# Friction problem - Relation between coefficient of friction

• Saitama
In summary, the man's ability to slide the box is determined by the inequality μ'm'g<F<μmg. Based on this, it is evident that in the case where μ<μ' and m<m', the box will never slide regardless of the specific values for μ, μ', m, and m'. Therefore, the correct answer is B.

## Homework Statement

A man of mass m is applying a horizontal force to slide a box of mass m' on a rough horizontal surface. It is known that the man does not slide. The coefficient of friction between the shoes of the man and the floor is ##\mu## and between the box and the floor is ##\mu'##. In which of the following cases it is certainly not possible to slide the box?
A) μ>μ', m<m'
B) μ<μ', m<m'
C) μ<μ', m>m'
D) μ>μ', m>m'

## The Attempt at a Solution

If man applies a force F on box, due to Newton's third law, he also experiences a force F in the opposite direction. According to the question, F<=μmg and F<=μ'm'g. Also, since it is given that man does not slide, F has to be less than or equal to μmg. The box can slide if μ'm'g<F<μmg. The block never slides if μmg<μ'm'g. But I don't see how to find relation between the coefficient of friction and masses by considering the above inequalities.

Any help is appreciated. Thanks!

Pranav-Arora said:
The box can slide if μ'm'g<F<μmg. The block never slides if μmg<μ'm'g.
OK.

But I don't see how to find relation between the coefficient of friction and masses by considering the above inequalities.
Go through the set of choices and see which ones make that second inequality true.

Doc Al said:
Go through the set of choices and see which ones make that second inequality true.

Call f as the friction force on man and f' on box. For the first case,
Let μ=0.6, μ'=0.5, m=3 kg and m'=5kg. Then f=18N and f'=25N. Here f<f' so A is the answer but the given answer is B.

Pranav-Arora said:
Call f as the friction force on man and f' on box. For the first case,
Let μ=0.6, μ'=0.5, m=3 kg and m'=5kg. Then f=18N and f'=25N. Here f<f' so A is the answer but the given answer is B.
Don't plug in specific numbers. You want an answer that will make it impossible to slide for any number in the given range.

What's an easy way to ensure that μmg<μ'm'g? One of the given choices ensures that will inequality will be met.

Doc Al said:
What's an easy way to ensure that μmg<μ'm'g? One of the given choices ensures that will inequality will be met.

I am still confused. The inequality can be rearranged as m'>(μ/μ')m. For the first case, μ/μ'>1 so I guess (μ/μ')m may become greater than m' so first is false. Is this a correct way to put it?

Pranav-Arora said:
The inequality can be rearranged as m'>(μ/μ')m. For the first case, μ/μ'>1 so I guess (μ/μ')m may become greater than m' so first is false. Is this a correct way to put it?
Yes. That shows that choice A won't work.

Now look at choice B.

Doc Al said:
Now look at choice B.

In this case μ<μ' and m<m'. Rearranging as before, m'>(μ/μ')m. Already, m < m' and since (μ/μ')<1, the product on the RHS becomes more smaller and hence it is always true. Correct?

Pranav-Arora said:
In this case μ<μ' and m<m'. Rearranging as before, m'>(μ/μ')m. Already, m < m' and since (μ/μ')<1, the product on the RHS becomes more smaller and hence it is always true. Correct?
Yes.

1 person
Doc Al said:
Yes.

Thanks a lot Doc Al!

## What is the coefficient of friction?

The coefficient of friction is a dimensionless quantity that measures the amount of resistance between two surfaces in contact. It is represented by the symbol μ and is a ratio of the force required to move an object over a surface to the force pressing the two surfaces together.

## How is the coefficient of friction determined?

The coefficient of friction can be determined experimentally by measuring the force required to move an object over a surface at different angles and dividing it by the normal force. It can also be calculated using the materials' properties, such as surface roughness and weight.

## What factors affect the coefficient of friction?

The coefficient of friction is affected by various factors, including the nature of the surfaces in contact, the roughness of the surfaces, the weight of the object, and the presence of any lubricants or contaminants.

## What is the relationship between the coefficient of friction and the force of friction?

The coefficient of friction and the force of friction are directly proportional to each other. This means that as the coefficient of friction increases, the force of friction also increases. This relationship can be expressed by the equation F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force.

## How does the coefficient of friction affect the motion of an object?

The coefficient of friction determines the amount of resistance that an object experiences when in contact with a surface. A higher coefficient of friction will result in a greater force of friction, which can slow down or prevent an object from moving. On the other hand, a lower coefficient of friction can allow an object to move more easily over a surface.