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
Ira Lisetskai [31]
3 years ago
13

A satellite in the shape of a solid sphere of mass 1,900 kg and radius 4.6 m is spinning about an axis through its center of mas

s. It has a rotation rate of 8.0 rev/s. Two antennas deploy in the plane of rotation extending from the center of mass of the satellite. Each antenna can be approximated as a rod of mass 150.0 kg and length 6.6 m. What is the new rotation rate of the satellite (in rev/s)
Physics
1 answer:
konstantin123 [22]3 years ago
5 0

Answer:

Therefore, the new rotation rate of the satellite is 6.3 rev/s.

Explanation:

The expression for conservation of the angular momentum (L) is

L_{i} = L_{f}  I_{i}\times\omega_{i} = I_{f}\times\omega_{f}

Where

I_{i}\ and \ \omega_{i} initial moment of inertia and angular velocity

I_{f}\ and \ \omega_{f} is the final moment of inertia and angular velocity

The expression of moment of inertia of the satellite (a solid sphere) is

I_{i} = \frac{2}{5}m_{s}r^{2}

Where m_{s} is the satellite mass

r is the  radus of the sphere

Substititute 1900kg for m and 4.6m for r

I_{i} = \frac{2}{5}m_{s}r^{2}\\\\ = \frac{2}{5}\times1900 kg\times (4.6 m)^{2} \\\\= 1.61 \cdot 10^{4} kgm^{2}

The final moment of inertia of the satellite about the centre of mass

I_{f} = I_{i} + 2\timesI_{x} \\\\= 1.61 \cdot 10^{4} kgm^{2} + 2\times\frac{1}{3}m_{x}l^{2}

Where m_{x} is the antenna's mass and

I is the length of the antenna

I_{f} = 1.61 \cdot 10^{4} kgm^{2} + 2\times\frac{1}{3}150.0 kg\times(6.6 m)^{2} \\\\= 2.05 \cdot 10^{4} kgm^{2}

So, the Final rotation rate of the satellite is:

I_{i}\times\omega_{i} = I_{f}\times\omega_{f} \\\\\omega_{f} = \frac{I_{i}\times\omega_{i}}{I_{f}} \\\\= \frac{1.61 \cdot 10^{4} kgm^{2}\times8.0 \frac{rev}{s}}{2.05 \cdot 10^{4} kgm^{2}} \\\\= 6.3 rev/s

Therefore, the new rotation rate of the satellite is 6.3 rev/s.

You might be interested in
A screw having 50% efficiency is driven by a rod and 25 cm. The pitch of the screw is 1/10cm Calculate velocity ratio and mechan
neonofarm [45]

(a) The velocity ratio of the screw is 1570.8.

(b) The mechanical advantage of the screw is 785.39.

<h3>Velocity ratio of the screw</h3>

The velocity ratio of the screw is calculated as follows;

V.R = 2πr/P

where;

  • P is the pitch = 1/10 cm = 0.1 cm = 0.001 m
  • r is radius = 25 cm = 0.25 m

V.R = (2π x 0.25)/(0.001)

V.R = 1570.8

<h3>Mechanical advantage of the screw</h3>

E = MA/VR x 100%

0.5 = MA/1570.8

MA = 785.39

Learn more about mechanical advantage here: brainly.com/question/18345299

#SPJ1

4 0
2 years ago
What happens when the objects submerged in a fluid at rest?​
Talja [164]
It will act upon a buoyant force on the magnitude of which is equal to weight of the fluid
3 0
2 years ago
A 180 cm length of string has a mass of 5.0 g. it is stretched with a tension of 8.6 n between fixed supports. (a) what is the w
Svetlanka [38]
P               U               S                 S                 Y


<span>Joy is planning to purchase a sweater that costs $30 dollars at her local department store. The sweaters are on sale for 20% off. Which steps are needed to find the sale price of the sweater?</span>
5 0
3 years ago
In a large centrifuge used for training pilots and astronauts, a small chamber is fixed at the end of a rigid arm that rotates i
RSB [31]

a) The length of the arm of the centrifuge is 10.9 m

b) The angular acceleration is 2.7 rad/s^2

Explanation:

a)

In a uniform circular motion, the centripetal acceleration is given by

a_c=\omega^2 r

where:

\omega is the angular speed of the circular motion

r is the radius of the circle

For the centrifuge in this problem, we have:

\omega=1.7 rad/s is the angular speed

The centripetal acceleration is 3.2 times the acceleration due to gravity (g=9.8 m/s^2), so:

a_c=3.2 g = 3.2(9.8)=31.4 m/s^2

Therefore, we can re-arrange the previous equation to find r, the radius of the circle (which corresponds to the length of the arm of the centrifuge):

r=\frac{a_c}{\omega^2}=\frac{31.4}{1.7^2}=10.9 m

b)

In the second part of the exercise, the centrifuge speeds up from an initial angular speed of 0 to a final angular speed of 1.7 rad/s. The total acceleration experienced at the final moment is

a=4.4 g

So, 4.4 times the acceleration due to gravity.

The total acceleration is the resultant of the centripetal acceleration (a_c) and the tangential acceleration (a_t):

a=\sqrt{a_c^2+a_t^2}

We know that:

a = 4.4g

a_c = 3.2 g

So, we can find the tangential acceleration:

a_t = \sqrt{a^2-a_c^2}=\sqrt{(4.4g)^2-(3.2g)^2}=29.6 m/s^2

The angular acceleration is related to the tangential acceleration by

\alpha = \frac{a_t}{r}

where r = 10.9 m is the length of the centrifuge. Substituting,

\alpha = \frac{29.6}{10.9}=2.7 rad/s^2

Learn more about centripetal and angular acceleration here:

brainly.com/question/2562955

brainly.com/question/9575487

brainly.com/question/9329700

brainly.com/question/2506028

#LearnwithBrainly

8 0
3 years ago
A(n) 93 kg clock initially at rest on a horizontal floor requires a(n) 610 N horizontal force to set it in motion. After the clo
denpristay [2]

Answer:0.669

Explanation:

Given

mass of clock 93 kg

Initial force required to move it 610 N

After clock sets in motion it requires a force of 514 N to keep moving it with a constant velocity

Initially static friction is acting which is more than kinetic friction

thus 613 force is required to overcome static friction

\mu _smg=610

\mu _s\times 93\times 9.8=610

\mu _s=0.669

5 0
3 years ago
Other questions:
  • a soccer player kicks a ball with a speed of 30 m/s at an angle of 10. how long does the ball stay in the air?
    12·2 answers
  • The force generated by a long muscle varies as it contracts through its range of movement. At which point is the greatest force
    7·1 answer
  • How much work is required to pull a wagon 6 meters if you use 70 N of force?
    9·1 answer
  • A frog falls from its rainforest tree. If we ignore wind resistance, (a) how much time does it take the frog to fall a distance
    15·1 answer
  • Replace oxygen sensor but light still on
    7·1 answer
  • A beam of unstable K mesons, traveling at a speed of 32c, passes through two counters 9.00 m apart. The particles suffer a negli
    6·1 answer
  • Which best illustrates projectile motion
    12·2 answers
  • Question 25
    10·1 answer
  • Which statement best describes the difference between acceleration and velocity?
    10·1 answer
  • How many neutrons are in the nucleus of an atom with an atomic mass of 80 A.M.U. and an atomic number of 35?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!