# Negative Force

1. Oct 15, 2010

### Carlos Dutra

Hey people,

I searched by this question in the forum but don´t found the answer. I have a simple doubt about this theory in mechanic.

The question is: There is negative force?

I know that when I am working in math with a vector that represents a force I can use the negative signal to represents it is in the opposite direction, like a convention. In the college people always say that the negative force don´t exists, but to me this can exist just like the positive force (that is a convention too) and negative direction.

Thanks.
Carlos Dutra

Sorry the english, I am a brazilian.

2. Oct 15, 2010

### arildno

Well, I think the ones denying this is referring to the MAGNITUDE of a force, rather than its direction.

And magnitude is a non-negative quantity.

3. Oct 15, 2010

### Carlos Dutra

I just don´t understood why magnitude is a non-negative quantity. If this is just a convention I have the same reasons to believe that i can´t be positive too.

4. Oct 15, 2010

### arildno

Look at its definition.

5. Oct 15, 2010

### Carlos Dutra

Can you indicates to me a bibliography where I can found this definitions? I make a search in few books about mechanics and don´t found anything explicit.

6. Oct 15, 2010

### arildno

How is the magnitude of a vector defined?
Surely, you know that?

7. Oct 17, 2010

### SinghRP

Newton' 2nd law of motion: Force = Time rate of change of momentum. Here both force and momentum are vectors (magnitude and direction), and they are in the same direction. A force along x causes momentum to increase along x in time. If a body is in motion along x and if you apply a force along -x, the body will loose momentum along +x, and it will decelerate along +x. Force is the cause (gravity, electrical, magnetic, ...); momentum change is the effect (regardless of the type of force).

Now about mass. There are two types of mass: gravitational and inertial. Gravitational mass appears in the gravitational force; inertial mass appears in momentum. By convention, inertial mass (matter or antimatter) is positive, and the gravitational mass of matter is positive. The sign of antimatter gravitational mass is wide open. Reason: we do not have the relationship between gravittational and electromagnetic interactions. If we ever find out that antimatter gravitational mass is negative, lo behold!, physics will chage significantly.

8. Oct 17, 2010

### Nabeshin

Would be analogous to saying a triangle has a side with negative length. Unless you're willing to say that, you should also oppose a force with negative magnitude.

9. Oct 18, 2010

### Carlos Dutra

arildno

If I knew that I would not be here asking humbly.

SinghRP

Thanks for the explanation, it made things clearer.

Nabeshin

Yes, this question about negative appear in the calculus too, when I subtract the area under the x axes in the integral of a function.
I guess the example can be used with money too, It would be strange to say minus 10 dollars, but if we're talking about a debt we can write for -10 dollars in the bank balance, or just say they were charged 10 dollars.

---

In short, the magnitude of a vector always is positive, by a convention. But I can refer to the force like negative, meaning that its direction is reversed of the reference adopted. Just like the example:

If A is a vector that represents a force I can find B, a vector that is a vector representing a force too, and B will be negative.

B = 0 - A

But we don´t use it because it sounds weird.

10. Oct 18, 2010

### arildno

Carlos:

There are lots of quantities for which it is sensible to specify a "direction", i.e where there are both positive and negative quantities.
This doesn't really mean anything other that
a) There is a "natural" way to add such quantities,
and:
b) Some such additions will end up in a suitable.."nothing".

But, it doesn't thereby follow that ALL types of quantities we may encounter will have such a structure.

For example, what should "negative length" mean?
The length of a segment is exactly the same, however we choose to orientate it in space.
While it is very easy to define addition (and subtraction) operators on such lengths, it is rather meaningless to define "negative lengths".

Similarly, what would it mean that a tree has -10 leaves?