# Minimum coefficient of static friction

• emily081715
In summary, the conversation discusses finding the minimum coefficient of static friction needed for a person to walk on an icy driveway with a 19 degree incline. There is confusion about whether to use degrees or radians when plugging in the angle to the tan function on a calculator. The correct answer does not involve the acceleration due to gravity.
emily081715

## Homework Statement

If the incline of the driveway is 19 ∘ from the horizontal, what must the minimum coefficient of static friction be between your shoes and the ice?

Fs=uN

## The Attempt at a Solution

i need help figuring out my error, i assumed that the N force was equal to mgcosθ and Fs was equal to mgsinθ. the masses must cancel out and following what is written on my paper, i got and answer of 0.15. this is incorrect and i need help finding out why

emily081715 said:
i need help figuring out my error, i assumed that the N force was equal to mgcosθ and Fs was equal to mgsinθ. the masses must cancel out and following what is written on my paper, i got and answer of 0.15. this is incorrect and i need help finding out why

haruspex said:
i don't understand?

emily081715 said:
i don't understand?
Did you plug the 19 degrees into the tan function of a calculator? It can probably be set to expect angles to be specified in degrees or radians, but you have to make sure you select the right one.

haruspex said:
Did you plug the 19 degrees into the tan function of a calculator? It can probably be set to expect angles to be specified in degrees or radians, but you have to make sure you select the right one.

so my original answer was in my radians and i did 9.8 tan (19) in degrees and got 3.4 as the answer, is that to big?

emily081715 said:
so my original answer was in my radians and i did 9.8 tan (19) in degrees and got 3.4 as the answer, is that to big?
Why the 9.8? g is not part of the coefficient.

emily081715 said:
so my original answer was in my radians and i did 9.8 tan (19) in degrees and got 3.4 as the answer, is that to big?
well actually i know its incorrect

emily081715 said:
well actually i know its incorrect
so just tan (19)

emily081715 said:
so just tan (19)
Yes.

## What is the minimum coefficient of static friction?

The minimum coefficient of static friction is a measure of the minimum amount of force required to keep an object at rest on a surface. It is a dimensionless number that represents the ratio of the maximum frictional force to the normal force between the object and the surface.

## How is the minimum coefficient of static friction determined?

The minimum coefficient of static friction is determined through experimentation and measurement. It involves gradually increasing the applied force on an object until it begins to move. The minimum coefficient of static friction is then calculated by dividing the magnitude of the maximum frictional force by the normal force.

## What factors affect the minimum coefficient of static friction?

The minimum coefficient of static friction is influenced by several factors, including the nature of the surfaces in contact, the weight and geometry of the object, and the roughness of the surfaces. It is also affected by external factors such as temperature and humidity.

## Why is the minimum coefficient of static friction important?

The minimum coefficient of static friction is an important concept in physics and engineering because it helps determine the stability and safety of objects on a surface. It is also used in designing structures and machines to ensure that they can withstand the necessary forces without slipping.

## How does the minimum coefficient of static friction differ from the coefficient of kinetic friction?

The minimum coefficient of static friction is typically higher than the coefficient of kinetic friction. This is because it takes more force to overcome the static friction and initiate motion than it does to maintain motion. The coefficient of kinetic friction is also affected by factors such as the speed of the object and the presence of lubricants.

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