1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nuetrik [128]
2 years ago
9

One way to provide artificial gravity (i.e., a feeling of weight) on long space voyages is to separate a spacecraft into two par

ts at the ends of a long cable, and set them rotating around each other. A craft has been separated into two parts with a mass of 70600 kg each, at the ends of a cable with their centers of mass 155 m apart, rotating around the center point of the cable with a period of 385.3 seconds.
1) If the cable is reeled in so that the the centers of the two pieces are now only 119.35 m apart, what will the new period be?
2) What happens to the angular momentum L and kinetic energy K of the system consisting of both pieces of the space ship when the two pieces are pulled closer to the center?
Physics
1 answer:
stira [4]2 years ago
6 0

Answer:

1)  T = 649.86 s, 2)   L₀ = L_f,   \frac{K_o}{K_f} = 4.8

Explanation:

1) As the system of the two bodies is isolated, its angular momentum is conserved

             

initial instant.  r₀ = 155 m, T₀= 385.3 s

      L₀ = I₀ w₀

final instant. r = 119.35 m

      L_f = I w

      L₀ = L_f

      I₀ w₀ = I w

      w = \frac{I_o}{I}  \ w_o

let's consider each object as punctual

      I = m r²

at angle velocity and period are related

         w = 2pi / T

     

we substitute

      \frac{2\pi }{T} = \frac{m r^2}{m _o^2 } \ \frac{2\pi }{T_o}

      \frac{1}{T} = ( \frac{r}{r_o} )^2 \ \frac{1}{T_o}

       T = (\frac{r_o}{r} )^2 \ T_o

let's calculate

       T = ( \frac{155}{119.35} )^2 \ 385.3

        T = 649.86 s    

2) The angular momentum is conserved because the system is isolated.

Let's look for kinetic energy

        K_total = 2 K = 2 (½ I w²)

        K_total = I 4π² / T²

        K_total = 2m r² 4 π² / T²

 

for r = 155 m

         K₀ = 8π² m r₀² / T₀²

for r = 119.35 m

          K_f = 8π² m r² / T²

the relationship is

        \frac{K_o}{K_f} = ( \frac{r_o \ T}{ r \  \ T_o} )^2

        \frac{K_o}{K}  = ( \frac{ 155 \ \ \ 649.86}{ 119.35 \ 385.3})^2

       \frac{K_o}{K_f} = 4.8

You might be interested in
When an oxygen atom forms an ion, it gains two electrons. What is the electrical charge of the oxygen ion?
Mashutka [201]
-2. This is because it is gaining electrons. Electrons are negative. Therefore it is a negative charge.
6 0
3 years ago
Which of the following states of matter has a definite volume? A. liquids only B. solids only C. liquids and gases only D. solid
Naily [24]
The answer is B because solids have a definite shape and volume
8 0
3 years ago
Read 2 more answers
A skydiver is falling at constant velocity. If a force of 600 N is pulling down on the skydiver, how much force must be acting u
skelet666 [1.2K]

Well, if the skydiver is at constant velocity, than there’s no acceleration, as stated by Newton’s first law. Thus the total net force would equate to 0. In order to make this statement true, the answer would have to be exactly 600 N.

7 0
3 years ago
Read 2 more answers
John is traveling north at 20 meters/second and his friend Betty is traveling south at 20 meters/second. If north is the positiv
Tpy6a [65]
I think it's just 20/20
3 0
3 years ago
Read 2 more answers
Which statement best describes the law of conservation of energy?
Phantasy [73]
<span>The correct option is C. Energy cannot be created or destroyed. This statement is known as law of conservation of energy, and it implies that whenever a certain form of energy does change, the loss of this form of energy must have converted into an another type of energy. A typical example is an object falling to the ground: initially, the object has gravitational potential energy. As the object falls down, it loses potential energy (since its altitude from the grounf decreases), but it acquires kinetic energy (because its velocity increases). In this example, potential energy has converted into kinetic energy, but the total energy of the object has remained constant.</span>
8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the lowest level of waves on the electromagnetic energy spectrum?
    7·1 answer
  • Particles of atoms
    8·1 answer
  • You are In-line skates at the top of a small hill. Your potential energy is equal to 1000 J. The last time we checked, your mass
    9·1 answer
  • If the line graph had a broken line between the points
    14·1 answer
  • A 4.0 kilogram train going right at 6.0 meters per second bumps into a toy wagon moving the same direction at 2.0 meters per sec
    7·1 answer
  • What is one exsample of a closed economy​
    5·2 answers
  • PLEASE HELP What is it called when the moon passes through the penumbra of Earth’s shadow?(1 point)
    8·1 answer
  • A Force Play is when the defense...
    5·1 answer
  • Newton's Third Law predicts that during a collision between two carts, when the sum of the forces acting on the system are zero:
    13·1 answer
  • I need to write a police story.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!