# Friction Force on Banked Curves

1. Mar 21, 2012

### jnlbctln

1. The problem statement, all variables and given/known data

A car weighing 3220 lbs rounds a curve a 200 ft radius banked at an angle of 30deg. Find the friction force acting on the tires when the car is traveling at 60mph. Coefficient of friction is 0.9.

2. Relevant equations

i rotated the axes such that y-axis is collinear with Fn

and x-axis is collinear with Ff

I tried equilibrating the y-components i get Fn = 4,724.6 lb , then Ff=(0.9)(4,724.6) = 4252.14 lb

while on equilibrating the x-components i got Ff= 1743.25lb

PS. I have read from my book that Ff=(u)(Fn) is only true if skidding is impending or v is at maximum.. how come? so what's the meaning og 4252.14?

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 21, 2012

### Staff: Mentor

Why do that? It might not be the best idea here, since there is a horizontal acceleration.
Instead, identify the forces in a FBD. Then apply Newton's 2nd law to the horizontal and vertical components.
That's correct. For static friction, μFn gives the maximum possible friction force. So you cannot use that here, since there's no reason to think that you are at the limit of static friction. Instead, call that friction force Ff and solve for it.

3. Mar 21, 2012

### jnlbctln

Thanks for reply sir! I still some blurry ideas in my mind but i wanna gather it first to have a better follow question :)

4. Mar 21, 2012

### Staff: Mentor

Good. Get to work!

5. Mar 21, 2012

### jnlbctln

Another question sir! What if i got that Fn= 4724 lb then mutiplied it by u=.9 . What does that quantity mean? does it mean something at all? or it does not exist?

6. Mar 21, 2012

### Staff: Mentor

First a question for you: How did you arrive at Fn = 4724 lb?

7. Mar 21, 2012

### jnlbctln

I used FBD. I get Ff= 1743 and Fn= 4724.

8. Mar 21, 2012

### Staff: Mentor

Show me exactly what you did.

9. Mar 21, 2012

### jnlbctln

ahh..haha, i'm sorry for that silly answer.haha.. here's my solution

Summation of forces horizontal

(Fn)Sin30 + (Ff)(Cos30) = Fc
(Fn)(sin30) + (ff)(cos 30)= (Wv^2)/(gr)
(Fn)(sin30) + (ff)(cos 30)= ((3220)(88^2))/((32.2)(200))

(Fn)(sin30) + (ff)(cos 30)= 3872 <--------Equation (1)

Summation of Forces vertical

(Fn)(Cos30) = (Ff)(Sin30) + W

(Fn)(cos30) - (Ff)(sin30) = 3220 <--------Equation (2)

Solving this two equations simultaneously we get, Fn= 4724 and Ff = 1743

From there, If i used the fact that Ff=(u)(Fn) could not be used, I conclude that Ff=1743 must be the true value of the Frictional Force not Ff=(0.9)(4724) since it does not impend to skid nor have the maximum velocity.

What bothers me is that value, the Ff=(0.9)(4724), what does it mean? does it really mean something ? does that frictional force exist? or what? :)

10. Mar 22, 2012

### Staff: Mentor

I didn't check your arithmetic, but that's exactly the right approach.

(So you didn't really 'rotate the axes', despite what you said in your first post. Good.)
Good.

μN represents the maximum possible static friction between two surfaces with a given normal force. It's not particularly useful in this problem.

An example where it might be useful would be if you had to figure out the maximum speed that you could safely negotiate a given banked curve. In that case, to find the maximum speed, you would set the friction force to its maximum possible value.

11. Mar 22, 2012

### jnlbctln

(I don't know how to quote , ahaha)

Thanks. Actually I had 2 solutions , one is rotating the axes (because my professor told us that in that sense we can eleminate the use of simultaneous equation) and i also use the unrotated one which fairly the same. nevertheless i got the answer. hehe

From ur last statement, i think i cant use that Ff=(0.9)(4724) for getting the max speed since on getting that Fn=4724 i already used the 60 mph speed. What I did to get the max speed is substituting the Fn equation (from summation of forces in y (i this one i rotated the axis for convinience)) to the (u)(Fn) of the another equation (the summation of forces on x axis). :)

12. Mar 22, 2012

### Staff: Mentor

Actually, rotating the axes is a good idea--as long as you do it properly, which you obviously did. (Most folks forget to take components of the acceleration and just assume that the 'vertical' forces cancel.)

Right. You can't use that, since Fn depends on the speed.

Sounds good to me!