Find Gravitational & Centripetal Forces on Mass in Rotating Sphere

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In summary, the homework statement says that there is a sphere with the mass of the Earth and the same radius that rotates at a constant speed. The sphere has the same period as the Earth and has a mass of a kg that sits on the surface. There is a grav force on the mass and a centripetal force on the mass. The difference in magnitude between the two forces is not known, but it is suggested that the acceleration of free fall for the mass is around 9.8 m/s2.
  • #1
Jamessamuel
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Homework Statement


There's a sphere with the mass of the Earth and same radius.It rotates at constant speed. It hhas the period of the earth. a mass of a kg sits on the surface.
1) find grav force on mass
2) find centripetal force on mass
3) find the difference in magnitude between them
4) suggest a value of acceleration of free fall for the mass.

Homework Equations

The Attempt at a Solution


Cant do last part; the way I see it is that the centripetal force does not exist separately; it is criteria for circular motion at constant speed. So clearly the gravitational force over-provides, but I don't understand how this excess is related to the acceleration.
 
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  • #2
What is the definition of "free fall"?

Note for (2): latitude is not given.
 
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  • #3
Motion where the only force acting is weight
 
  • #4
So what is the weight of the object close to the surface?
 
  • #5
mg, where g is the GFS at that point, so is it the grav force?
 
  • #6
When you say latitude isn't given, what is the significance of that?
 
  • #7
mg, where g is the GFS at that point, so is it the grav force?
No - you are asked to find the acceleration.
Acceleration and force are different physical concepts - important not to mix them up.
What the question is basically asking is what the acceleration would be if there was no ground to stop it falling.
(Note: the centripetal force is the difference between the object's weight and the normal force to the surface.)

When you say latitude isn't given, what is the significance of that?
Compare the centripetal force sitting on the equator to that when sitting on a pole.
What about latitudes in between?
 
  • #8
Jamessamuel said:
When you say latitude isn't given, what is the significance of that?
How far is the mass from the axis of rotation.
By the way, I agree with you that it is not right to ask what is the centripetal force on the mass. It would be better to ask what centripetal force is required by the mass in order to stay on the surface.
 
  • #9
Haruspex - its a whole radius away isn't it?
Mr.Bridge- so if we removed the surface the reaction force would disappear. The only acting force would be the grav force?
 
  • #10
1433761790376.jpg
 
  • #11
Jamessamuel said:
Haruspex - its a whole radius away isn't it?
How far are you away from the Earth's axis of rotation now?
 
  • #12
Pretty far , I am english so certainly on a smaller radius than the mass in the question, which is on the equator.
 
  • #13
The acceleration due to gravity and centripetal force are in the same direction if you are on the equator. I would use the equator as your teacher probably expected. Then it's easy to add the two acceleration vectors together. And g is easy if we use the standard r at the equator. And then Ac is easy if we use the equator. Note you will have to find v by looking up r. I'm thinking this is what your teacher wants you to do.

And the gravitational force idea just states that any two masses attract each other with the same force. But one can also see that an object on the surface is also changing direction( if not exactly on a rotational pole) so there must be centripetal force as well. And Fc Is supplied by the force of gravity.
 
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  • #14
The actual question:
1433777769338.jpg
 
  • #15
Jamessamuel said:
Pretty far , I am english so certainly on a smaller radius than the mass in the question, which is on the equator.
This is the first time you have stated it is on the equator. This is why Simon asked for the latitude.
 
  • #16
pgardn said:
The acceleration due to gravity and centripetal force are in the same direction if you are on the equator. I would use the equator as your teacher probably expected. Then it's easy to add the two acceleration vectors together. And g is easy if we use the standard r at the equator. And then Ac is easy if we use the equator. Note you will have to find v by looking up r. I'm thinking this is what your teacher wants you to do.

And the gravitational force idea just states that any two masses attract each other with the same force. But one can also see that an object on the surface is also changing direction( if not exactly on a rotational pole) so there must be centripetal force as well. And Fc Is supplied by the force of gravity.
This is backwards.
Centripetal force is not some extra force that you can add on to gravity. It is a required component of the resultant force, namely, that necessary to keep the object traveling on the arc. See https://www.physicsforums.com/insights/frequently-made-errors-pseudo-resultant-forces/
The two forces acting on the mass are gravity and the normal force from the surface. The resultant of the two is the centripetal force. The apparent weight of the mass is equal and opposite to the normal force.
 
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  • #17
Ah

Because the normal is a 3rd law reaction to what is the weight pushing down
 
  • #18
Jamessamuel said:
Ah

Because the normal is a 3rd law reaction to what is the weight pushing down
To the apparent weight, yes.
 
  • #19
Technically the 3rd law reaction to the weight of the object due to the Earth is the weight of the Earth due to the object. This force acts at the center of mass of the Earth and points towards the object.

The normal force to the ground is the reaction to the force of the object pressing into the ground. It can be a tad confusing because "how hard we press against the ground" is what we commonly think of as "weight". In physics, "weight" is a technical term for the force of gravity on an object, so it should be used carefully.
 

Related to Find Gravitational & Centripetal Forces on Mass in Rotating Sphere

1. What is the difference between gravitational force and centripetal force?

Gravitational force is the force of attraction between two objects with mass, while centripetal force is the force that keeps an object moving in a circular path. Gravitational force depends on the masses of the objects and the distance between them, while centripetal force depends on the object's mass, velocity, and radius of the circular path.

2. How do you calculate the centripetal force on an object in a rotating sphere?

The formula for calculating centripetal force is F = m*v^2/r, where F is the force, m is the mass of the object, v is the velocity, and r is the radius of the circular path. In the case of a rotating sphere, the radius would be the distance from the center of the sphere to the object.

3. Is the gravitational force on an object in a rotating sphere affected by the rotation?

Yes, the gravitational force is affected by the rotation of the sphere. This is because the rotation of the sphere changes the distance between the object and the center of the sphere, which is a factor in calculating the gravitational force. As the distance changes, the gravitational force will also change.

4. How does the mass of the object affect the gravitational force in a rotating sphere?

The mass of the object does not affect the gravitational force in a rotating sphere. The gravitational force only depends on the masses of the objects and the distance between them, regardless of whether one or both objects are in motion.

5. Can you calculate the gravitational force and centripetal force on an object in a rotating sphere if the velocity is not known?

No, the velocity is a necessary component in calculating both the gravitational force and centripetal force in a rotating sphere. Without knowing the velocity, these forces cannot be accurately calculated.

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