the surfaces, using smoother surfaces, or reducing the weight of the object. Additionally, reducing the surface area in contact can also decrease the force of friction. However, it is important to note that completely eliminating friction is not possible as it is a natural force that occurs whenever two surfaces are in contact.

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