# How to find the minium coefficient of static friction?

• ARJewell
In summary, to determine the minimum coefficient of static friction needed to prevent any movement in a system with a frictionless pulley, the formula F=ma is used, where a must be equal to zero. The acceleration in this case would be 2.8m/s^2 and the tension in the connecting string is 84 N. Further calculations are needed to determine the minimum coefficient of static friction.
ARJewell

## Homework Statement

For a system (with frictionless pulley) Mewsubk = .25 and the system is initially at rest. The mass of block 1 is 16 kg and the mass of block 2 is 12 kg. Determine the minimum coefficient of static friction needed to prevent any movement.

F=ma

## The Attempt at a Solution

I have no idea how to figure it out.
I figured out the acceleration to be 2.8m/s^2 because:
a= 12kg*9.8m/s^2 - .25*16kg*9.8m/s^2/(16kg+12kg)
I figured out the tension in the connecting string to be 84 N because:
T=mewsubk*m1g+m1a

Any help on how to figure out minimum coefficient of static friction?

Welcome to PF!

Hi ARJewell ! Welcome to PF!

(have a mu: µ and try using the X2 tag just above the Reply box )
ARJewell said:
… Determine the minimum coefficient of static friction needed to prevent any movement.

F=ma

No, if movement is prevented (or even, in a different question, where the block is just moving), a must be zero!

Try again.

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

The coefficient of static friction is a dimensionless quantity that represents the force required to overcome the static friction between two surfaces in contact. It is denoted as μs and is dependent on the nature of the surfaces in contact.

## 2. How is the coefficient of static friction different from coefficient of kinetic friction?

Coefficient of static friction is the ratio of the maximum static frictional force to the normal force between two surfaces, while coefficient of kinetic friction is the ratio of the kinetic frictional force to the normal force between two surfaces in motion.

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

The coefficient of static friction is affected by the nature of the surfaces in contact, the roughness of the surfaces, and the amount of force pressing the surfaces together.

## 4. How can the coefficient of static friction be measured?

The coefficient of static friction can be measured by conducting a simple experiment where a block is placed on a surface and gradually inclined until it starts to slide. The angle at which the block starts to slide is known as the angle of repose, and the coefficient of static friction can be calculated using the formula μs = tanθ.

## 5. How can the minimum coefficient of static friction be determined?

The minimum coefficient of static friction can be determined by conducting the same experiment as mentioned earlier, but with different weights on the block. The minimum coefficient of static friction is the value at which the block just starts to slide, and it is denoted as μs(min).

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