# Banked Road Physics Problem: Maximum Speed Calculation

• mr1709
In summary: ##=\tan(\theta+\frac{\arctan(\mu)}{1-\arctan(\mu)))####=\tan(\theta+\frac{1}{1-\arctan(\mu)))####=\tan(\theta+28.5)##
mr1709
1. Homework Statement
A car is moving along a banked highway on a ramp that is banked at an angle of 14 degrees to the horizontal. The radius of curvature of the bank is 264m and the coefficient of static friction is 0.67. What is the max speed that the car can travel and safely stay on the ramp? (Ans: The max speed to negotiate the turn on a banked curve is 28.5 m/s)

## The Attempt at a Solution

. [/B]
Attempt at solution in uploaded picture. I don't think i did anything wrong...is the solution manual possibly incorrect?

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mr1709 said:
A car is moving along a banked highway on a ramp that is banked at an angle of 14 degrees to the horizontal. The radius of curvature of the bank is 264m and the coefficient of static friction is 0.67. What is the max speed that the car can travel and safely stay on the ramp? (Ans: The max speed to negotiate the turn on a banked curve is 28.5 m/s)

the maximum speed comes around 50 m/s- your

attempt shows 54m/s, so, please check the calculation
i could not get your free body diagram? in my opinion f(.n) = mg .cos(theta) and

mg sin (theta) should act along the slope and frictional force should be mu (s).f(n).

Your solution looks fine to me. What book is this from?

drvrm said:
in my opinion f(.n) = mg .cos(theta)
I would not make that assumption. (That would hold for the standard block sliding down an incline problem, but not for this problem where the acceleration is horizontal, not parallel to the surface.)

Doc Al said:
Your solution looks fine to me. What book is this from?

Im not sure. It was a print out sheet my physics teacher gave the class to practice for our upcoming test. Thanks for input

I agree with 53.5 m/s.
There is a slightly easier way to get there.
##mg=N\cos(\theta)-\mu N\sin(\theta)##
##m\frac{v^2}r=N\sin(\theta)+\mu N\cos(\theta)##
Dividing
##\frac{v^2}{gr}=\frac{\tan(\theta)+\mu}{1-\mu\tan(\theta)}##
##=\tan(\theta+\arctan(\mu))##

## What is a banked road physics problem?

A banked road physics problem involves analyzing the forces acting on a vehicle traveling on a banked road. These forces include the gravitational force, normal force, and centripetal force.

## What is the purpose of studying banked road physics?

The purpose of studying banked road physics is to understand the principles behind the design and construction of roads to ensure safe and efficient travel for vehicles. It also helps in the analysis of accidents and determining the appropriate speed for a specific banked road.

## What factors affect the banked angle of a road?

The banked angle of a road is affected by the speed of the vehicle, the radius of the curve, and the coefficient of friction between the tires of the vehicle and the road surface. Other factors such as the weight and size of the vehicle also play a role.

## How does the banked angle of a road affect the force on a vehicle?

The banked angle of a road affects the force on a vehicle by allowing for a component of the normal force to act as the centripetal force, which helps keep the vehicle moving in a circular motion. This reduces the amount of friction needed, resulting in a smoother ride for the vehicle.

## How can banked road physics be applied in real-life situations?

Banked road physics can be applied in real-life situations such as designing roads and highways, analyzing car accidents, and determining the optimal speed for a specific curve on a road. It is also used in motorsports to design tracks and help drivers navigate curves safely and efficiently.

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