A child starts running from rest along a circ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The child starts from rest with constant tangential acceleration $a$. After time $t$,the tangential velocity is $v = at$.The radial (centripetal)

Vedclass · Accepted Answer

$\frac{[a^{4} t^{4}+a^{2} r^{2}]^{1/2}}{g r}$

Vedclass · Answer

(C) The child starts from rest with constant tangential acceleration $a$. After time $t$,the tangential velocity is $v = at$.The radial (centripetal) acceleration is $a_r = \frac{v^2}{r} = \frac{(at)^2}{r} = \frac{a^2 t^2}{r}$.The total acceleration $a_{net}$ experienced by the child is the vector sum of tangential and radial accelerations: $a_{net} = \sqrt{a_t^2 + a_r^2} = \sqrt{a^2 + \left(\frac{a^2 t^2}{r}\right)^2} = \sqrt{a^2 + \frac{a^4 t^4}{r^2}}$.Slipping starts when the required frictional force equals the limiting friction,i.e.,$F_{net} = m a_{net} = \mu m g$.Thus,$\mu g = \sqrt{a^2 + \frac{a^4 t^4}{r^2}} = \sqrt{\frac{a^2 r^2 + a^4 t^4}{r^2}} = \frac{1}{r} \sqrt{a^2 r^2 + a^4 t^4}$.Therefore,$\mu = \frac{[a^4 t^4 + a^2 r^2]^{1/2}}{r g}$.

Similar Questions

$A$ car is moving on a circular level road of curvature $300\,m.$ If the coefficient of friction is $0.3$ and acceleration due to gravity is $10\,m/s^2,$ the maximum speed the car can have is ........ $km/hr.$

In a motorcycle stunt called the "well of death",the track is a vertical cylindrical surface of $18\, m$ diameter. What should be the minimum speed of the motorcyclist in $m/s$ to prevent him from sliding down? The coefficient of friction is $0.8$ and take $g = 10\, m/s^2$.

$A$ car of mass $m$ moves on a banked road having radius $r$ and banking angle $\theta$. To avoid slipping from the banked road,the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is:

What is the maximum safe speed of a car on a flat road of radius $40 \, m$ in $m \, s^{-1}$? The coefficient of friction between the road and the tires is $0.25$. (Take $g = 10 \, m \, s^{-2}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module