Know 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 at which the centrifuge should be operated, we need to use the relationship between the centripetal force acting on the red blood cell and the angular speed of the centrifuge.
1. Start by expressing the centripetal force acting on the red blood cell using the formula for centripetal force: F = m * ω^2 * r, where F is the force, m is the mass, ω is the angular speed, and r is the radius.
2. Rearrange the formula to solve for the angular speed (ω): ω^2 = F / (m * r).
3. Substitute the given values into the formula: F = 4.0 x 10^-11 N, m = 3.0 x 10^-16 kg, and r = 14.0 cm (convert to meters by dividing by 100).
4. Calculate ω^2: ω^2 = (4.0 x 10^-11 N) / ((3.0 x 10^-16 kg) * (0.14 m)).
5. Take the square root of ω^2 to find ω: ω = sqrt((4.0 x 10^-11 N) / ((3.0 x 10^-16 kg) * (0.14 m))).
6. Finally, convert the angular speed from radians per unit of time to revolutions per unit of time by multiplying by (1 / (2π)).
This will give you the number of revolutions per second at which the centrifuge should be operated.
To find the number of revolutions per second at which the centrifuge should be operated, we can use the following steps:
1. Start with the force acting on the red blood cell, given as 4.0 x 10^-11 N.
2. Multiply the force by the radius of the centrifuge, which is 14.0 cm (convert it to meters by dividing by 100):
F = 4.0 x 10^-11 N * 0.14 m = 5.6 x 10^-12 kg·m/s^2.
3. Calculate the gravitational force acting on the red blood cell by multiplying its mass with the acceleration due to gravity, g:
Fg = m * g = (3.0 x 10^-16 kg) * 9.8 m/s^2 = 2.94 x 10^-15 N.
4. Equate the gravitational force to the force acting on the red blood cell as it settles out of the plasma:
Fg = F => 2.94 x 10^-15 N = 5.6 x 10^-12 kg·m/s^2.
5. Rearrange the equation to solve for the acceleration of the red blood cell:
a = F/m = (5.6 x 10^-12 kg·m/s^2) / (3.0 x 10^-16 kg) ≈ 1.87 x 10^4 m/s^2.
6. The acceleration of an object moving in a circular path is given by a = r * ω^2, where r is the radius and ω is the angular velocity.
7. Rearrange the equation to solve for the angular velocity:
ω = √(a / r) = √[(1.87 x 10^4 m/s^2) / (0.14 m)] ≈ 141.4 rad/s.
8. Finally, convert the angular velocity from radians per second to revolutions per second:
ω = 141.4 rad/s * (1 revolution / 2π rad) ≈ 22.5 revolutions/s.
Therefore, the centrifuge should be operated at approximately 22.5 revolutions per second.