Question

Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g (88.2 m/s2) without losing consciousness. HINT (a) If a human centrifuge has a radius of 4.91 m, what angular speed (in rad/s) results in a centripetal acceleration of 9g? rad/s (b) What linear speed (in m/s) would a person in the centrifuge have at this acceleration? m/s Need Help? Read It Watch It MY N

Answer 1

v = ωr = (4.39 rad/s)(4.91 m) ≈ 21.54 m/s

Step-by-step explanation:

(a) To calculate the angular speed (ω) of the human centrifuge that results in a centripetal acceleration of 9g, we can use the formula for centripetal acceleration: a = ω²r, where a is the centripetal acceleration, ω is the angular speed, and r is the radius of the centrifuge. Solving for ω, we get:

ω = √(a/r) = √((9g)/r)

Substituting the values for g (9.8 m/s²) and r (4.91 m), we get:

ω = √((9 * 9.8 m/s²)/(4.91 m)) ≈ 4.39 rad/s

(b) To calculate the linear speed (v) of a person in the centrifuge at this acceleration, we can use the formula v = ωr, where v is the linear speed, ω is the angular speed, and r is the radius of the centrifuge. Substituting the values for ω (4.39 rad/s) and r (4.91 m), we get:

v = ωr = (4.39 rad/s)(4.91 m) ≈ 21.54 m/s