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
tiny-mole [99]
3 years ago
7

What is the distance from axis about which a uniform, balsa-wood sphere will have the same moment of inertia as does a thin-wall

ed, hollow, lead sphere of the same mass and radius R, with the axis along a diameter, to the center of the balsa-wood sphere?
Physics
1 answer:
andrey2020 [161]3 years ago
3 0

Answer:

D_{s} ≈ 2.1 R

Explanation:

The moment of inertia of the bodies can be calculated by the equation

     I = ∫ r² dm

For bodies with symmetry this tabulated, the moment of inertia of the center of mass

Sphere               Is_{cm} = 2/5 M R²

Spherical shell   Ic_{cm} = 2/3 M R²

The parallel axes theorem allows us to calculate the moment of inertia with respect to different axes, without knowing the moment of inertia of the center of mass

    I = I_{cm} + M D²

Where M is the mass of the body and D is the distance from the center of mass to the axis of rotation

Let's start with the spherical shell, axis is along a diameter

     D = 2R

    Ic = Ic_{cm} + M D²

    Ic = 2/3 MR² + M (2R)²

    Ic = M R² (2/3 + 4)

    Ic = 14/3 M R²

The sphere

    Is =Is_{cm} + M [D_{s}²

    Is = Ic

    2/5 MR² + M D_{s}² = 14/3 MR²

    D_{s}² = R² (14/3 - 2/5)

    D_{s} = √ (R² (64/15)

    D_{s} = 2,066 R

You might be interested in
The Yerkes Primate Center has existed (or has been in existence) since the 1960s and has a focus in two major areas: Immunology
dybincka [34]

Answer:

Research towards increasing the understanding of progressive illnesses, such as Parkinson’s and Alzheimer’s diseases.

Explanation:

The Yerkes Primate center was established in 1930 by Robert Yerkes, in Orange Park, Florida. But was moved to its present location in Emory University.

The center has its focus on two major area of research, which are  Immunology and Vaccine, and research towards  increasing the understanding of progressive illnesses, such as Parkinson’s and Alzheimer’s diseases.

6 0
3 years ago
Aristotle was a true scientist. True or false?
leonid [27]
No, because he was a philosopher 
4 0
3 years ago
Read 2 more answers
An airplane is flying through a thundercloud at a height of 2 000 m. (this is a very dangerous thing to do because of updrafts,
tester [92]
It is given that an<span> airplane is flying through a thundercloud at a height of 2000 m.
</span><span>
Since the parity of charges is opposite and the airplane lies between the two charges and both the electric fields are in the same direction at the plane. Therefore, the magnitudes of the electric field at the aircrafts will add up.
Now, check the image to see the calculations:

</span>

4 0
3 years ago
Read 2 more answers
Match each measurement tool with what it measures.
Zarrin [17]
Thermometer-temperature
Wind vane -wind direction
Anemometer- both wind speed (and direction)
Hygrometer- humidity
5 0
3 years ago
A cylinder with a piston contains 0.250 mol of oxygen at2.40x105 Pa and 355 K. The oxygen may be treated as an ideal gas.The gas
Nikitich [7]

Answer:

= 285 Joules

Explanation:

a) answer can be found out in attachment

(b) The temperature for the isothermal compression is the same as the temp at the end of the isobaric expansion. Since pressure is held constant but volume doubles, we use the ideal gas law:

p V = nR T          to see that the temperature also doubles.

.So...   temp for isothermal compression =   355×2 = 710 K

.(c)   The max pressure occurs at the top point. At this point, the volume is back to the original value but the temperature is twice the original value. So the pressure at this point is twice the original, or

max pressure = 2×240000 Pa =  480000 Pa  =   4.80 x 10^5 Pa

(d) total work done by the piston = workdone during isothermal compression - work done during expansion =

=  nRT ln(V initial / V final)-p (V initial - V final)

=   nRT ln(2) - nR(T final - T initial)  

= 0.250× 8.314 ×710×ln(2)-0.250×8.314× (710 - 355)

=     285 Joules

7 0
3 years ago
Other questions:
  • Radiation is energy that is (5 points) not transferred at all transferred by direct contact of two objects transferred by moving
    8·1 answer
  • What value must q2 have if the electric potential at point a is to be zero?
    15·1 answer
  • What are the characteristics and ph level of acids?
    9·1 answer
  • The gear motor can develop to 1/2 hp when it turns at 300 rev/min. If the shaft has a diameter of 1/2 in. determine the maximum
    11·1 answer
  • Gabriel is performing an experiment in which he is measuring the energy and work being done by a ball rolling down a hill.Which
    8·2 answers
  • In order to transmit information via radio waves, the waves need to be changed somehow. For car radios this can happen in two wa
    10·1 answer
  • What will most likely happen if a sound wave moves from the air through a solid
    8·1 answer
  • A heavier person will have a lower blood level due to a greater amount of ___ in their
    12·1 answer
  • How much heat does it take to raise the temperature of 10.0 kg of water by 1.0 C?
    15·1 answer
  • Why is the importance and need of environmental science increasing in today world ​
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!