Answer to Question #158161 in Mechanics | Relativity for Aisha

Question

A 1Kg object is tied with a 2m rope and making uniform circular motion on the horizontal surface. the coefficient of friction is 0.2. if the rope can succeed maximum tension of 20N, what is the maximum velocity of the object

Answer 1

Lets  solve the problem

First of all we write the x and y motion equations

the object travel in a uniform circular motion in a horizontal surface

y - coordinate -> $N = F_{net} + T$

x - coordinate -> $F_{fric} = ma$

$F_{fric} = \mu N = \mu (F_{net} + T) = \mu (ma+T) = ma$

$ma - \mu ma = \mu T \to a = \large\frac{\mu T}{m(1-\mu)} = \frac{v^2}{R}$

$v = \large\sqrt{\frac{\mu TR }{m(1-\mu)}} = \sqrt{\frac{0.2*20*2}{1*(1-0.2)}}$ = $3.16 \frac{m}{s}$