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

5076.5

Step-by-step explanation:

Answer 2

L = 5076.5 kg m² / s

Step-by-step 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)` =
`(1)/(M) \sum x_(i) m_(i)`i

x_{cm} =
`(1)/(m+m) ( 0 + l m)`

x_{cm} =
`(1)/(2m) lm`

x_{cm} =
`(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