Centripetal Force Homework: Find Car Speed to Lose Contact w/ Road

[Tommie Robinson]

Homework Statement

Find the speed at which a car of mass M will lose contact with the frictionless road

Homework Equations

Centripetal/Centrifugal forces (maybe?)

The Attempt at a Solution

I used OneNote to attempt this problem[/B]
https://onenote.com/webapp/pages?to...0EkvVRJz3ZRVraisuhYOUH0&id=636551577043927699

 

[stockzahn]

Find the speed at which a car of mass M will lose contact with the frictionless road

If there would be no friction between the road and the car ($\mu=0$), what force should keep the car on the curved path?

 

[Tommie Robinson]

If there would be no friction between the road and the car ($\mu=0$), what force should keep the car on the curved path?

Centripetal force right? I was thinking that if the centrifugal force was bigger than the centripetal the car would veer off. Or is that incorrect, because centrifugal is fictitious?

 

[stockzahn]

I was thinking that if the centrifugal force was bigger than the centripetal the car would veer off.

That's correct, but without friction, where should the centripetal force come from?

 

[Tommie Robinson]

That's correct, but without friction, where should the centripetal force come from?

Looking at the image...I know that gravity is a type of centripetal force but what role does it play on car roads? I thought that velocity played a bigger part because the centripetal force is keeping the velocity circular

 

[stockzahn]

Looking at the image...I know that gravity is a type of centripetal force but what role does it play on car roads? I thought that velocity played a bigger part because the centripetal force is keeping the velocity circular

In the picture I posted, I just wanted to draw all acting forces (by neglecting the drag/air resistance). There is no force acting against the centrifugal force. Therefore the question must be different than you posted it or the answer is: At any velocity $\neq 0$.

 

[Tommie Robinson]

In the picture I posted, I just wanted to draw all acting forces (by neglecting the drag/air resistance). There is no force acting against the centrifugal force. Therefore the question must be different than you posted it or the answer is: At any velocity $\neq 0$.

Wait I am a little confused, you meant the centripetal force right? Not centrifugal? And I thought that centripetal forces had to come with a centrifugal, is that not the case? Is it because there is no friction? So regardless of the speed, since there is no friction, the car will just slide towards the center?

 

[stockzahn]

Wait I am a little confused, you meant the centripetal force right? Not centrifugal? And I thought that centripetal forces had to come with a centrifugal, is that not the case? Is it because there is no friction? So regardless of the speed, since there is no friction, the car will just slide towards the center?

You are right, the two forces have to come together, where the centripetal force is a real force and the centrifugal force is a fictitious or pseudo force. So without friction, there is no centripetal force to deviate the car from the straight path - and since there is no centripetal force, the car's driver does not feel any centrifugal force as well.

And yes, if there is no friction the driver is not able to follow any curve, as "flat" as it could be. However, I propose the following: For a dry street the coefficient of friction is about $\mu=0.7$. What would be in this case the maximal velocity to keep the car on the curved path, assuming the radius of the curve is 100 m?

 

[Tommie Robinson]

You are right, the two forces have to come together, where the centripetal force is a real force and the centrifugal force is a fictitious or pseudo force. So without friction, there is no centripetal force to deviate the car from the straight path - and since there is no centripetal force, the car's driver does not feel any centrifugal force as well.

And yes, if there is no friction the driver is not able to follow any curve, as "flat" as it could be. However, I propose the following: For a dry street the coefficient of friction is about $\mu=0.7$. What would be in this case the maximal velocity to keep the car on the curved path, assuming the radius of the curve is 100 m?

Thank you for giving me extra practice and help! Notice where I put the centrifugal (basically equal to friction), is that okay to do?

 

[stockzahn]

View attachment 221042
Thank you for giving me extra practice and help! Notice where I put the centrifugal (basically equal to friction), is that okay to do?

Thank you for taking it and well done!

 

[stockzahn]

View attachment 221042
Notice where I put the centrifugal (basically equal to friction), is that okay to do?

PS.: I'm not sure, if I interpret your drawing correctly, but just to be sure: The centripetal force is the real one due to the real friction. The centrifugal force is felt only due to the inertia of the car, which is deviated from its linear and constant motion.

 

[CWatters]

The drawing in the OP is unclear... Is the car going around a bend or over a hill?

 

[Tommie Robinson]

The drawing in the OP is unclear... Is the car going around a bend or over a hill?

Sorry, it's around a bend

 

[kuruman]

Find the speed at which a car of mass M will lose contact with the frictionless road

OP's initial post #1 says the road is frictionless and the figure posted on onedot.com shows a banked road. It looks like the offered solutions and assistance are off the mark.

 

[haruspex]

OP's initial post #1 says the road is frictionless and the figure posted on onedot.com shows a banked road. It looks like the offered solutions and assistance are off the mark.

Quite so.
I also note that if the road is frictionless there is only one speed at which it will stay on the road.

 

[haruspex]

I thought that centripetal forces had to come with a centrifugal,

Not exactly. You have to choose your reference frame.

If you choose an inertial frame, e.g. a fixed point and direction in space, then there is no centrifugal force. No centripetal force "acts" either, i.e. it is not an applied force. Centripetal force is that component of the net applied force which is orthogonal to the velocity.
In the present case, the applied forces are only gravity and the normal force. Since both of these are orthogonal to the velocity their resultant is also normal to it, so their resultant constitutes the centripetal force.
For the vehicle to stay on the road, you need this resultant to be horizontal and of the right magnitude to produce the circular motion of the right radius, i.e. an acceleration of v²/r.

If you take the reference frame of the car then that frame is rotating, so non-inertial. By definition, the car is not accelerating in this frame, so there is no centripetal force. Instead, to explain the fact that the car is not accelerating despite the unbalanced forces it experiences one has to invent the fictitious centrifugal force.

If you do the algebra, you find that the centrifugal force in the one view is equal and opposite to the centripetal force in the other view.

 

[CWatters]

OP's initial post #1 says the road is frictionless and the figure posted on onedot.com shows a banked road. It looks like the offered solutions and assistance are off the mark.

I can't open the onenote link in the OP or the onedot link above.

Problem makes a lot more sense if it's a banked track. Try making a drawing of the rear view of the car half way around the bend and mark on it the forces.
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