Force of static friction

[LuminousTruth]

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If there is a block on the incline, and the incline is raised, how does that affect the force of static friction?

TBR says the force of static friction increase as angle is the angle is increased.

That makes sense conceptually, but I thought from the formula: Fs=us*N => Force of static friction would be umgcos(x): This would show that as the angle x is increased (from 0 to 45), the force of static friction seem to decrease (since umgcos(0) is maximum).

Am I interpreting the equation incorrectly?

 

[stevvo111]

If there is a block on the incline, and the incline is raised, how does that affect the force of static friction?

TBR says the force of static friction increase as angle is the angle is increased.

That makes sense conceptually, but I thought from the formula: Fs=us*N => Force of static friction would be umgcos(x): This would show that as the angle x is increased (from 0 to 45), the force of static friction seem to decrease (since umgcos(0) is maximum).

Am I interpreting the equation incorrectly?

That formula is for the "max static force", the reason static friction increases with angle is because with angle there is something acting on the block so the static friction is actually opposing something.

Flat table with a block has a max static friction of= us*N, but since no external force is acting on it, the actual static friction force=0. When inclined, gravity starts to act on the block to push it down the incline, now static friction force opposes this force and so actual static friction force>0. Once you hit threshold angle, block starts moving and fs once again becomes=0 and now you have a lesser fk acting on it.


Hope that's correct and helpful.

 

[noobtech]

Thanks stevvo111; your explanation was perfect.
It would be unfair to ask, "what happens to the frictional force when the incline is raised?"
Because the answer depends on whether the crate was moving.

if it were already moving, then the normal component decreased hence F(fric) decrease.

An clearly question to answer would be "what happens to the max static friction force as the incline is raised?" ...in this case, it would decrease.

For what the OP was stating, the statement will only hold for a non-moving crate.

Am I right?

 

[Meredith92]

That formula is for the "max static force", the reason static friction increases with angle is because with angle there is something acting on the block so the static friction is actually opposing something.

Flat table with a block has a max static friction of= us*N, but since no external force is acting on it, the actual static friction force=0. When inclined, gravity starts to act on the block to push it down the incline, now static friction force opposes this force and so actual static friction force>0. Once you hit threshold angle, block starts moving and fs once again becomes=0 and now you have a lesser fk acting on it.


Hope that's correct and helpful.

Hey guys,
sorry to revive this thread, but i'm still pretty confused...
so TBR says that when you increase angle you have a greater force of static friction, but do we have any equation for that?

Fstatic max=us mgcostheta as theta increases the value for f static MAX decreases.

but somehow the force of static friction increase as angle is increased? how does this make sense??

Also, related to this question, I'm confused about a passage that involved putting blocks at different angles until they fall... TBR asked the question attached, and i dont understand why the answer is D not C. Doesnt the Fstatic drop at a certain point and Fkinetic take over, making it fall? I must be misunderstanding something conceptually here🙁

 

[Meredith92]

Okay I've thought about it (and reread Giancoli's chapter) - let me know if this explanation makes sense:

Giancoli says "Static friction will oppose any applied force up to a maximum of Ustatic x Fnormal"
So it is true that the max static friction will decrease as angle increases (and mgcostheta decreases)... but what is really important is that the force due to gravity parallel to the surface (and directly opposing static friction) is mgsintheta increases!! This means that at a certain angle the force opposing friction will be greater than the maximum friction at that angle and then the frictional force turns from static to kinetic and the object stats moving.

So basically Fstatic increases to oppose whatever force until it reaches its max.

This all makes sense now but i still dont understand the graphs I posted. Why is D right over C? Shouldnt Fstatic reach a max when the box begins to fall?

Is it that F static never really decreases? instead it TURNS INTO F kinetic? therefore C isnt accurate? it would only be accurate if the y axis was Ffriction instead of specifically Fstatic

 

[Postictal Raiden]

Okay I've thought about it (and reread Giancoli's chapter) - let me know if this explanation makes sense:

Giancoli says "Static friction will oppose any applied force up to a maximum of Ustatic x Fnormal"
So it is true that the max static friction will decrease as angle increases (and mgcostheta decreases)... but what is really important is that the force due to gravity parallel to the surface (and directly opposing static friction) is mgsintheta increases!! This means that at a certain angle the force opposing friction will be greater than the maximum friction at that angle and then the frictional force turns from static to kinetic and the object stats moving.

So basically Fstatic increases to oppose whatever force until it reaches its max.

This all makes sense now but i still dont understand the graphs I posted. Why is D right over C? Shouldnt Fstatic reach a max when the box begins to fall?

Is it that F static never really decreases? instead it TURNS INTO F kinetic? therefore C isnt accurate? it would only be accurate if the y axis was Ffriction instead of specifically Fstatic

I'm as confused about this as you are, so take my words with a grain of salt.

Static frictional force is the force that opposes other forces that cause an object to slide on a surface. In this case, it opposes the gravitational force (mgsintheta) to prevent the box from sliding on the inclined surface. Once the gravitational force overcomes the maximum of the static frictional force, the box starts to slide, and the only force that is now resisting the gravitational force is the kinetic frictional force.

Like kinetic frictional force, static frictional force is a function of the normal force. However, both frictional forces differ in the friction coefficient. Also, as you mentioned, as theta increases, cos(theta) decreases. Here is what I think: As the angle of incline increases, the gravitational force acting on the box increases, so the static frictional force must also increase to resist this force. Therefore, the static friction coefficient must increase to offset the increase in gravitational force and the decrease in cos(theta).

In regards to the graph, there is no reason to suspect that C is the correct one because the static friction only increases until it hits its maximum and then it ceases to exist. Kinetic frictional force will takes its place in resisting the gravitational force acting on the sliding box.

 

[Meredith92]

I'm as confused about this as you are, so take my words with a grain of salt.

Static frictional force is the force that opposes other forces that cause an object to slide on a surface. In this case, it opposes the gravitational force (mgsintheta) to prevent the box from sliding on the inclined surface. Once the gravitational force overcomes the maximum of the static frictional force, the box starts to slide, and the only force that is now resisting the gravitational force is the kinetic frictional force.

Like kinetic frictional force, static frictional force is a function of the normal force. However, both frictional forces differ in the friction coefficient. Also, as you mentioned, as theta increases, cos(theta) decreases. Here is what I think: As the angle of incline increases, the gravitational force acting on the box increases, so the static frictional force must also increase to resist this force. Therefore, the static friction coefficient must increase to offset the increase in gravitational force and the decrease in cos(theta).

In regards to the graph, there is no reason to suspect that C is the correct one because the static friction only increases until it hits its maximum and then it ceases to exist. Kinetic frictional force will takes its place in resisting the gravitational force acting on the sliding box.

Thanks for helping me out! What you said about the graphs definitely makes sense.
I think I've figured out my other confusion now. I think youre on the right track but im 99% positive that the coefficient itself doesnt change.

As you said, mgsintheta (the component of gravity) is increasing as the incline angle increases... the frictional force increases as well because it needs to oppose it to keep it motionless. While mgsintheta is increasing, mgcostheta is decreasing..... so we reach a point where the maximum possible static friction force is LESS than the gravitational force- which is when it starts to move.

All we care about is what the max static frictional force is (which we can calculate) and static frictional force will continue to increase to oppose the gravitational force acting on it UNTIL it reaches the max static frictional force at a certain angle. I'm glad I did this problem because i never really thought of friction like this before, and this clarified A LOT for me! (hope it did for you as well and did not confuse you!)

 

[Postictal Raiden]

Thanks for helping me out! What you said about the graphs definitely makes sense.
I think I've figured out my other confusion now. I think youre on the right track but im 99% positive that the coefficient itself doesnt change.

As you said, mgsintheta (the component of gravity) is increasing as the incline angle increases... the frictional force increases as well because it needs to oppose it to keep it motionless. While mgsintheta is increasing, mgcostheta is decreasing..... so we reach a point where the maximum possible static friction force is LESS than the gravitational force- which is when it starts to move.

All we care about is what the max static frictional force is (which we can calculate) and static frictional force will continue to increase to oppose the gravitational force acting on it UNTIL it reaches the max static frictional force at a certain angle. I'm glad I did this problem because i never really thought of friction like this before, and this clarified A LOT for me! (hope it did for you as well and did not confuse you!)

You are right. I did some googling after making the post and realized that the coefficient doesn't change. Thank you for clarifying it.

 

[mehc012]

You are right. I did some googling after making the post and realized that the coefficient doesn't change. Thank you for clarifying it.

You guys are spot on now...it's important to remember here that Fs ≤ μkFn
The coefficient doesn't have to change because the equation only describes the upper limit of Fs, not the absolute value.