Question

Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 40.0 s to speed up from rest to its top speed of 1 rotation every 1.50 s. The astronaut is strapped into a seat 6.20 m from the axis.What is the astronaut's tangential acceleration during the first 40.0 s?How many g's of acceleration does the astronaut experience when the device is rotating at top speed? Each 9.80 m/s^2 of acceleration is 1 g.

Answer 1

Answer

Time period T = 1.50 s

time t = 40 s

r = 6.2 m

a)

Angular speed ω = 2π/T

                              = $\dfrac{2\pi }{1.5}$  

                              = 4.189 rad/s

Angular acceleration α = $\dfrac{\omega}{t}$

                                      = $\dfrac{4.189}{40}$

                                      = 0.105 rad/s²

Tangential acceleration a = r α = 6.2 x 0.105 = 0.651 m/s²

b)The maximum speed.

       v = 2πr/T

          = $\dfrac{2\pi \times 6.2}{1.5}$

          = 25.97 m/s

So centripetal acceleration.

        a = $\dfrac{v^2}{r}$

          = $\dfrac{25.97^2}{6.2}$

          =  108.781 m/s^2

          = 11.1 g    

in combination with the gravitation acceleration.

$a_{total} = \sqrt{(11.1g)^2+g^2}$

$a_{total}= 11.145 g$