Circular Motion - Satellites Problem

In summary, the conversation discusses two satellites, S1 and S2, orbiting the Earth at different distances and speeds. The ratio of the centripetal force on S1 to the centripetal force on S2 is found by dividing S1 by S2, resulting in a ratio of 4. The equation used is F = mvsqrd/r, with the mass being equal and constant for both satellites.
  • #1
Galileo_Galilei
9
0

Homework Statement


Two satellites of equal mass, S1 and S2, orbit the earth. S1 is orbiting at a distance r from the Earth's center at speed v. S2 orbits at a distance 2r from the Earth's center at speed (v/squareroot2) . The ratio of the centripetal force on S1 to the centripetal force on S2 is,

A. 1/8

B. 1/4

C. 4

D. 8


Homework Equations



F = mvsqrd/r


The Attempt at a Solution



I just couldn't figure this one out at all... its frustrating, i tried playing around with the equation but i kept getting nonsense.
 
Physics news on Phys.org
  • #2
You have the correct equation. Show what you did to find F_1 and F_2 (the two centripetal forces).
 
  • #3
Ok. So since the mass is equal its constant, so we just have

F = Vsquared/r

So then, S1 = Vsquared/r

S2 = (v/squareroot2)squared/2r
= (vsquared/2)/2r
= (2vsquared*r)/2


S1 = Vsquared/r

S2 = (2vsquared*r)/2


Hmm.. so now?
 
  • #4
Galileo_Galilei said:
Ok. So since the mass is equal its constant, so we just have

F = Vsquared/r

Ultimately, that's all you need, but it would be more correct to leave the mass in until the very end.

So then, S1 = Vsquared/r

Right.

S2 = (v/squareroot2)squared/2r
= (vsquared/2)/2r
= (2vsquared*r)/2

Correcct until [tex]F_{S2}=m\frac{\frac{v^2}{2}}{2r}[/tex]
Then you have an algebra error.

Hmm.. so now?

The problem asks you to take calculate a ratio, ie, divide one of the forces by the other. (Incidentally, that's why you can leave the mass in until the very end: both forces have the term 'm' so the masses cancel).
 
  • #5
Oh, yeah, algebra got me there.

So it'd have to then be:

[tex] S2 = {\frac{v^2}{4r}}[/tex]

Ah, so now it gives me a much simpler division to do. When i divide those S1/S2 after multiplying and cancelling i get 4r/r.

Awesome, so the answer is 4. Thanks for pointing out the algebra mistake.
 

1. What is circular motion?

Circular motion is a type of motion in which an object moves along a circular path at a constant speed. This type of motion is characterized by a centripetal force, which continuously pulls the object towards the center of the circle.

2. How do satellites stay in orbit?

Satellites stay in orbit due to a balance between their forward motion and the pull of gravity towards the center of the Earth. This creates a circular motion around the Earth, allowing the satellite to stay in its designated orbit.

3. How is the speed of a satellite calculated?

The speed of a satellite in orbit can be calculated using the formula: v = √(GM/r), where v is the speed, G is the gravitational constant, M is the mass of the Earth, and r is the distance between the satellite and the center of the Earth.

4. What factors affect the orbit of a satellite?

The orbit of a satellite can be affected by several factors, including the mass and size of the satellite, the altitude of the orbit, and the gravitational pull of other celestial bodies, such as the Moon and the Sun.

5. How does the orientation of a satellite affect its orbit?

The orientation of a satellite, also known as its inclination, can affect its orbit by changing the angle at which it orbits around the Earth. A higher inclination can result in a more elliptical orbit, while a lower inclination can create a more circular orbit.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
618
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
799
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
8
Views
1K
Back
Top