Banked Curve- find the Velocity when static MU=0

[Phoenixtears]

SOLVED

(Green means correct)

Homework Statement

A a 14600 kg *rubber-tired car moves on a concrete highway curve of radius 71 m is banked at a 12° angle.

(a) What is the normal force acting on the car?
168971N

(b) What is the speed with which the car can take this curve without sliding? (Assume s = 0.)
m/s

Homework Equations

2nd law statements

a= V^2/ r

The Attempt at a Solution

So I began part a by drawing force diagrams and then 2nd law statements. I was left with:

n= mg/ cos@
n= (14600)/ cos12
n=168971

That was correct. I then attempted to move along to part b. I began this by saying that the total force is static friction, therefore:

Fs(the maximum)= Mass(V(maximum)^2)/r
V^2= (mu)*gr


However, with mu=0 then this all totals to zero. I'm not sure how to get around this. Plus, logically if the coefficient of static friction is zero, then no matter what wouldn't the car slide??

Thanks in advance!

~Phoenix

 

[BerryBoy]

My only interpretation of this question is this:

- The car will slide DOWN side ways because there is no friction on the road. If he went super-fast (over-exaggeration of course), the car would slide UP because of the effective weight from it's the centrifugal force (not centripetal). So you are asked for the speed at which the car will not slide up or down the bank.

That is my interpretation of the question.

Best Regards,
Sam

 

[baba89]

I would like to clarify that the coefficient of static friction being zero does not necessarily mean that the car will slide. It simply means that the maximum friction force that can be exerted on the car is zero. In this case, the car will still be able to take the curve without sliding if the centripetal force required for circular motion is provided by other forces, such as the normal force and the gravitational force.

To find the velocity at which the car can take the curve without sliding, we can use the equation a = v^2/r, where a is the centripetal acceleration, v is the velocity, and r is the radius of the curve. Rearranging this equation, we get v = √(ar).

Since the car is not sliding, the centripetal acceleration is equal to the maximum static friction force divided by the mass of the car, which can also be expressed as μmg. Therefore, the final equation for the velocity is v = √(μmgr). Plugging in the given values, we get v = √(0 * 14600 * 9.8 * 71), which simplifies to v = 0 m/s. This means that the car can take the curve at any speed without sliding, since the maximum friction force is zero.

In conclusion, even though the coefficient of static friction is zero, the car can still take the curve without sliding as long as the other forces (normal force and gravitational force) provide enough centripetal force.