no matter how i work it out, i keep getting the wrong answers. please help!!! i only have two more submissions before it closes on me.
A sample of blood is placed in a centrifuge of radius 14.0 cm. The mass of a red blood cell is 3.0 x 10^-16 kg, and the magnitude of the force acting on it as it settles out of the plasma is 4.0 x 10^-11 N. At how many revolutions per second should the centrifuge be operated?
To find the number of revolutions per second the centrifuge should be operated at, we can use the relationship between force, mass, and centripetal acceleration. The centripetal force acting on the red blood cell is given by the equation:
F = m * (v^2 / r)
Where F is the force, m is the mass, v is the velocity of the object, and r is the radius of the centrifuge.
In this problem, we are given the mass of the red blood cell (m = 3.0 x 10^-16 kg) and the force acting on it (F = 4.0 x 10^-11 N). The radius of the centrifuge (r) is also given as 14.0 cm, which we need to convert to meters (since SI units are used in physics).
r = 14.0 cm = 0.14 m (converting cm to m)
We can rearrange the equation for centripetal force to solve for the velocity (v):
v = sqrt((F * r) / m)
Now, we have all the values needed to calculate the velocity. Plugging in the numbers:
v = sqrt((4.0 x 10^-11 N * 0.14 m) / 3.0 x 10^-16 kg)
v = sqrt(5.6 x 10^-12 N*m / 3.0 x 10^-16 kg)
v = sqrt(1.87 x 10^4 m^2/s^2)
v ≈ 136.7 m/s
Finally, we need to convert the velocity to revolutions per second. Since the centrifuge completes one revolution when a point on its edge travels a distance equal to its circumference (2πr), the velocity can be related to the number of revolutions per second (f) by:
v = 2πrf
Rearranging the equation to solve for f:
f = v / (2πr)
Plugging in the velocity and radius values:
f = 136.7 m/s / (2π * 0.14 m)
f ≈ 153.6 revolutions per second
Therefore, the centrifuge should be operated at approximately 153.6 revolutions per second.
r = .14 meter
w = omega, angular rate in radians/sec
Ac = w^2 r
F = m Ac
4*10^-11 = 3 *10^-16 (w^2)(.14)
w^2 = 9.52 * 10^5 = 95.2 * 10^4
w = 9.76 * 10^2 radians/second
rev = 2 pi radians
976 rad/s * 1 rev/2pi rad = 155 rev/s