Question

Two masses are tied together and one is tied to a center post on a frictionless table. The cords are of equal length R=10 cm, as shown. Both masses rotate on the table making 100 revolutions per minute. m1 = m2 = 2kg. (See Figure below) What is the centripetal acceleration of m1 ? What is the tension T2 ? What is the tension T1 ?

Answer 1

Angular velocity is

$\omega =100 rev/min=\frac{100}{60}\times2\pi =10.472 rad/s$

Centripetal acceleration for m will be

$a=r_1\omega^2=0.10\times10.472^2=10.97m/s^2$

Equation for mass mass m1 is

$T_1-T_2=m_1r_1\omega^2$

and for mass m2 is

$T_2=m_2r_2\omega^2=2\times0.20\times10.472^2=43.865$

By putting value of T2 we get

$T_1=T_2+m_1r_1\omega^2=43.865+2\times0.10\times10.472^2=65.8N$