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 spherical, non-conducting shell of inner radius = 10 cm and outer radius = 15 cm carries a total charge Q = 13 μC distributed
Vaselesa [24]

Answer:

E = 1580594.95 N/C

Explanation:

To find the electric field inside the the non-conducting shell for r=11.2cm you use the Gauss' law:

\int EdS=\frac{Q_{in}}{\epsilon_o}   (1)

dS: differential of the Gaussian surface

Qin: charge inside the Gaussian surface

εo: dielectric permittivity of vacuum =  8.85 × 10-12 C2/N ∙ m2

The electric field is parallel to the dS vector. In this case you have the surface of a sphere, thus you have:

\int EdS=ES=E(4\pi r^2)   (2)

Qin is calculate by using the charge density:

Q_{in}=V_{in}\rho=\frac{4}{3}(r^3-a^3)\rho  (3)

Vin is the volume of the spherical shell enclosed by the surface. a is the inner radius.

The charge density is given by:

\rho=\frac{Q}{V}=\frac{13*10^{-6}C}{\frac{4}{3}\pi((0.15m)^3-(0.10m)^3)}\\\\\rho=1.30*10^{-3}\frac{C}{m^3}

Next, you use the results of (3), (2) and (1):

E(4\pi r^2)=\frac{4}{3\epsilon_o}(r^3-a^3)\rho\\\\E=\frac{\rho}{3\epsilo_o}(r-\frac{a^3}{r^2})

Finally, you replace the values of all parameters, and for r = 11.2cm = 0.112m you obtain:

E=\frac{1.30*10^{-3}C/m^3}{3(8.85*10^{-12}C^2/Nm^2)}((0.112m)-\frac{(0.10)^3}{(0.112m)^2})\\\\E=1,580,594.95\frac{N}{C}

hence, the electric field is 1580594.95 N/C

7 0
3 years ago
How many Joules of potential
s2008m [1.1K]

Answer:

40 j, 80j.

Explanation:

P.E= mgh. G=10 m/s².

For 4m, P.E=1*10*4=40 joules.

For 8m, P.E=1*10*8=80 joules.

4 0
3 years ago
Help.. mee..<br><br><br> ;-; <br> Dont answer if you dont know I dont want to fail this
timama [110]

Answer:

It would be B because the warm air heats up and then burns the marshmallow. And the heat and the marshmallow were touching each other

Explanation:

5 0
2 years ago
Read 2 more answers
Are you like you are because of your genes or because of your environment?
meriva
You are who you are because of your enviorment. It depends if your in a healthy environment or a toxic one which changes your act. (Hope this helps)
5 0
3 years ago
Read 2 more answers
Before the start of a trip, air in a tire is at 320 kPa gage pressure and 27°C temperature. At the end of the trip the tire pres
tia_tia [17]

Answer:

The temperature of air in the tire is 55.57 ºC

Explanation:

Please look at the solution in the attached Word file

Download docx
7 0
3 years ago
Other questions:
  • What’s the maximum height of the second hill? Use your answer from part E and the formula PE=m•g•h to determine the answer. Assu
    8·2 answers
  • Write any two importance of health education​
    15·1 answer
  • Raven throw a baseball directly downward from a terrace froma speed of 5.0 m/s. How fast it will be moving when it hits the path
    13·1 answer
  • Torque can be calculated by multiplying the force
    5·1 answer
  • True or False. If a desk is pushed at a
    13·1 answer
  • (a) If a flea can jump straight up to a height of 0.440 m, what is its initial speed as it leaves the ground? (b) How long is it
    12·1 answer
  • Two blocks, 1 and 2, are connected by a rope R1 of negligible mass. A second rope R2, also of negligible mass, is tied to block
    10·1 answer
  • Mind being a helping hand? I know ABSOLUTELY nothing about air resistance.. It's still science for me so I guess I'll put it as
    8·1 answer
  • Sally and Sam are in a spaceship that comes to within 16,000 km of the asteroid Ceres. Determine the force Sally experiences, in
    9·1 answer
  • Q/C S Starting with the definition of work, prove that at every point on an equipotential surface, the surface must be perpendic
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!