A typical red blood cell has a mass of 3.0 10-16 kg. A blood sample placed in a centrifuge is subjected to a force of 4.6 10-11 N when the centrifuge is operated at 138 rev/s. What is the diameter of the centrifuge?

To determine the diameter of the centrifuge, we first need to determine its radius. Let the radius be r. To do this, we'll make use of the centripetal force formula, which is given by:

Fc = m*a

where Fc is the centripetal force acting on the red blood cell (4.6 * 10^-11 N), m is the mass of the red blood cell (3.0 * 10^-16 kg), and a is the centripetal acceleration.

The centripetal acceleration of an object rotating in a circle is given by the formula:

a = r*w^2

where r is the radius of the circle, and w is the angular velocity of the object (in radians per second).

First, we need to convert the given revolutions per second (138 rev/s) to radians per second:

Angular velocity (w) = (138 rev/s) * (2 * pi radians/rev) = 866.04 radians/s

Now, we can substitute the centripetal acceleration formula into the centripetal force formula:

Fc = m * r * w^2

We want to solve for r (radius), so let's rearrange the equation:

r = Fc / (m * w^2)

Now, plug in the values:

r = (4.6 * 10^-11 N) / ((3.0 * 10^-16 kg) * (866.04 radians/s)^2)

After calculating, we get:

r ≈ 0.029 m

Now double that value to get the diameter:

Diameter = 2 * r ≈ 2 * 0.029 m ≈ 0.058 m

So, the diameter of the centrifuge is approximately 0.058 meters or 58 mm.

To find the diameter of the centrifuge, we can use the following equation:

F = (m * v^2) / r

Where:
F is the centrifugal force (4.6 * 10^-11 N)
m is the mass of the red blood cell (3.0 * 10^-16 kg)
v is the angular velocity (in radians per second) (138 rev/s * 2π rad/rev)
r is the radius of the centrifuge (unknown)

First, let's calculate the angular velocity in radians per second:

v = 138 rev/s * 2π rad/rev
v = 276π rad/s

Now, let's rearrange the equation to solve for the radius (r):

r = (m * v^2) / F

Plug in the given values:

r = (3.0 * 10^-16 kg * (276π rad/s)^2) / (4.6 * 10^-11 N)

Now, let's calculate it:

r ≈ 8.85 * 10^-5 m

Finally, to find the diameter, multiply the radius by 2:

diameter = 2 * r
diameter ≈ 2 * 8.85 * 10^-5 m
diameter ≈ 1.77 * 10^-4 m

Therefore, the diameter of the centrifuge is approximately 1.77 * 10^-4 meters.

To determine the diameter of the centrifuge, we need to use the formula for centripetal force:

Fc = (mv²) / r

Where:
- Fc is the centripetal force
- m is the mass of the object
- v is the velocity of the object
- r is the radius (or diameter) of the circular path

In this case, the centripetal force is given as 4.6 x 10^-11 N, the mass of the object (red blood cell) is 3.0 x 10^-16 kg, and the velocity is given as 138 rev/s.

First, let's calculate the velocity in meters per second (m/s):
Since the revolution per second (rev/s) is a unit of angular velocity, we need to convert it to linear velocity to use in the equation.

The linear velocity, v, can be calculated using the formula:
v = ωr

Where:
- ω is the angular velocity (138 rev/s)
- r is the radius (or diameter) of the circular path (which we want to find)

We need to find the radius (or diameter) first. Let's consider that the centrifuge is operating in a circular path. A blood cell is moving along this path.

Rearranging the equation ω = v / r, we have:
r = v / ω

Now, substitute the given angular velocity and calculate the radius:
r = v / ω
r = 2πr / T

Where:
- T is the time for one revolution (which we can calculate as 1 / rev/s)
- r is the radius

Let's calculate the radius in meters:
T = 1 / (138 rev/s) = 0.00724637681 s/rev (rounded)

The radius of the circular path is:
r = v / ω
r = (2π * r) / T

Next, let's calculate the centripetal force using the given mass:
Fc = (mv²) / r
Fc = (3.0 x 10^-16 kg) * (v²) / r

Now, we can rearrange the formula to solve for r:
r = (3.0 x 10^-16 kg) * (v²) / Fc

Finally, substitute the given values and calculate the radius:
r = [(3.0 x 10^-16 kg) * (2π * r / 0.00724637681 s/rev)²] / (4.6 x 10^-11 N)

Solving this equation for r should give us the radius (or diameter) of the centrifuge.