A centrifuge for separation of sugar crystals in molasses must exert a force of 6 N/g. If the filter drum has a radius of 350 mm, determine the required speed in the revolution per minute

I tried the following
F = 6 = 10^-3*a
a = 6000 = ω^2*r

To determine the required speed in revolutions per minute (RPM) for the centrifuge, we can apply Newton's second law of motion.

The force exerted by the centrifuge (F) is given as 6 N/g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). We need to convert the force to SI units before proceeding with the calculations. As 1 N = 1 kg·m/s^2, the force in SI units is 6 N/g * 9.8 m/s^2 = 58.8 N.

To find the acceleration (a) of the centrifuge, we divide the force (F) by the mass of the object being separated. However, the problem does not provide information about the mass of the object. It only provides the force per unit of mass. Therefore, we cannot calculate the acceleration directly using Newton's second law.

However, we can use the given force (F) to calculate the acceleration due to centrifugal force (a_c). Centrifugal force is given by the equation Fc = m*a_c, where m is the mass of the object being separated.

In this case, the centrifugal force (Fc) is equal to the force exerted by the centrifuge (F), which is 58.8 N. Therefore, Fc = m*a_c = 58.8 N.

The equation for centrifugal force is also given by Fc = ω^2*r, where ω is the angular velocity (in radians per second) and r is the radius of the filter drum.

By equating the two equations for centrifugal force, we have:

m*a_c = ω^2*r

Since m is the mass of the object being separated and a_c is the acceleration due to centrifugal force, we can substitute these variables with F/(g*m) and ω^2*r, respectively:

F/(g*m) = ω^2*r

To find the required speed ω, we rearrange the equation:

ω = sqrt(F/(g*m*r))

Now, let's calculate the required speed. However, please note that we need information about the mass (m) of the object being separated in order to complete the calculation.