Question

Block A with mass m_A

mA

​ is placed on a horizontal surface S. Surface S is attached to a vertical axis. Block A is attached to this vertical axis via a massless rope. The distance between block A and the axis is R

R.

Between block A and surface S there is static friction with static friction coefficient \mu_{\rm s}

μs

​.

The whole system rotates around the axis of rotation (see figure) with angular frequency \omega=2\pi/T

ω=2π/T where T

T is the time of one revolution of rotation. The angular frequency \omega

ω is so large that the static friction force is maximum.

Calculate the tension in the rope.

Answer 1

$m_Aa=m_Av^2/R=m_A\omega^2R=F_{fr}+T$

where F_fr is friction force,

T is tension

$F_{fr}=\mu_sm_Ag$

$T=m_A\omega^2R-\mu_sm_Ag$