Zorro swings from a small chandelier, which is supported by 5 vertical chains, e

Question

Zorro swings from a small chandelier, which is supported by 5 vertical chains, each of length 6.9 m. The tension T in each chain reaches a maximum of 340 N, at the chandelier’s lowest point, when Zorro’s center-of-mass is 1 m directly below the chandelier. What is the combined angular speed, w (in rad/s), of the chains, Zorro, and the chandelier at this moment, measured with respect to the point on the ceiling where the 5 chains are attached? The chandelier weighs 126 N, while Zorro weighs 711 N. Neglect the weight of the chains.

Answer is: 1.14

Explanation / Answer

So at the point in question, we'll have two forces due to gravity pulling down, two centripetal forces pulling down and then 5 forces of tensions upward. This gives the following equation:

Wc+Wz+Fc-c+Fc-z=5T

Substituting in the known values gives:

126+711+(126/9.8)vc2/rc+(711/9.8)vz2/rz= 1700

(126/9.8)vc2/rc+(711/9.8)vz2/rz= 863

Now we can relate linear velocity to angular velocity with v=r

The angular velocity will be the same for the whole system, so substituing this in will eliminate a variable and put the variable we are looking for into the equation so:

(126/9.8)2rc+(711/9.8)2rz= 863

We can figure out the radius of the chandelier's motion is 6.9m and zorros is 7.9m

(126/9.8)2(6.9)+(711/9.8)2(7.9)= 863

661.862=863

=1.142 rad/sec

Hope that helps

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