Final answer:
The speed of the centrifuge is approximately 39.27 m/s.
Step-by-step explanation:
To find the speed of the centrifuge, we can use the formula for centripetal acceleration:
a = r * ω²
where a is the centripetal acceleration, r is the length of the centrifuge's arm, and ω is the angular velocity.
We are given the value of the centripetal acceleration as 3.04 g, which is equal to 3.04 times the acceleration due to gravity. We can convert this to meters per second squared by multiplying by 9.8 m/s², giving us a centripetal acceleration of 29.792 m/s².
Plugging in the values into the formula, we get:
29.792 m/s² = 21 m * ω²
Solving for ω, we find:
ω = sqrt(29.792 m/s² / 21 m) ≈ 1.87 rad/s
The linear speed of the centrifuge can be found by multiplying the angular velocity by the radius. Since the radius is equal to the length of the centrifuge's arm, we get:
speed = ω * r = 1.87 rad/s * 21 m ≈ 39.27 m/s
Therefore, the speed of the centrifuge is approximately 39.27 m/s.