Answer:
Time will be 2.13 sec
Explanation:
We have given that distance r = 14.3 cm =[tex]=\frac{14.3}{100}=0.143m[/tex]
Coefficient of static friction [tex]\mu =0.4[/tex]
Angular acceleration is given by [tex]\alpha =2.45rad/sec^2[/tex]
We know that frictional force is given by [tex]F=\mu mg[/tex]
And centrifugal force is given by [tex]F=\frac{mv^2}{r}[/tex]
When coin just starts moving
[tex]\mu mg=\frac{mv^2}{r}[/tex]
We know that [tex]v=\omega r[/tex] , here [tex]\omega[/tex] is angular velocity
According to first equation of motion we know that
[tex]\omega =\omega _{i}+\alpha t[/tex]
As [tex]\omega _i=0[/tex]
so [tex]\omega =\alpha t[/tex]
[tex]\mu g=\frac{\left ( r\alpha t \right )^2}{r}[/tex]
[tex]\frac{\mu g}{r}=a^2t^2[/tex]
[tex]t=\frac{\sqrt{\frac{\mu g}{r}}}{α}[/tex]
[tex]t=\frac{\sqrt{\frac{0.4\times 9.8}{0.143}}}{2.45}=2.13sec[/tex]
