Why do attractive force have a negative sign? like F= -GMm/r^2

[mutineer123]

Why do attractive force have a negative sign? The book says its because one must be moving toward the other. But how does it make it negative? I don't understand. Can anyone explain the law of gravitation formula?? F= -GMm/r^2

 

[Vorde]

It shouldn't. Except when dealing with vectors. Where does it say there should be a negative?

The reason there is a negative with vectors is that you can imagine that the vector is a arrow pointing in the direction of the object being attracted to you, so because it is being attracted to you the arrow shouldn't be pointing away from the direction its being pulled, it should be pointing towards the direction it is being pulled, hence the negative.

 

[Drakkith]

I don't see a negative in the formula on wiki: http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation

 

[mutineer123]

kk got it thanks. Hey can I ask you guys another question? What exactly is the difference between centripetal force and gravitational force?? Are they the same? WHY IS acceleration (of free fall) the (resultant) force of the difference between gravitational and centripetal force??

 

[I like Serena]

Hi mutineer123!

Centripetal force is the force required to keep an object in its (typically circular) orbit.
Only if the gravitational force matches the required centripetal force, will an object actually be in the corresponding orbit.

Normally, acceleration is an absolute.
It says how much an object accelerates with respect to a so called inertial frame.

However, if we're looking at the orbit of a planet, we can talk about the acceleration with respect to the orbit of this planet.
In that case the required centripetal force that will keep the planet in its orbit will match the gravitational force on the planet.

If we look at an object nearby the planet, it will also respond to the gravitational force, keeping it in the same orbit as the planet.
Any difference is an acceleration of the object with respect to the planet.

 

[tasnim rahman]

Centripetal force is our way of describing a theoretical force that moves an object in a circular path. In reality, this force can be provided any force. For the satellite its the gravitational force; for a coin at rest on a rough circular rotating disc, its the frictional force; for a stone, tied to a string, that is whirled around in a circle, its the tension in the string.

 

[Khashishi]

The negative sign is the result of a sign convention. The force is a vector quantity, so the sign depends on the implied direction. In polar coordinates, "r" points outward from the origin. So if the direction is not explicitly stated, it is usually taken to be positive = out.

 

[Dale]

Why do attractive force have a negative sign? The book says its because one must be moving toward the other. But how does it make it negative? I don't understand. Can anyone explain the law of gravitation formula?? F= -GMm/r^2

Attractive forces tend to reduce the distance between the two objects, so reducing distance is given a negative sign.

 

[mutineer123]

Hi mutineer123!

Centripetal force is the force required to keep an object in its (typically circular) orbit.
Only if the gravitational force matches the required centripetal force, will an object actually be in the corresponding orbit.

Normally, acceleration is an absolute.
It says how much an object accelerates with respect to a so called inertial frame.

However, if we're looking at the orbit of a planet, we can talk about the acceleration with respect to the orbit of this planet.
In that case the required centripetal force that will keep the planet in its orbit will match the gravitational force on the planet.

If we look at an object nearby the planet, it will also respond to the gravitational force, keeping it in the same orbit as the planet.
Any difference is an acceleration of the object with respect to the planet.

So if there is any difference will the object stay in the orbit or fall down?

 

[A.T.]

So if there is any difference will the object stay in the orbit or fall down?

It might also go into a non circular (elliptical) orbit.

 

[sophiecentaur]

Why do attractive force have a negative sign? The book says its because one must be moving toward the other. But how does it make it negative? I don't understand. Can anyone explain the law of gravitation formula?? F= -GMm/r^2

It's probably easiest to think in terms of what effect the attractive force can have on separation. It will reduce the separation if it's allowed to (not sufficient other forces to cancel it out) - so the effect is negative on the separation.

 

[I like Serena]

So if there is any difference will the object stay in the orbit or fall down?

If the gravitational force is greater than the required centripetal force for a (circular) orbit, then the object will follow a different orbit.
Typically this would be an elliptical orbit.

Seen from a planet, it will look like the object is falling down.

 

[Dadface]

Back to the original question.mutineer,am I right in assuming that you're following the AQA A2 course?If so the minus sign is a convention used by AQA.I don't think it's used by the other boards.

 

[sophiecentaur]

Typically this would be an elliptical orbit.

Seen from a planet, it will look like the object is falling down.

...
And then going back up again... And so on .. .