# Friction coefficient and slope

#### Johulus

I have problem with determining the friction coefficient. On the slope the weight of an object is divided into components: the force parallel to the slope and the force perpendicular to the slope. Force of friction is equal to the friction coefficient times the perpendicular force and force that makes the object go down the slope is equal to weight of the object times sine of inclination angle. If the velocity of the object is constant then the sum of forces that interact with the object must be 0. Then force of friction must be equal by value to the force that makes the object go down the slope. From that equation I get that the friction coefficient is equal to sine of the inclination angle divided by cosine of the inclination angle.
Task says I should calculate the friction coefficient if the inclination is: a) 30° b) 45° c) 60° . I encounter a problem when I want to determine the friction coefficient for slopes that have 45°or 60°. When I insert the values in equation , I get a value that is equal to 1, which is very odd, or I get a value greater than 1. And as I know, the friction coefficient should be less than 1. One another thing that is odd about this is that I got higher values for the friction coefficient when the slope was steeper, but I would expect the values of the friction coefficient to be smaller proportionally to the increase in inclination. What should I do here, could anybody help?

#### ChipB

PHF Helper
... I get that the friction coefficient is equal to sine of the inclination angle divided by cosine of the inclination angle.
Yes, this is correct if the object slides at constant rate (i.e. zero acceleration).

Task says I should calculate the friction coefficient if the inclination is: a) 30° b) 45° c) 60° . I encounter a problem when I want to determine the friction coefficient for slopes that have 45°or 60°. When I insert the values in equation , I get a value that is equal to 1, which is very odd, or I get a value greater than 1. And as I know, the friction coefficient should be less than 1.
There is no rule that says the friction coefficient must be less than 1.

One another thing that is odd about this is that I got higher values for the friction coefficient when the slope was steeper, but I would expect the values of the friction coefficient to be smaller proportionally to the increase in inclination.
If the slope is very small, the coefficient must be small - otherwise the friction force would be too large and the object would decelerate. And if the slope is large, the coefficient must be large in order to keep the object from accelerating.