# Minimal coefficient of friction

• Karol
In summary, the minimal coefficient of friction required for the rectangle to be held by the horizontal rope and the friction on the wall is 0.3. This is calculated by finding the distance from the wall to the center of mass and using the equation for friction force, f=μN.

## Homework Statement

The rectangle in the drawing is held by the horizontal rope and the friction on the wall.
What's the minimal coefficient of friction

## Homework Equations

Friction force: f=μN

## The Attempt at a Solution

Moments round the point of contact with the wall. the side of the rectangle is a, half the diagonal to the center is ##\sqrt {a}##. the distance of the CoM to the wall: ##\sqrt {a}\cdot\sin 55^0=1.16a##
$$1.16a\cdot mg=T\cdot \sin 10^0\rightarrow T=6.68mg$$
$$6.68mg\cdot\mu=mg\rightarrow\mu=0.15$$
It should be 0.3

#### Attachments

• Snap1.jpg
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So from the wall to the center of mass is 1.16 times the length of a side ? That's in mid-air ! ;)

Is it a square or rectangle? If it's a square check your calculation for "half the diagonal".

BvU said:
So from the wall to the center of mass is 1.16 times the length of a side ? That's in mid-air !
I thank you very much BvU for i didn't laugh so much for some time

I believe what you used for the normal force is incorrect.

The distance of CoM from the wall: ##\frac{a}{\sqrt{2}}\cdot\sin 55^0=0.58a##
$$0.58a\cdot mg=T\cdot \sin 10^0\rightarrow T=3.41mg$$
$$3.41mg\cdot\mu=mg\rightarrow\mu=0.3$$

## 1. What is the definition of minimal coefficient of friction?

The minimal coefficient of friction, also known as the coefficient of static friction, is a measure of the amount of force required to move an object over a surface, without it slipping.

## 2. How is the minimal coefficient of friction determined?

The minimal coefficient of friction is determined by conducting experiments where an object is placed on a surface and gradually increased force is applied until the object begins to move. The coefficient is then calculated by dividing the applied force by the weight of the object.

## 3. What factors affect the minimal coefficient of friction?

The minimal coefficient of friction is affected by several factors, including the type of surface the object is moving on, the smoothness of the surface, and the weight and shape of the object itself. Additionally, the presence of lubricants or contaminants on the surface can also impact the coefficient of friction.

## 4. How is the minimal coefficient of friction important in everyday life?

The minimal coefficient of friction plays a crucial role in many everyday activities, such as walking, driving, and even sitting in a chair. It helps us move and maintain balance on different surfaces, and also allows machines and vehicles to operate smoothly and efficiently.

## 5. Can the minimal coefficient of friction be reduced to zero?

No, the minimal coefficient of friction cannot be reduced to zero. Even with the use of lubricants and other techniques, there will always be some amount of friction present between two surfaces. However, it can be minimized to a very low level, which allows for smoother movement and less wear and tear on surfaces.

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