Car going around banked curve with no friction

In summary, a racecourse with a radius of 200m and a 10 degree banking can allow a car to negotiate the curve at a maximum speed of 18.59 m/s without friction, using the formula tanTheta = v^2/gR and Newton's second law. The acceleration can be calculated using F = ma, but the normal force will need to be determined through a perpendicular force equation.
  • #1
chaotiiic
26
0

Homework Statement


a racecourse is designed with curves with a radius of 200m and a 10degree banking. What is the maximum speed a car can negotiate the curve without friction?


Homework Equations


Newtons 3 laws


The Attempt at a Solution


tanTheta = v^2/gR
tan10 = v^2/(9.8 * 200m)
v = 345 m/s^2

is this right?
 
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  • #2
hi chaotiiic! :smile:
chaotiiic said:
tanTheta = v^2/gR
tan10 = v^2/(9.8 * 200m)

formula looks ok

are you sure about the 345 ?

(and speed is m/s, not m/s2)
 
  • #3
tiny-tim said:
hi chaotiiic! :smile:


formula looks ok

are you sure about the 345 ?

(and speed is m/s, not m/s2)

so is it 0.1763 = v^2/1960
v^2=345.6
v=18.59m/s
 
  • #4
yes! :smile:

(are you ok now, or is there anything you're still not sure about?)​
 
  • #5
tiny-tim said:
yes! :smile:

(are you ok now, or is there anything you're still not sure about?)​

thankyou.
im actually still confused about everything. the only reason i was able to answer this problem is because there's a problem identical in my book to the one i asked. my teacher gives out quizzes before lectures so hopefully ill understand when i go to class later today.
 
  • #6
ok, so you don't understand the reason for the formula? …
chaotiiic said:
tanTheta = v^2/gR

like almost all dynamics questions, it all boils down to good ol' Newton's second law (F = ma) …

you know the acceleration (as a function of v),

and although you know the weight, you don't know the normal force …

so you do F = ma perpendicular to the unknown (normal) force :smile:
 

1. What is a banked curve with no friction?

A banked curve with no friction refers to a curved track or road that is tilted at an angle, allowing objects to move around it without any resistance from friction. This type of curve is often used in race tracks or roller coasters to allow for higher speeds and smoother turns.

2. How does a car move around a banked curve with no friction?

A car moves around a banked curve with no friction due to the force of gravity and the centripetal force. The angled surface of the curve exerts a normal force on the car, which acts as the centripetal force, pushing the car towards the center of the curve. This, combined with the force of gravity pulling the car downward, allows the car to maintain its speed and direction around the curve.

3. What happens if there is friction on a banked curve?

If there is friction present on a banked curve, it can cause the car to slow down and potentially slide off the track. This is because the friction force acts in the opposite direction of the car's motion, reducing the centripetal force and causing the car to lose its grip on the track.

4. How does the angle of a banked curve affect the car's speed?

The angle of a banked curve can affect the car's speed by altering the amount of centripetal force acting on the car. A steeper angle will result in a greater normal force and therefore a greater centripetal force, allowing the car to maintain a higher speed around the curve. However, if the angle is too steep, it can cause the car to lose control and potentially flip over.

5. Are there any real-life examples of banked curves with no friction?

Yes, there are many real-life examples of banked curves with no friction. Some examples include race tracks, roller coasters, and banked turns on highways. These structures are designed specifically to reduce the effects of friction and allow for smoother and faster movement around curves.

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