2 questions regarding circular motion and the law of gravity

In summary: so to find the angular velocity needed, just divide 1000 by the radius of the arm in cm and that will give you the angular velocity needed.
  • #1
Koolaid
11
0
hello i am new to the forums. But I have been working on a packet of problems and I got them all done but i have been stuck on these two for a good hour. I have tried to search to internet for possible equations i could use but can't find any that will work or maybe i am just over looking them so i decided to post here and see what some other peoples thoughts are. But I am looking for some guidance on what equations to use.

~Thanks in advance

Homework Statement



An Earth satellite is orbiting at a distance from the Earth's surface equal to one Earth radius (4000miles). At this location, the acceleration due to gravity is what factor times the value of g at the Earth's surface?

-thoughts
i think I am ight be using

F = GMm/r@2

where G is the universal gravitational constant.

G = 6.67*10-11 N-m2/kg2

and F = mg2. Homework Statement

What angular velocity (in revolutions/second) is needed for a centrifuge to produce an acceleration of 1000g at a radius arm of 15cm?

-thoughts

none at the moment
 
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  • #2
Hi, koolaid. Welcome to PF!

Here are a couple of hints:

#1: Usually, how would you go about finding g at a point at some distance from an object?

#2 What kind of acceleration does the object undergo?
 
  • #3
neutrino said:
Hi, koolaid. Welcome to PF!

Here are a couple of hints:

#1: Usually, how would you go about finding g at a point at some distance from an object?

#2 What kind of acceleration does the object undergo?


well for #1 i updated my post

for #2 wouldn't be tangetal acceleration so [tangetal acceleration = radius * angular acceleration] (a=r*a) right?
or would it be centripetal acceleration i am not sure [ centripetal acceleration = tangental velocity squared / radius] (a=v^2/r)
 
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  • #4
Koolaid said:
well for #1 i updated my post
Well, what you've provided is the force on an object of mass 'm' (or 'M') due to the other. The acceleration would be GM/r2 (assuming M is the Earth's mass). You have been provided the distance (from the centre) as twice the Earth's radius. Use that to find that to find the acceleration as a multiple of g (at the surface of the Earth).
for #2 wouldn't be tangetal acceleration so [tangetal acceleration = radius * angular acceleration] (a=r*a) right?
or would it be centripetal acceleration i am not sure [ centripetal acceleration = tangental velocity squared / radius] (a=v^2/r)

Since it has not been mentioned that the speed is changing, it mustrefer to the centripetal accelaration. Write it down in terms of the angular velocity.
 
  • #5
#1. still don't know g or m cause you only have G = 6.67E-11 and r = 4000mi = 6.437E6 m then multiply by 2 = 1.2874E7 m .

#2. a=rw [ centripetal acceleration = radius * angular velocity]
 
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  • #6
Koolaid said:
#1. still don't know g or m cause you only have G = 6.67E-11 and r = 4000mi = 6.437E6 m then multiply by 2 = 1.2874E7 m .

You need not know the values. Moreover, m is not needed since the answer requires you to find only the acceleration due to gravity.

g(r) = GM/r^2

r = 2R , where R is Earth's radius. Therefore,

g(r) = GM/(2R)^2
...
Can you do it from here?
...

#2. a=rw [ centripetal acceleration = radius * angular velocity]
The magnitude of centripetal acceleration = w^2*r
 
  • #7
i am still lost.. i am just not really making the "connection" for both
 
  • #8
Koolaid said:
[An Earth satellite is orbiting at a distance from the Earth's surface equal to one Earth radius (4000miles). At this location, the acceleration due to gravity is what factor times the value of g at the Earth's surface?
You "need" practically none of the values you have given because the question asks "what factor times the value of g at the Earth's surface". That is, the acceleration at twice the distance from the center of the earth is what number times the acceleration at the surface of the earth? You are really only asked how gravitational accelaration depends on distance from the center of the earth. You don't need to know G, you don't need to know the mass of the earth, you don't need to know the radius of the earth. And, although you must use it, you don't even need to know g! (g, the acceleration due to gravity at the Earth's surface is 9.81 m/s2.)

(And be careful not to confuse "G" with "g"!)

What angular velocity (in revolutions/second) is needed for a centrifuge to produce an acceleration of 1000g at a radius arm of 15cm?
You should know the formula: [itex]a= R \omega^2[/itex] where a is the accelleration, R is the radius arm and [itex]\omega[/itex] is the angular velocity (in radians/second- there are [itex]2\pi[/itex] radians in one revolution).
 
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  • #9
ok i got the first question all done.

What angular velocity (in revolutions/second) is needed for a centrifuge to produce an acceleration of 1000g at a radius arm of 15cm?

but for question 2. i am not sure how to incorporate the 1000 g into the problem.

the radius also needs to be in meters os its .15 meters
 
  • #10
Koolaid said:
ok i got the first question all done.



but for question 2. i am not sure how to incorporate the 1000 g into the problem.

the radius also needs to be in meters os its .15 meters

1000g means one thousand times the acceleration due to gravity [on earth], i.e. [itex]1000 \times 9.81[/itex]. So, to rephrase the question, what is the angular velocity required such that the centripetal acceleration is 9810m/s2?
 
  • #11
wow those were simple now that I think about it lol… well now i understand them.. thank you to everyone that helped
 

1. What is circular motion and how is it related to the law of gravity?

Circular motion is the movement of an object along a circular path. It is related to the law of gravity because the force of gravity acts as a centripetal force, causing objects to move in a circular path around a larger object.

2. How does the mass and distance between objects affect the force of gravity in circular motion?

The force of gravity in circular motion is directly proportional to the mass of the objects involved. This means that as the mass of one or both objects increases, the force of gravity also increases. The distance between the objects also affects the force of gravity, with an increase in distance resulting in a decrease in the force of gravity.

3. Can an object be in circular motion without the force of gravity?

No, circular motion requires a centripetal force to keep the object moving in a circular path. The force of gravity is the most common centripetal force, but other forces such as tension or friction can also act as a centripetal force.

4. What is the difference between circular motion and elliptical motion?

Circular motion is when an object moves in a perfect circle, while elliptical motion is when an object moves in an oval or elliptical path. The force of gravity is still responsible for both types of motion, but the shape of the path is determined by the speed and direction of the object's motion.

5. How does the law of gravity apply to objects in the solar system?

The law of gravity applies to objects in the solar system in the same way it applies to objects on Earth. The larger objects such as planets and moons exert a stronger force of gravity due to their larger mass, while smaller objects such as comets and asteroids have a weaker force of gravity. This force of gravity keeps objects in orbit around larger objects, creating the circular or elliptical motion observed in the solar system.

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