Question

Two astronauts, each having a mass of 74.3 kg are connected by a 13.1 m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.65 m/s. a. Calculate the magnitude of the initial angular momentum of the system by treating the astronauts as particles.

Answer 1

Answer:

5076.5

Explanation:

Answer 2

Answer:

  L = 5076.5 kg m² / s

Explanation:

The angular momentum of a particle is given by

         L = r xp

         L = r m v sin θ

the bold are vectors, where the angle is between the position vector and the velocity, in this case it is 90º therefore the sine is 1

as we have two bodies

       L = 2 r m v

let's find the distance from the center of mass, let's place a reference frame on one of the masses

        $x_{cm}$ = $\frac{1}{M} \sum x_{i} m_{i}$i

        x_{cm} = $\frac{1}{m+m} ( 0 + l m)$

        x_{cm} = $\frac{1}{2m} lm$

        x_{cm} = $\frac{1}{2}$

        x_{cm} = 13.1 / 2 = 6.05 m

let's calculate

          L = 2  6.05  74.3  5.65

          L = 5076.5 kg m² / s