Calculating Safe Velocity: Why Is 4th Option Incorrect?

[Shivam]

Homework Statement

A car of mass 1000kg is moving on a horizontal circle of radius 200m. Coefficient of friction between ground and tyres is 0.2.Find the friction force acting on the tyres if the car is moving with speed of 30m/s.
(1)1000N
(2)20N
(3)2000N
(4)None of these

Answer according to book is 3rd option.

Relevant Equations

V(max)=√Rgu (u is coefficient of friction, also v is maximum safe speed at which car can take turn safely)

1). I calculated maximum safe velocity using the equation -

V(max)=√200x10x0.2
=20m/s
So the speed at which car is traveling is greater than the safe speed.. So the car should skid. So why 4th option is not correct ?

 

[jbriggs444]

So the speed at which car is traveling is greater than the safe speed.. So the car should skid. So why 4th option is not correct ?

I am with you. The car cannot be turning in a circle under the influence of friction alone. There must be another force acting. We are not provided with any information about that force. Accordingly, the magnitude (and direction) of the force of friction is indeterminate.

However, the intent of the questioner seems clear. Since the required force exceeds that of static friction, we are to assume that the car skids out of the circle and that the request is actually for the force of friction while this skid is in progress. The fact that the coefficient of friction is stated without any qualifier about "static" or "kinetic" is a hint that this is the intent.

 

[Gaussian97]

Well, I suppose that it's because even if the card is not moving in a circle and it's skidding, the force due to friction doesn't change, so is still 2kN.

 

[Shivam]

Thanks for the reply.. I think the question just wanted to know value of frictional force.

 

[kuruman]

I do not disagree with the above, but there is another interpretation. The problem as stated above says "A car of mass 1000kg is moving on a horizontal circle of radius 200m." It has already been established above (and I agree) that the car cannot be following a circular path of radius 200 m at 30 m/s. However, what evidence is there that the car is following a curved path that includes sliding? Specifically, moving at 30 m/s in a straight line along a diameter also satisfies the statement of the problem. In that case the wheels would roll without slipping, the force of friction would be indeterminate and option (4) would be the correct answer. Now, if option (4) were not included, then yes option (2) is more likely it. One might object, "Well, if the car is going in a straight line, why mention the circle at all?" To which I will respond with another question, "By the same token, if the car is not going around in a circle why mention the circle at all?" I think this is a poorly crafted multiple choice question.

BTW, I had a colleague who once told me that he always put down "None of the above" as an option. It was his insurance in case he figured out the "correct" answer incorrectly. I was not impressed.

 

[jbriggs444]

I think this is a poorly crafted multiple choice question.

Agree. I was surprised that none of the answers matched the centripetal force that would need to exist for circular motion at the stipulated speed and radius.

 

[Gaussian97]

Well, I think is the same case as the typical problem of an inclined plane with friction. You may be told to compute the acceleration, but maybe the problem turns to have so much friction that the object doesn't move at all. This is very usual to distinguish if a student really understands what is doing or if simply is applying the equations without thinking at all.

And the fact that they are telling you that is following a circle is fundamental for the problem, the answer could be different if, for example, the car was following an ellipse.

 

[haruspex]

Well, I think is the same case as the typical problem of an inclined plane with friction. You may be told to compute the acceleration, but maybe the problem turns to have so much friction that the object doesn't move at all. This is very usual to distinguish if a student really understands what is doing or if simply is applying the equations without thinking at all.

And the fact that they are telling you that is following a circle is fundamental for the problem, the answer could be different if, for example, the car was following an ellipse.

But it doesn't quite work here. We are told the car is moving in a circle at a given radius and a given speed, which is not possible with the given friction coefficient.
There are several ways it could have been worded better, e.g. the car hits a section with a lower coefficient.