Medium
What is optimum speed? Write its equation.
(N/A) Optimum speed is the speed at which a vehicle can negotiate a banked curve without relying on friction between the tires and the road surface. At this speed,the necessary centripetal force is provided entirely by the horizontal component of the normal force.
The equation for optimum speed $(v_0)$ on a banked road with banking angle $(\theta)$ and radius of curvature $(r)$ is given by:
$v_0 = \sqrt{rg \tan \theta}$
where:
$r$ = radius of the curve
$g$ = acceleration due to gravity
$\theta$ = angle of banking
The equation for optimum speed $(v_0)$ on a banked road with banking angle $(\theta)$ and radius of curvature $(r)$ is given by:
$v_0 = \sqrt{rg \tan \theta}$
where:
$r$ = radius of the curve
$g$ = acceleration due to gravity
$\theta$ = angle of banking
Explore More
Similar Questions
In the case of a conical pendulum,if $T$ is the tension in the string and $\theta$ is the semi-vertical angle of the cone,then the component of tension which balances the centrifugal force in the equilibrium position is
The speed of a car is increased by $10\%$. If the angle of banking remains constant,the radius of the turn must be changed from $20 \ m$ to ........ $m$.
Medium
View Solution$A$ horizontal curve on a racing track is banked at a $45^o$ angle. When a vehicle goes around this curve at the curve's safe speed (no friction needed to stay on the track),what is its centripetal acceleration?
Medium
View Solution$Assertion$ : There is a stage when frictional force is not needed at all to provide the necessary centripetal force on a banked road.
$Reason$ : On a banked road,due to its inclination the vehicle tends to remain inwards without any chances of skidding.
$Reason$ : On a banked road,due to its inclination the vehicle tends to remain inwards without any chances of skidding.
MediumAIIMS 2016
View Solution$A$ circular freeway entrance and exit are commonly banked to control a moving car at $14 \ m/s$. To design a similar ramp for $28 \ m/s$,one should:
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo