What is the radius of the highway?

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In summary, the conversation discusses determining the radius of a highway curve with a 6% banking angle, where vehicles will travel at 120km/h. The individual provides their attempt at solving the problem, converting units and using equations to find a potential solution of 1.08km. They also mention another equation involving velocity, gravity, and the banking angle as a possible alternative.
  • #1
twenty5
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Homework Statement


Determine the radius of a highway curve which has a banking angle of 6% over which vehicles will travel at 120km/h


Homework Equations


I've started with:
Fx = -Fcentripetal = (mv2)/r = -Fnsin6
(mv2)/2 = mgsin6

converted my km/h => m/s ... 33.3m/s


The Attempt at a Solution



pretty much just subbed in the values


-Fc = -Fnx
-mv2/r = -mgsin6
-33.32/r = -9.81sin6
-33.3/-9.81sin6 = r
r = 1.08km?


is this correct?
 
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  • #2
velocity = sqrt(g*r*tan[theta])

Try your values in there and see what you come out with (it's just another version of yours above).

Otherwise, it looks OK to me.

Jared
 
Last edited:
  • #3
ah kay, thank youuuu ^^ is there like a thank button somewhere?
 

What is the radius of the highway?

The radius of a highway is a measure of the curvature of the road. It is the distance from the center of the road to the edge of the road.

Why is the radius of the highway important?

The radius of the highway is an important factor in determining the speed and safety of drivers. A smaller radius means a sharper turn, which requires drivers to slow down. A larger radius allows for higher speeds and smoother turns.

How is the radius of the highway calculated?

The radius of the highway can be calculated using the formula R = v^2/a, where R is the radius, v is the speed of the vehicle, and a is the lateral acceleration. This formula takes into account the speed and turning force of the vehicle.

What factors can affect the radius of the highway?

The radius of the highway can be affected by a number of factors, including the design of the road, the terrain, and the speed limit. Other factors such as weather conditions and traffic volume can also impact the radius of the highway.

How does the radius of the highway impact the environment?

The radius of the highway can have a significant impact on the environment. A smaller radius means more land is needed for the road, which can lead to deforestation and destruction of natural habitats. A larger radius can also require more materials to construct, resulting in a higher carbon footprint.

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