Answer:
32.9242311983 m/s
1.40506567727g
35.3405770759 rpm
Explanation:
v = Linear Velocity of the capsule
[tex]a_c[/tex] = Centripetal acceleration = [tex]12.5g=12.5\times 9.81[/tex]
r = Radius of the centrifuge = 8.84 m
l = Person's height = 2 m
Centripetal acceleration is given by
[tex]a_c=\frac{v^2}{r}\\\Rightarrow v=a_cr\\\Rightarrow v=\sqrt{12.5\times 9.81\times 8.84}[/tex]
The linear speed of the capsule is 32.9242311983 m/s
The radius would be
[tex]r=\sqrt{r^2+\dfrac{l^2}{4}}\\\Rightarrow r=\sqrt{8.84^2+\dfrac{2^2}{4}}\\\Rightarrow r=8.89638128679\ m[/tex]
The centripetal acceleration
[tex]a_{c2}=\dfrac{32.9242311983^2}{8.89638128679\times 9.81}g\\\Rightarrow a_{c2}=12.4207805891g[/tex]
Change in acceleration from Pythagoras law
[tex]a=\sqrt{a_{ch}^2-a_{c2}^2}\\\Rightarrow a=\sqrt{12.5^2g^2-12.4207805891^2g^2}\\\Rightarrow a=1.40506567727g[/tex]
The difference is 1.40506567727g
Velocity
[tex]v=\omega r\\\Rightarrow v=2\pi Nr\\\Rightarrow N=\dfrac{v}{2\pi r}\\\Rightarrow N=\dfrac{32.9242311983}{2\pi 8.89638128679}\\\Rightarrow N=0.589009617932\ rev/s[/tex]
[tex]N=0.589009617932\times 60=35.3405770759\ rpm[/tex]
The speed is 35.3405770759 rpm
