Coefficient of Kinetic Friction for incline

In summary, the coefficient of kinetic friction for objects moving at a constant speed on an incline in two dimensions is equal to tan(x), where x is the incline angle. This equation should hold true for simple scenarios without acceleration, but may not work for more complex situations.
  • #1
Feldoh
1,342
3
This really isn't a homework question -- but it does involve my homework. Say you've got a box sliding down an incline of x degrees at a constant speed, I somehow got that that coefficient of kinetic friction is equal to tan(x). Will this always hold true for objects moving at a constant speed on an incline in two dimensions?

Basically I solved for the normal force:
[tex]F_{Net}=0[/tex]
[tex]F_N-F_g_y=0[/tex]
[tex]F_N=mgcos(x)[/tex]

Then for the coefficient of friction:
[tex]F_{Net} = 0[/tex]
[tex]F_f-F_g_x = 0[/tex]
[tex]F_f = F_g_x[/tex]
[tex]\mu_kF_n = F_g_x[/tex]
[tex]\mu_k = (F_g_x)/(F_N)[/tex]
[tex]\mu_k = mgsin(x)/mgcos(x)[/tex]
[tex]\mu_k = tan(x)[/tex]

Where [tex]F_{g_x}[/tex] is the horizontal component of the force of the gravitational field, and [tex]F_{g_y}[/tex] is the vertical component.

I was just wondering, it's sort of situational but it is a shortcut none-the-less if it does actually work.
 
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  • #2
Yes, this equation should hold true for situations like you have described above. Of course if you have more complicated scenarios, such as one with acceleration, this won't hold.
 
  • #3
G01 said:
Yes, this equation should hold true for situations like you have described above. Of course if you have more complicated scenarios, such as one with acceleration, this won't hold.

Awesome, thanks for the fast reply. :smile:
 
  • #4
No problem.
 

What is the coefficient of kinetic friction for an incline?

The coefficient of kinetic friction for an incline is a measure of the amount of friction between two surfaces when one is sliding or moving along the other. It is denoted by the symbol μk and is a dimensionless quantity.

How is the coefficient of kinetic friction for an incline calculated?

The coefficient of kinetic friction for an incline is calculated by dividing the force of friction acting on an object on the incline by the normal force between the object and the incline. This can be expressed as μk = Ff/FN.

What factors affect the coefficient of kinetic friction for an incline?

The coefficient of kinetic friction for an incline is affected by the nature of the surfaces in contact, the roughness of the surfaces, and the applied force. It also depends on the angle of the incline and the weight of the object sliding on the incline.

How does the coefficient of kinetic friction for an incline affect the motion of an object?

The coefficient of kinetic friction for an incline determines the amount of resistance an object experiences while sliding down the incline. A higher coefficient of friction will result in a slower and more controlled motion, while a lower coefficient of friction will result in a faster and less controlled motion.

Can the coefficient of kinetic friction for an incline be greater than 1?

Yes, the coefficient of kinetic friction for an incline can be greater than 1. This indicates that the force of friction is greater than the normal force, resulting in a motion that is completely stopped or reversed. This is known as static friction, and it must be overcome in order for the object to begin moving.

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