Circular Motion and Friction

1. May 5, 2017

HaoPhysics

1. The problem statement, all variables and given/known data
A car drives along a curved track. The frictional force exerted by the track on the car is:

a. greater than the frictional force exerted by the car on the track
c. opposite in direction to the frictional force exerted by the car on the track
d. zero if the car's speed is constant
e. dependent on the radius of the track

2. Relevant equations
mV2/R = Centripetal force
Ffr = Fc if the car is to not slide

3. The attempt at a solution
So the track must exert a frictional force on the car equal to its centripetal force as it rounds the circle to prevent it from slipping. And this centripetal force is dependent on the radius of the track R.

So from this I think the answer could be E.

But also, between any two objects A and B, the friction A exerts on B is equal and opposite in direction to the frictional force B exerts on A.

So from this I think the answer could be C.

The book says the answer is C. But I want to know why it can't be E.

2. May 5, 2017

kuruman

E is also a correct answer.
Because the book says so. Seriously, though, E looks correct to me because the force of static friction needed is $f_s=\frac{mv^2}{R}$. Of course it also depends on the speed and mass of the car, not only on the radius of the track, but I don't see an "only" in E.

3. May 5, 2017

HaoPhysics

Thanks for the input! And yes, I feel that a part of the secondary education program is learning to question the books.

4. May 5, 2017

CWatters

E is badly worded? The friction force is inversely dependant/proportional on the radius.

5. May 5, 2017

kuruman

Not just the books. Question everything.

6. May 5, 2017

HaoPhysics

That is also a good point.

7. May 5, 2017

HaoPhysics

Very true. I like your signature quote.

8. May 5, 2017

kuruman

In my understanding, "dependent" could possibly mean linearly, inversely, inversely squared, exponentially, whatever. As long as there is a "radius" (independent variable) on the right side, the force of friction (dependent variable) is "dependent" regardless the functional form. If the author of the question meant "directly proportional", then it is a poorly phrased question. Again in my opinion.