Question
Asked Nov 16, 2019
15 views

The two pieces of the spacecraft are returned to their initial configuration with a period of 226.8 seconds. A radiation leak is detected in one of the engines. An escape pod from each section of the spacecraft are ejected as indicated in the figure. Notice that the direction of rotation for the two pieces of the spacecraft is also indicated in the figure.



The escape pods each have a mass of 13200 kg and are ejected with a speed of 79.13 m/s along the directions indicated in the figure with θ = 27 degrees.

What is the new period of the remaining spacecraft after the two escape pods are ejected?

 

*Original Scenario* - One way to provide artificial gravity (i.e., a feeling of weight) on long space voyages is to separate a spacecraft into two parts at the ends of a long cable, and set them rotating about their center of mass. A craft has been separated into two parts with a mass of 87900 kg each, at the ends of a cable with their centers of mass 91 m apart, rotating around the center point of the cable with a period of 226.8 seconds.

pod path
pod path
Escape Pods
help_outline

Image Transcriptionclose

pod path pod path Escape Pods

fullscreen
check_circle

Expert Answer

star
star
star
star
star
1 Rating
Step 1

Consider the total mass of the system before the pods are removed be M, the mass of a pod after it is removed be mp, the speed of the pod be vp, and the initial period be T.

 

The given values are,

help_outline

Image Transcriptionclose

M 87900 kg d 91 m T 226.8 s m2 13200 kg =79.13 m/s

fullscreen
Step 2

There are two pods, the total angular momentum of the pods is doubled of the angular momentum of a pods. Thus, the initial angular momentum of the pods can be calculated as,

help_outline

Image Transcriptionclose

L, 2L 21,0 Ма? ) 2л =2 Т п.Ма? Т

fullscreen
Step 3

The total angular momentum of the system will be the sum of the angular momentum of the spacecraft, the angular momentum of the one pod that is at 27o which moves opposite to the rotation of the spacecraft, and the angular ...

help_outline

Image Transcriptionclose

d -v, cos270+ +mc2) (-, cos90) Lf L +LL2 L22 I,a P d? 2л d %32(м-т, M -m.v cos27° 2 4 T я(М -т,)d d mv cos27° 2

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Science

Physics