Maximum velocity on a banking curve formula

In summary, the conversation discusses finding the maximum velocity for a car turning on a banked curve and the use of the normal force in the calculation. The formula for the normal force is different from the textbook, and the conversation explains the reason for this difference. It is determined that the perpendicular component of the net force is equal to N-mgcosθ.
  • #1
oranboron
4
0
http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/imgmech/carbank.gif

I had a problem in my textbook asking me to find the maximum velocity for a car turning on a banked curve.

After i drew my freebody diagram i had the same formula for centripetal force as hyperphysics above (Fx).

However when i tried getting my result my answer was wrong... I didn't know what i was doing wrong so i searched hyperphyics and found their vmax formula turned incredibly different from mine. Then i saw that they had a second equation. I was able to finally figure out that they isolated for the normal force, n = mg/(costheta - usintheta) in Fy and substituted it into the Fx formula.

BUT the value for the normal force is different from what i had before. I had n = mgcostheta

Why couldn't i use that value for N in my version of Fx = Fcentripetal ?

Thank you for your help.
 
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  • #2
The normal force would only equal mg cosθ if there were no component of acceleration perpendicular to the incline, which is not the case here.
 
  • #3
Ok, so if i understand it correctly. Since there is now a net force being applied to the centre and it has a component perpendicular to the incline. This perpendicular force itself is the value of N - mgcosθ ?

Thank you for your patience and help.
 
  • #4
oranboron said:
Since there is now a net force being applied to the centre and it has a component perpendicular to the incline. This perpendicular force itself is the value of N - mgcosθ ?
Right, that's the component of the net force perpendicular to the incline.
 

FAQ: Maximum velocity on a banking curve formula

What is the formula for calculating maximum velocity on a banking curve?

The formula for calculating maximum velocity on a banking curve is v = √(rgtanθ), where v is the maximum velocity, r is the radius of the curve, g is the acceleration due to gravity, and θ is the angle of the banking curve.

How is the maximum velocity affected by the angle of the banking curve?

The maximum velocity is directly affected by the angle of the banking curve. As the angle increases, the maximum velocity also increases. This is because a steeper banking angle allows for a greater centripetal force to act on the object, enabling it to travel at higher speeds without slipping off the curve.

What is the significance of the radius of the curve in the maximum velocity formula?

The radius of the curve is a crucial factor in the maximum velocity formula. A larger radius allows for a higher maximum velocity, as the object has a longer distance to travel around the curve and can maintain a constant speed without slipping. A smaller radius, on the other hand, requires a lower maximum velocity to prevent slipping.

How does the acceleration due to gravity affect the maximum velocity on a banking curve?

The acceleration due to gravity plays a crucial role in determining the maximum velocity on a banking curve. As the acceleration due to gravity increases, the maximum velocity also increases. This is because a higher acceleration allows for a greater centripetal force to act on the object, enabling it to travel at higher speeds without slipping off the curve.

Are there any other factors that can affect the maximum velocity on a banking curve?

Aside from the angle and radius of the curve, as well as the acceleration due to gravity, there are a few other factors that can affect the maximum velocity on a banking curve. These include the friction between the object and the surface of the curve, the mass and shape of the object, and any external forces acting on the object. These factors can alter the amount of centripetal force acting on the object and therefore impact the maximum velocity.

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