A Guide to the Best Beaches in California

[Differentiate it]

Homework Statement

The book is stating that the force of static friction is greater than the force acting against it. I'm pretty sure the book the wrong. You can view the pictures for reference. Help would be appreciated!

Relevant Equations

W = ∆KE

 

[Orodruin]

Homework Statement:: The book is stating that the force of static friction is greater than the force acting against it. I'm pretty sure the book the wrong. You can view the pictures for reference. Help would be appreciated!
Relevant Equations:: W = ∆KE

View attachment 317589

Why would you think that the static friction cannot be larger than the component of gravity in the direction along the belt? Those do not form a third-law pair.

 

[Differentiate it]

Why would you think that the static friction cannot be larger than the component of gravity in the direction along the belt? Those do not form a third-law pair.

Because static friction is equal to the force it is acting against (well, until the force becomes large enough).

 

[Orodruin]

Because static friction is equal to the force it is acting against (well, until the force becomes large enough).

It seems to me you are misunderstanding Newton's third law.

 

[Differentiate it]

It seems to me you are misunderstanding Newton's third law.

Could you explain where I am going wrong?

 

[erobz]

Because static friction is equal to the force it is acting against (well, until the force becomes large enough).

If you were on a conveyor belt that moves at a constant velocity ( like conveyor belts typically move objects) then, if the object is not slipping the static friction must be equal/opposite the component of weight. However, if the conveyor belt is accelerating ( maybe on a startup ) and the object is being carried up without slipping, the static friction must be greater than the component of weight in the direction of motion.

 

[Differentiate it]

If you were on a conveyor belt that moves at a constant velocity ( like conveyor belts typically move objects) then, if the object is not slipping the static friction must be equal/opposite the component of weight. However, if the conveyor belt is accelerating ( maybe on a startup ) and the object is being carried up without slipping, the static friction must be greater than the component of weight in the direction of motion.

Ah, yes I get it. Thank you

 

[erobz]

Ah, yes I get it. Thank you

Is it possible that the confusion comes from seeing static friction quoted as a maximum $f_s = \mu_s N$ where $\mu_s < 1$?

If it is, I would say that confusion is justified. I don't have an explanation for what that applies too (but I too would like to hear it), other than to just know that if the conditions of acceleration up the ramp are met without slipping, it MUST be the case that the static force is greater than the component of weight in the direction of motion.

EDIT: I went back in the intro physics text book. I don't actually see it quoted as that. There is a table of material - material coefficients of static and kinetic friction. All but one of material pairs listed $\mu_s < 1$, But I see that "Rubber- Other Material" can range from $1\leq \mu_s \leq 4$.

I think I was just selectively remembering that most pairs of common materials $\mu_s < 1$.

This application would be "Rubber on Rubber" - which is probably (apparently expected to be) more than 1.

 

[jbriggs444]

The confusion that I see in this thread is a common one. And apparently cleared up now.

The mistaken intuition is that forces are "transitive". For instance, if you push on a rod with a force of 100 N then intuition says that the rod must push on the next thing with an equal force of 100 N.

Similarly, if gravity is pulling backward on a fellow with a force of <whatever> then intuition says that the force of static friction on the fellow's shoes must be resisting exactly that amount of force.

Of course, this intuition is wrong, wrong, wrong. Newton's second law is the tool that tells you how hard the rod or the fellow's shoes will be pushing on the next thing.

 

[Differentiate it]

The confusion that I see in this thread is a common one. And apparently cleared up now.

The mistaken intuition is that forces are "transitive". For instance, if you push on a rod with a force of 100 N then intuition says that the rod must push on the next thing with an equal force of 100 N.

Similarly, if gravity is pulling backward on a fellow with a force of <whatever> then intuition says that the force of static friction on the fellow's shoes must be resisting exactly that amount of force.

Of course, this intuition is wrong, wrong, wrong. Newton's second law is the tool that tells you how hard the rod or the fellow's shoes will be pushing on the next thing.

Yes, I get it. Thanks to you and @erobz for the explanation