Understanding the Relationship Between Mass and Inertia in Circular Motion

[loka]

Homework Statement

The Mass of an object doesn't affect the angle at which a curve must be banked. The law of inertia, however, states that the motion of any object is affected by its inertia, w/c depends on its mass. How can objects rounding banked curves obey the law of inertia if the amount of banking required for a curve of a given radius of curvature and speed is independent of mass?

Homework Equations

The Attempt at a Solution

Totally clueless! >.<

I just know it has something to do with N1:

Newton's first law of motion states that "An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force."

...and F_c=mv²/R

 

[Dick]

Ok, so mv^2/r is the centripetal acceleration that needs to be balanced by a frictional force. How does the equation for that frictional force depend on m?

 

[loka]

hmmm ok...so

F_c = mv²/R

F_f = mu*F_n
= mu*mg

F_c = F_f
mv²/R = mu*mg

so the masses cancel out?

...the thing is I don't even get what the question is asking?

 

[Dick]

Yes, the mass cancels out. Isn't that what the question is asking? There should be an angle in your friction but that's not even terribly important. The acceleration is proportional to mass and so is the friction.

 

[loka]

but am i not just proving what was already stated in the question? Which is that radius and speed don't rely on mass?

I'm just terribly confused of the question...shouldn't I incorporate N1 in my conclusion but I just don't seem to get it...

 

[Dick]

I think you should read the question again. It looks to me like it's asking why is the banking angle independent of mass if the inertia is dependent on mass. If the mass cancels, isn't that the answer? Am I reading it wrong? How are you reading it?

 

[loka]

Oooo that makes more sense...thanks for rephrasing it!

maybe I was just complicating the question...

Thanks again for your help. ^^,