Question

A small particle of mass $0.36$ g rests on a horizontal at a distance $25cm$ from the axis of spindle. The turntable is accelerated at a rate of $\alpha =\frac{1}{3}rad{s}^{-2}.$ The frictional force that the table exerts on the particle $2s$ after the startup is

• A. $40\mu N$
• B. $30\mu N$
• C. $50\mu N$
• D. $60\mu N$

Answer 1

Answer: (C)

$50\mu N$

Given: $r=25cm=0.25mm=0.36\times {10}^{-3}kg$

$a_t=\alpha r=\frac{1}{3}\left(.25\right)=0.083m/s^2$

$w_i=0$, angular velocity after 2 second $w=\alpha \left(2\right)=0.33\left(2\right)$

$w=0.66rad/s$

$a_c=r{w}^2=0.25(0.66{)}^2=0.109m/s^2$

Net $a=\sqrt{a_t^2+a_c^2}=0.137m/s^2$

Frictional force $f=ma=.36\times {10}^{-3}\times 0.137=50\mu N$