Dyson Sphere-Saçma sapan fizik 1 sorusu

[buZZeR]

Şöyle fantastik bi aygıttan mal bi kütleçekim sorusu çıkarmışlar:

http://en.wikipedia.org/wiki/Dyson_Sphere

Consider a solid, rigid spherical shell with a thickness of 100 m and a density of 3900 kg/m^3. The sphere is centered around the sun so that its inner surface is at a distance of 1.50×10^11 m from the center of the sun. What is the net force that the sun would exert on such a Dyson sphere were it to get displaced off-center by some small amount?

bunun cevabı 0, devamı:

What is the net gravitational force F_out on a unit mass located on the outer surface of the Dyson sphere described in Part A?

6.26×10^−3 N buldum bunu da.

What is the net gravitational force F_in on a unit mass located on the inner surface of the Dyson sphere described in Part A?

5.93×10^−3 N da bu.

Bunlarda problem yok da son şıkkı anlayabilmiş değilim:

The gravitational attraction of the sun would make the inner surface of the Dyson sphere described in Part A uninhabitable, because everything on the inner surface would slowly accelerate toward the sun. One way to solve this problem would be to create artificial gravity through rotation. Assume that the Dyson sphere rotates at a constant angular speed around an axis through its center so that earthlike gravity is re-created along the inner equator of the Dyson sphere. Take the radius of the Earth to be 6.38×10^6 m and the mass of the Earth to be 5.97×10^24 kg.

What is the linear speed v of a unit mass located at the inner equator of such a sphere?

Hint'leri var bir de sorunun, onların da pek yardımı dokunmadı.

Hint 1. How to approach the problem
Because of the constant rotation of the sphere, the mass at the inner equator moves along a circular path with constant angular speed; thus it has only a centripetal acceleration. There must be then a net force directed toward the center of the sphere. The only forces acting on the mass are the gravitational force of the sun and the normal force exerted by the surface of the sphere. To create the same gravitational conditions as on earth, the normal force exerted on the mass at the inner equator must be equal to the normal force exerted on a unit mass at earth's equator, since the normal force corresponds to the acceleration felt by a person on the inner surface of the Dyson sphere.

Hint 2. Find the net force at the inner surface of a rotating hollow sphere
Consider a spinning hollow sphere with a particle located at its center. Let F_g be the magnitude of the gravitational force that the particle exerts on a unit mass located on the inner surface of the sphere and let n be the magnitude of the normal force exerted by the surface of the sphere on the unit mass. What is the magnitude of the net force F_net acting on the unit mass?

(hintte bile problem soruo hibineler) F_g+n

Hint 3. Find the normal force acting on a unit mass on earth's surface
What is the magnitude of the normal force n acting on a unit mass located on the surface of the earth?

n=9.81 N (yerçekimi ivmesi işte, napıcaksam dünyanın kütlesini falan kullanıp bunu bulmak için)

Now use this result to find the net force acting on a unit mass at the inner equator of the Dyson sphere. Then use Newton's 2nd law to express the net force in terms of the centripetal acceleration. Recall that the centripetal acceleration is proportional to the square of the linear speed.

Hint 4. Equation for centripetal acceleration

Recall that the equation relating the centripetal acceleration a_c of an object spinning about a point a distance r away at a speed v is given by:

a_c = v^2/r

Bu kadar şeye rağmen çözemedim ben bu kıçı kırık soruyu. Evet.

[buZZeR]

işlem hatası yapmışım ondan olmuomuş sorun yok tamam. isteyen piskopat buyursun çözsün tabi.