physics question

for physics homework i have a problem that i am not sure which way to calculate static friction (with Fny or Fn) I know that you guys will know...all help is much appreciated.

A 3.60degree banked circular highway curve is designed for traffic moving at 16.7m/s. The radius of the curve is 200m. What is the minimum coefficient of friction between the tries and the road that will allow the cars to take the turn without sliding off the road?

Thanks again...
-Todd

Originally posted by TDR1
for physics homework i have a problem that i am not sure which way to calculate static friction (with Fny or Fn) I know that you guys will know...all help is much appreciated.

A 3.60degree banked circular highway curve is designed for traffic moving at 16.7m/s. The radius of the curve is 200m. What is the minimum coefficient of friction between the tries and ...[text shortened]... hat will allow the cars to take the turn without sliding off the road?

Thanks again...
-Todd

Just so you know, nobody likes answering someone's homework problem from scratch. Try the problem, give us your solution, and RHP in general will be happy to help you through it. If you get stuck somewhere, ask about the part you don't understand. At the very least, be sneaky about it (i.e. don't tell us it's a homework problem). That being said, here are some hints.

1) Assess the situation.

What are we dealing with? We have a car driving in a circle (centripetal acceleration) on a banked highway (gravity and slopes). What are we looking for? We want to find the coefficient of friction (friction) that will keep the cars on the road as they drive around the curve. This means that some forces will have to balance (sum of forces). Which ones? If you're having trouble here, think about what would happen if you changed the magnitude of the forces. Would the car move inward or outward?

2) Gather your equations.

We know that we're dealing with: (a) centripetal acceleration; (b) gravity and slopes; (c) friction; and (d) sum of forces. What equations do you know that relate to these areas? If you know right off the bat which ones apply, write them down. If you don't, look them up and then write them down. All of them. You never know which ones might become handy.

3) Identify your constants and your variables.

What have we been given in the problem? We know the highway is sloped inward at 3.6 degrees (theta = 3.6 degrees), the traffic will be moving at 16.7 m/s (v = 16.7 m/s), the radius of the curve is a constant 200 m (r = 200 m), and we're looking for the coefficient of friction that will keep the cars on the road (mu = ?). Compare these constants and variables to the list of equations you wrote out in step (2). Do any of them leap out at you? If they don't, try working backwards. What do we need to know to get the coefficient of friction? What do we need to know to gather the information to get the coefficient of friction? And so on back up the chain. You know you've got the whole thing when the answer to these questions becomes a constant you've already been given.

4. Crunch the numbers.

This step is straightforward, but keep your eye out for mistakes - both typographical and systematic. Always ask yourself after each sub0calculation "does this answer make sense?". If it doesn't seem physically possible, double-check your calculations.

5. Rephrase the question when writing the answer.

This step help to make sure you actually answered the question. If you can't rephrase the question to answer it, chances are you haven't answered the question yet.

So with that in mind, good luck answering the question. When you've made some headway, come back and tell us what you've got. We'll help you more specifically then.

ok here's what ill have....
M=mass
Fn=normal force
Fc= centripetal force
Fg= gravitational force
Fs= force of static friction

from a free body diagram we get that
0=Fnety=Fn(y)+Fg
Fnetx=Fc= Fn(X)+Fs
in the case of banked curves i believe the Fn(x) can be represented by Fg*tan(theta), where theta is the angle of the bank relative to the horizontal
so Fnetx=Fc=Fg*tan(theta)+Fs
so because mass is ungiven and substituting given values we have
also, in the
M( (16.7^2)/200)=( M*9.8*tan3.60)+Fs
isolating Fs
Fs=.777*M

now here is where the problems arise:
typically on flat surfaces Fs=Fn*(coefficient of static friction)
however i am not sure that this is true for banked curves because Fn is not perpendicular to Fg(Y). So i think that
Fs=Fn(Y) *(coefficient of static friction)
because 0=Fnety= Fg+ Fn(Y) we know that Fn(Y)=Fg

so....
Fs=Fn(y)*(coefficient of static Friction)
.777*M=9.8M*(coefficient of static friction)

minimum coefficient of static friction=.079

thanks
-Todd