The concept required to solve the given problem is work-energy theorem in rotational kinematics.
Initially, convert the angular speed of centrifuge from rpm to radians per second by using conversion factor. Then, use work-energy theorem to find the work done on the centrifuge.
The rotational kinetic energy K of a rotating object is given by following expression.
Here, I is the moment of inertia, and is the angular speed.
According to work-energy theorem in rotational kinematics, the work done W on a rotating object is equal to change in rotational kinetic energy of the object.
Here, I is the moment of inertia, is the final angular speed, and is the initial angular speed.
The final angular speed of the centrifuge is,
Convert the units for final angular speed from rpm to radians per second.
According to work-energy theorem in rotational kinematics, the work done W on a rotating object is equal to change in rotational kinetic energy of the object.
Substitute 523.59 rad/s for 0 rad/s for and for I in the above equation.
Ans:
The work done is 4386.3 J.
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