hi i have a physics question i don't understand
here is the question
A sample of blood is placed in a centrifuge of radius 15 cm. the mass of the corpuscle is 3.0*10^-16 kg, and the magnitude of the force required to make it settle out of the plasma is 4.0X10^-11 N. At how many revolutions per second should the centrifuge be operated?
thanks
Force= centripetal force
Force= m(radius*angular speed)
r is in meters.
solve for angular speed, it will be in radians/sec. To convert it to rev/sec, divide by 2pi.
To solve this question, we can start by rearranging the formula for centripetal force:
Force = m * (radius * angular speed)
Where:
- Force is the magnitude of the force required to make the corpuscle settle out of the plasma (4.0 * 10^-11 N)
- m is the mass of the corpuscle (3.0 * 10^-16 kg)
- radius is the radius of the centrifuge (15 cm = 0.15 m)
- angular speed is what we need to calculate
Now we can substitute the values into the equation:
4.0 * 10^-11 N = (3.0 * 10^-16 kg) * (0.15 m * angular speed)
Next, let's solve for the angular speed. Dividing both sides of the equation by (3.0 * 10^-16 kg * 0.15 m):
(4.0 * 10^-11 N) / (3.0 * 10^-16 kg * 0.15 m) = angular speed
Using a calculator, you'll get:
angular speed = 8.888... * 10^12 rad/s (radians per second)
To convert this angular speed to revolutions per second, divide by 2π (approximately 6.28):
revolutions per second = (8.888... * 10^12 rad/s) / (2π)
Using a calculator, you'll get:
revolutions per second ≈ 2.82 * 10^12 rev/s
Therefore, the centrifuge should be operated at approximately 2.82 * 10^12 revolutions per second for the corpuscle to settle out of the plasma.