Race car on a banked curve?

[collegelife101]

If a race car is on a banked curve, I can see how the normal force and static friction contribute to Fc. But what about gravity? Wouldn't its horizontal component also contribute?

I'm asking because of this question: A race car is traveling around a banked curve on a racetrack, meaning the road is not flat, but at an angle with the horizontal. Why can cars travel faster on a banked racetrack?

The normal force contributes to the centripetal force since the ground is at an angle, so the cars are less likely to slip.

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[Teleologist]

I think you're right.

 

[DrknoSDN]

If a race car is on a banked curve, I can see how the normal force and static friction contribute to Fc. But what about gravity? Wouldn't its horizontal component also contribute?

I'm asking because of this question: A race car is traveling around a banked curve on a racetrack, meaning the road is not flat, but at an angle with the horizontal. Why can cars travel faster on a banked racetrack?

The normal force contributes to the centripetal force since the ground is at an angle, so the cars are less likely to slip.

After reading it a few times I'm still not sure what your suggesting about gravity.

There is no horizontal component to gravity. Gravity is a force only in the downward direction.
The horizontal component of the normal force is what they were implying was helping with the centripetal force.

 

[lexw]

heres an older post that might help
http://forums.studentdoctor.net/thr...roblem-on-the-mcat-practice-materials.416444/

My interpretation is that on a flat road the force would be the centripetal force = friction force stopping the car from sliding outwards. Whereas in a curve, the x component of gravity is also contributes to keeping the car on the track so the centripetal force = friction force + mgsintheta. Keeping all the other variables the same we see that v should increase. someone correct me if im wrong.

 

[syoung]

Depends on how you draw your free body diagram. Be very strict in how you assign your vectors. It will be clear.

 

[Teleologist]

You want to give us an example problem?

 

[syoung]

when i get home tonight

 

[syoung]

A 2000 kg car travels around a curve that is banked at a 30 degree angle. If the maximum force of friction is 1500 N, determine the maximum and minimum speeds that the car can take the curve without slipping. Assume the radius of the curve is 100 meters.

 

[DrknoSDN]

A 2000 kg car travels around a curve that is banked at a 30 degree angle. If the maximum force of friction is 1500 N, determine the maximum and minimum speeds that the car can take the curve without slipping. Assume the radius of the curve is 100 meters.

This question is unsolvable as it is written. (I believe...)
You did not provide the coefficient of static friction. This problem is worded how a stationary object sliding off a ramp would be worded.

The reason I say the coefficient is needed is because as the car banks around the curve it is going to produce a force normal to the embankment based on angle and the centripetal acceleration (artificial gravity).
i.e. you will have a normal force from gravity, and different normal force to oppose the momentum of the car pushing into the ground as it banks. (friction force is dependent on velocity, and not constant.)

Let me phrase it another way. If you remove gravity, a car banking around a turn could still turn (with high friction tires) because the cars inertia will be pushing it into the embankment. This, in addition to the static friction force of the tires and the force normal to the embankment (produced by the momentum of the vehicle) would be dependent on instantaneous velocity and thus requires some multivariable calc and the coefficient of static friction.

If that car example seems unbelievable just envision a very large very rapidly spinning space station. As it spins fast enough there is a point you would be experiencing centrifugally created 'artificial gravity', and by extension, normal forces in a zero G environment =D. (if you want some lulz "That's No Moon!" )

[Edit after more research]

Depends on how you draw your free body diagram. Be very strict in how you assign your vectors. It will be clear.

Also quick google reverse image search of this picture (if your using it for the hypothetical) found here:
http://www.ic.sunysb.edu/Class/phy141md/doku.php?id=phy141:lectures:8
google search results

Says the following:
"Roads designed for high speed traffic will often used banked turns to increase the maximum speed for which slipping does not occur. A well designed banked turn means the car should not rely on friction. (It also makes the problem easier..)"

This diagram is for calculating how to completely negate friction, not determine min max velocity from max friction. (Which makes the problem harder..)

 

[Teleologist]

This question is unsolvable as it is written. (I believe...)
You did not provide the coefficient of static friction. This problem is worded how a stationary object sliding off a ramp would be worded.

The reason I say the coefficient is needed is because as the car banks around the curve it is going to produce a force normal to the embankment based on angle and the centripetal acceleration (artificial gravity).
i.e. you will have a normal force from gravity, and different normal force to oppose the momentum of the car pushing into the ground as it banks. (friction force is dependent on velocity, and not constant.)

We have the force of friction that is opposing the centripetal acceleration of the car and the component of weight of the car parallel to the plane. Why would we need the coefficient of static friction?

OP, is one of the velocities about 20 m/s?

 

[DrknoSDN]

We have the force of friction that is opposing the centripetal acceleration of the car and the component of weight of the car parallel to the plane. Why would we need the coefficient of static friction?

OP, is one of the velocities about 20 m/s?

I can say minimum is 20.6 m/s if you ignore the momentum of the car and you assume that friction is 1500N at all velocities.

Also you only have the component of weight of the car parallel to the plane assuming it is stationary. Like I said it sounds like a stationary sliding ramp problem.

How about this. Think of a 1kg ball sitting on a flat surface. Easy to see that the normal force is 10N opposite gravity. Now roll the ball into a halfpipe (U shaped pipe). Is the normal force still 10N at the bottom of the pipe? No, you need to first calculate the potential energy the ball had above the pipe and then turn that into KE, once you solve for velocity you can plug that into the centripetal acceleration equation (with radius of curvature of the pipe) to get the centrifugal force the ball is applying to the ground. The normal force is then mg + (1/2 mv^2/r).

This applies to the car scenario because as a car is driving along an embanked road it will be "pushing" into the ground increasing the normal force beyond what would be predicted from mgcos(theta). The real normal force would be dependent on velocity like the example I just provided. In physics class the normal force is usually calculated from just gravity (only to make things simple), but the normal force is just there to oppose any force applied to a surface so here you have multiple sources yielding a net normal force. The normal force is dependent on the velocity of the vehicle + gravity.

I'm open to be debated on it, and acknowledge that there are many ways to approach a problem like this. Maybe I'm missing the simple one.

 

[DrknoSDN]

Solved::: (lol @ self for not checking wikipedia before longwinded explanations above 😵)
Plug and chug to your hearts content.

Equations taken from this wikipedia article that explain the solution in detail.

Vmax:

Vmin:

Quote:
"This [top] equation provides the maximum velocity for the automobile with the given angle of incline, coefficient of static friction and radius of curvature. By a similar analysis of minimum velocity, the following [2nd] equation is rendered:"

Wiki link:
http://en.wikipedia.org/wiki/Banked_turn#Banked_turn_with_friction

Higher up on that page shows the bank turn w/o friction. Much less math.

 

[Teleologist]

So is 20 m/s the correct minimum velocity?

 

[syoung]

We have the force of friction that is opposing the centripetal acceleration of the car and the component of weight of the car parallel to the plane. Why would we need the coefficient of static friction?

OP, is one of the velocities about 20 m/s?

You're going to have to be more specific than about 20 m/s.

 

[Teleologist]

You're going to have to be more specific than about 20 m/s.

What's the answers then?

 

[syoung]

Consider 2 cases for that problem:

Max velocity at a specific radius and banked (degree) occurs AGAINST a max friction that prevents the car from spinning out.

Min velocity at a specific radius and banked (degree) occurs against a min friction that prevents the car from sliding down towards the center.