Question

Two balls have the same mass of 5.00 kg. Suppose that these two balls are attached to a rigid massless rod of length 2L, where L = 0.550 m.
One is attached at one end of the rod and the other at the middle of the rod.
If the rod is held by the open end and rotates in a circular motion with angular speed of 45.6 revolutions per second,

(a) What is the tension for the first half of the rod, i.e., between 0 and L if the pivot point is chosen as origin?

(b) What is the tension for the second half of the rod, i.e., between L and 2L if the pivot point is chosen as origin?

Answer 1

Answer:

Explanation:

Given

mass of balls $m= 5 kg$

$N=45.6 rev/s$

angular velocity $\omega =2\pi N=286.55 rad/s$

Length of Rod $2L=1.1 m$

Tension in the Second half of rod

$T_2=m\omega ^2(2L)=2m\omega ^2L$

$T_2=5\times (286.55)^2\times 1.1$

$T_2=451.609 kN$

For First Part

$T_1-T_2=m\omega ^2L$

$T_1=T_2+m\omega ^2L$

$T_1=3 m\omega ^2L$

$T_1=3\times 5\times (286.55)^2\times 0.55$

$T_1=677.41 kN$