Static Friction & Incline

[MedPR]

As you increase the angle of incline, the static friction force increases. I kind of understand this, but not completely.

I get that friction is the force opposing motion. So the force of motion down an incline is mgsintheta. As theta increases, mgsintheta increases so the opposing force, friction, must increase to prevent the object from sliding.

The equation for friction on an incline plane, however, is μmgcostheta. As theta increases, costheta decreases (cos90=0). What's up with that?

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[milski]

As you increase the angle of incline, the static friction force increases. I kind of understand this, but not completely.

I get that friction is the force opposing motion. So the force of motion down an incline is mgsintheta. As theta increases, mgsintheta increases so the opposing force, friction, must increase to prevent the object from sliding.

The equation for friction on an incline plane, however, is μmgcostheta. As theta increases, costheta decreases (cos90=0). What's up with that?

μ mgcosθ is the actually μ N, where N is the normal. As you increase the angle, the normal decreases. With a vertical ramp there is no normal pushing the object against it and no static friction.

Also, μ mg cosθ is the maximum for the friction force - it can be lower than that if the force acting in the other direction is smaller.

That actually explains why increasing θ at some point allows the object to slide down. The push down force, mg sinθ increases, the maximum friction μ mg cosθ decreases until the moment where mg sinθ becomes larger and the object starts sliding.

 

[chiddler]

i asked this question before i started using SDN on yahoo answers. Preface: you've seen how often i've been corrected. So...yeah. sorry in advance lol.

i thought the answers were helpful. Specifically, making the distinction of maximum static force vs actual applied static force.

First, lets look at maximum static force. Maximum static force is the highest at theta = 0 making the cos term = 1. What is actual static force on the object at theta = 0? Nothing. There's nothing pushing it across the surface.

45 degrees. Max static force is reduced to 70%. Assuming Ffriction > mgsin(theta), ie friction is stronger than gravity. Maximums static force is reduced. But lets compare it to the previous scenario. Here, the actual friction force on the block is a non zero value because gravity is pushing it against friction. Previously, nothing is pushing it against friction so friction force is 0.

And you can imagine that at 89 degrees, maximum static friction is almost 0.

So given all this, I think you can easily make predictions about maximum static force because it is simply the cos graph. But how much static friction actually is in place is more situation dependent.

 

[SaintJude]

Chiddler, are you disagreeing with milski? Milski said that as you increase angle of incline, the static friction force increases.

But you're saying as you increase angle of increase, maximum static friction decreases??

 

[milski]

Chiddler, are you disagreeing with milski? Milski said that as you increase angle of incline, the static friction force increases.

But you're saying as you increase angle of increase, maximum static friction decreases??

Both are correct. Maximum static friction decreases, the actual static friction increases. When they meet, the object starts sliding.

 

[chiddler]

Chiddler, are you disagreeing with milski? Milski said that as you increase angle of incline, the static friction force increases.

But you're saying as you increase angle of increase, maximum static friction decreases??

if i understood, he's saying the same thing that i am.

i'm saying as angle decreases, maximum possible static friction decreases. As angle increases, you start to add actual force as gravity starts to pull the box against friction. So static friction force increases.

So increasing angle decreases maximum static force. Increasing angle increases static friction force from gravity, then decreases.