Calculating Velocity for a Banked Curve: What Factors Affect the Best Speed?

In summary, the conversation is discussing finding the best velocity for a car on a road with given radius, length, and height measurements. The formula tan(theta) = v^2/rg is mentioned, but the empty theta variable is confusing. The conversation also suggests that the normal force is important in determining the best velocity.
  • #1
Visual1Up
12
0
Can someone start me in the right direction?

Radius = 105ft
length = 30 ft
height = 4ft
theta = ?
best velocity = ?

I am guessing I use ... tan(theta) = v^2/rg ... v = sqrt(rg tan(theta))

But the empty theta confuses me, and I am not sure how the length even fits in, thanks!,

-Mike
 
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  • #2
I would guess that the length and height are from the cross section of the road. If this is true, then you remember that for the best velocity, the normal force is the resultant of the weight and cent. acceleration force.
 
  • #3
I am not sure I follow exactly, could you explain some more? Thanks!
 

What is the velocity of a banked curve?

The velocity of a banked curve is the speed at which an object is moving along the curve. It is typically measured in meters per second (m/s) or kilometers per hour (km/h).

How is the velocity of a banked curve calculated?

The velocity of a banked curve can be calculated using the equation v = √(rgtanθ), where v is the velocity, r is the radius of the curve, g is the acceleration due to gravity, and θ is the angle of the banked curve.

What factors affect the velocity of a banked curve?

The velocity of a banked curve is affected by the angle of the bank, the radius of the curve, and the mass of the object moving along the curve. Other factors such as friction and air resistance may also have an impact.

Why is it important to consider the velocity of a banked curve?

The velocity of a banked curve is important because it determines the centrifugal force that acts on an object as it moves along the curve. If the velocity is too high, the object may experience a force that is greater than the force of friction, causing it to slide off the curve.

How does the velocity of a banked curve affect the stability of the object?

The velocity of a banked curve can affect the stability of an object by influencing the centrifugal force acting on it. If the velocity is too high, the object may experience a greater centrifugal force, making it more likely to lose stability and slide off the curve. On the other hand, a lower velocity may result in a more stable movement along the curve.

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