Answer :
Answer:
1000 kgm²/s, 400 J
1000 kgm²/s, 1000 J
600 J
Explanation:
m = Mass of astronauts = 100 kg
d = Diameter
r = Radius = [tex]\frac{d}{2}[/tex]
v = Velocity of astronauts = 2 m/s
Angular momentum of the system is given by
[tex]L=mvr+mvr\\\Rightarrow L=2mvr\\\Rightarrow L=2\times 100\times 2\times 2.5\\\Rightarrow L=1000\ kgm^2/s[/tex]
The angular momentum of the system is 1000 kgm²/s
Rotational energy is given by
[tex]K=I\omega^2\\\Rightarrow K=\frac{1}{2}(mr^2)\left(\frac{v}{r}\right)^2\\\Rightarrow K=mv^2\\\Rightarrow K=100\times 2^2\\\Rightarrow K=400\ J[/tex]
The rotational energy of the system is 400 J
There no external toque present so the initial and final angular momentum will be equal to the initial angular momentum 1000 kgm²/s
[tex]L_i=L_f\\\Rightarrow 2mv_ir_i=2mv_fr_f\\\Rightarrow v_f=\frac{v_ir_i}{r_f}\\\Rightarrow v_f=\frac{2\times 2.5}{0.5}\\\Rightarrow v_f=10\ m/s[/tex]
Energy
[tex]E_2=mv_f^2\\\Rightarrow E_2=100\times 10\\\Rightarrow E_2=1000\ J[/tex]
The new energy will be 1000 J
Work done will be the change in the kinetic energy
[tex]W=E_2-E\\\Rightarrow W=1000-400\\\Rightarrow W=600\ J[/tex]
The work done is 600 J