Max static force graph.

[SaintJude]

As I understand the maximum static friction value (at the threshold of motion) increases as the angle of elevation of an inclined plane increases. The only mathematical relationship we can easily determine regarding static force is that of the "maximum static force", (the peak) correct?

(Chiddler, where does your statement about "as angle decreases, maximum possible static friction decreases" fit in, for goodness sake? I'm So confused)

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[chiddler]

sorry D:

i drew

ps boxes are the same mass.

so the question to ask yourself is, if the box is just there with no outside forces on it besides gravity, how much friction force is it experiencing?

 

[milski]

This is a sample graph for an incline with increasing θ. When the gravity component parallel to the ramp (the graph starting from 0) is less than the maximum static friction, then the static friction is equal to it.

As you increase the angle (move right on the graph) the gravity component increases and the maximum static friction decreases. When they're equal, you still have the object at rest.

Once the gravity force component increases more than the maximum static friction force, the net force cannot be zero anymore and the object starts sliding down.

 

[milski]

As I understand the maximum static friction value (at the threshold of motion) increases as the angle of elevation of an inclined plane increases. The only mathematical relationship we can easily determine regarding static force is that of the "maximum static force", (the peak) correct?

(Chiddler, where does your statement about "as angle decreases, maximum possible static friction decreases" fit in, for goodness sake? I'm So confused)

If the object is not moving, you can determine that the net force on it is 0 and from there determine the static friction force. Obviously, it cannot exceed the maximum friction force - if that's the case, either something's wrong with your setup or the object is sliding down.

 

[SaintJude]

♫ I can see clearly now the rain is gone ♫ 😀 Before, I did not understand the distinction between the "force of static friction" and the maximum static force.

I totally understand now, thanks to both of you. The maximum static force decreases as level of inclination increases, due the decrease in the normal force.

The force of static friction increases as level of inclination increases because the static friction force matches the applied force (in the case of an incline plane the applied force = mgsingtheta) And as sin theta increases, the applied force increases and so the "reactionary" force of static friction increases.

And then once the applied force exceeds the maximum static force, the object begins to slide.

 

[milski]

The rain is gone! 👍