First slide

Static friction

Question

A car moves uniformly along a horizontal sine curve $y = a \sin (\frac{x}{α})$ , where a and $α$ are certain constants. The coefficient of friction between the wheels and the road is equal to k. The maximum constant speed at which the car can travel without sliding is

Difficult

A

$α \sqrt{\frac{k g}{a}}$
B

$- α \sqrt{\frac{k g}{a}}$
C

$k g \sqrt{\frac{α}{a}}$
D

$- k g \sqrt{\frac{α}{a}}$

Solution

The radius of curvature is
$\begin{matrix} f \leq f_{2} or f \leq k m g \\ Or \frac{m v^{2}}{R} \leq k m g \\ or \frac{v^{2}}{R} \leq k g \\ ∴ \frac{v_{max}^{2}}{R_{min}} = k g \\ ∴ v_{max} = \sqrt{kg R_{min}} \end{matrix}$
$\begin{aligned} \frac{x}{a} = \frac{π}{2} \\ ∴ R_{min} = \frac{α^{2}}{a} (from equ (i)) \\ v_{max} = \sqrt{\frac{k g α^{2}}{a}} = α \sqrt{\frac{k g}{a}} \end{aligned}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App