Friction: Body Movement on Slope

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SUMMARY

The discussion centers on the dynamics of a body on an inclined plane, specifically addressing the conditions under which it begins to move and whether it maintains constant speed or accelerates. The critical equations involve the static and kinetic friction coefficients (µs and µk) and the gravitational force components, expressed as F = ma. When the body starts to move, it accelerates according to the formula (g*cosθ - µk*g*sinθ)/m, indicating that friction plays a significant role in determining the motion of the body down the slope.

PREREQUISITES
  • Understanding of Newton's Second Law (F = ma)
  • Knowledge of static and kinetic friction coefficients (µs and µk)
  • Basic trigonometry, specifically the relationship between angles and slopes
  • Familiarity with gravitational force components on inclined planes
NEXT STEPS
  • Study the effects of varying angles on friction and acceleration in inclined planes
  • Learn about the derivation and application of the equations of motion for bodies on slopes
  • Explore the relationship between static and kinetic friction coefficients in practical scenarios
  • Investigate real-world applications of inclined plane dynamics in engineering and physics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in understanding the principles of motion on inclined surfaces.

DIrtyPio
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Hi. I have a question. A body is lying on a slope. We increase the slope until the body starts to move. So my question is, if we stop increasing the slope when the body starts to move will the body maintain constant speed going down until reaches the bottom, or will it accelerate?
 
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DIrtyPio said:
Hi. I have a question. A body is lying on a slope. We increase the slope until the body starts to move. So my question is, if we stop increasing the slope when the body starts to move will de body maintain constant speed going

Hi DIrtyPio! :smile:

Well, there's µs and µk …

so what does g*sinθ have to be …

i] when the body starts to move ?

ii] for the body to maintain constant speed ? :wink:
 
The body starts to move when MU*m*g*cos(theta) <= m*g*sin (theta). I suppose that the body will be accelerateing but I'm not sure. Oh, and by the way, can you tell me why can't I use properly the advanced editing tools, even though if I leave them homework they automatically are put there it sais I've did not tuse the correctly.
 
DIrtyPio said:
The body starts to move when MU*m*g*cos(theta) <= m*g*sin (theta). I suppose that the body will be accelerateing but I'm not sure. Oh, and by the way, can you tell me why can't I use properly the advanced editing tools, even though if I leave them homework they automatically are put there it sais I've did not tuse the correctly.

Hi DIrtyPio! :smile:

(I'm not sure what you mean by "advanced editing tools" … but I know the LaTeX isn't working at the moment.

But why didn't you copy my µ and θ? :wink:)

I don't think you're taking into account the distinction between µs and µk (static and kinetic coefficients of friction ).
 
I ran into this question on an exam and if I remember correctly it did not said that I shold care about static and kinetic friction coefficients. So I don't know the answer to this question and I think I don't either know how to solve it, so if you could tell me how to solve this problem that would be great. I know that the static friction coefficient is greater than the kinetic one but if I know only the static one can I calculate the kinetic one? But as you see my main problem is theoretic, so I don't need to calculate anything, I just want to know how the gravitational force acts upon that body, so will it accelerate or the speed will be constant. Because as I said I think that by Newtons II law the force determines the acceleration of a body I think that it will accelerate exponentially. Is this right?
 
DIrtyPio said:
I ran into this question on an exam and if I remember correctly it did not said that I shold care about static and kinetic friction coefficients.

mmm … just because it didn't say that you should, that doesn't mean that you shouldn't have …

the difference does matter: use F = ma to work out what happens :wink:
 
So it accelerates with g*cosθ until it reaches the end of the slope.
 
DIrtyPio said:
So it accelerates with g*cosθ until it reaches the end of the slope.

No!

It would only do that if there were no friction.
 
Yes... I've forgot about it, it accelerates with (G*cosθ-µk*G*sinθ)/m
 
  • #10
DIrtyPio said:
Yes... I've forgot about it, it accelerates with (G*cosθ-µk*G*sinθ)/m

But what is θ?

Remember, θ isn't given, you have to find it.
 
  • #11
θ is 90 degrees minus the slope.
 
  • #12
DIrtyPio said:
θ is 90 degrees minus the slope.

Yes, but what is the slope?

You have to find it.
 
  • #13
It is arctg θ
 

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