# Solving Banked Road Problem with Car Speeds of 48 km/h

• Bernie Hunt
In summary, the conversation is about calculating the banking angle theta for a curve with a radius of 30m so that a car can round the curve at 48km/h even if the road is frictionless. The equation used is tan(theta) = v^2 / gr, and the correct answer is 82.7 degrees. However, the book has a different answer of 31 degrees, leading to confusion and questions about units and forces. The conversation ends with a request for help in understanding the concept for an upcoming test.
Bernie Hunt
OK, last time I'll bother you guys today. I'm just having a tough time getting things to work out.

A curve of radius 30m is banked so that a car can round the curve at 48km/h even if the road is frictionless. Calculate the banking angle theta for these conditions.

I have;

tan(theta) = v^2 / gr

tan(theta) = 48^2 / (9.8 * 30)

tan(theta) = 7.8367

theta = 82.7 deg

The book has 31 deg.

Any ideas?

Thanks,
Bernie

48km/h is a dangerous thing to plug into an equation like that. As a habbit always plug the units in with their numbers

You will have to convert 48 km/h to m/s. Or, convert 30m to km and 9.8 m/s^2 to km/hr^2.

Argh, Thud, thud, thud ...
(The sound of beating my head on the desk again.(

That's the second time I made a units mistake last night. My montra for today will be "Check the units!"

Bernie

Help!

Okay, so I am doing a similar problem involving a car driving on a banked, circular track (theta=31degrees). I know that to find the centripetal acceleration, I am supposed to say that (mv^2)/r = nsin(theta). Then, I have to solve for n by saying that ncos(theta)=mg. However, I am confused... why can't n=mgcos(theta). My understanding is that two forces are equal in magnitude if the object doesn't move in either direction. The car doesn't move into the road or out of the road... or does it?? please help! I have a test on monday.

## 1. How do you determine the correct bank angle for a banked road?

The correct bank angle for a banked road can be determined using the formula: θ = tan^-1(v^2 / rg), where θ is the bank angle, v is the car's speed, r is the radius of the curve, and g is the gravitational acceleration. This formula assumes a frictionless surface and ideal conditions.

## 2. What is the purpose of a banked road?

A banked road is designed to help vehicles navigate curves at high speeds more safely and efficiently. The banked surface helps to counteract the centrifugal force and keep the vehicle on the road without relying solely on friction between the tires and the road surface.

## 3. Can any speed be safely driven on a banked road?

No, the banked angle of a road is designed for a specific speed and radius of the curve. Driving at a higher or lower speed can result in the car sliding off the road or experiencing discomfort for passengers due to the force of the turn.

## 4. How does the banked angle change for different speeds?

The banked angle of a road increases as the speed of the car increases. This is because the centrifugal force acting on the car also increases with speed, and the banked angle needs to be steeper to counteract this force.

## 5. Can a banked road be used for vehicles of all sizes and weights?

The banked angle of a road is determined based on the speed and radius of the curve, not the size or weight of the vehicle. However, heavier vehicles may experience more force on the banked curve and may require a different bank angle or speed to maintain stability.

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