1. Oct 19, 2011

### zoezoehzoe

1. The problem statement, all variables and given/known data

I am trying to find out if force in newtons can be negative.

If i know the magnitude of decelaration of a car ( a minus acceleration ) and i know the mass, do i multiply the - acceleration value by the mass, resulting in a minus value in newtons, or do i multiply the mass by the deceleration, resulting in a positive value in newtons.

2. Relevant equations

for example, 1500kg ( mass ) x -2 m s-2 ( acceleration ) = -3000 newtons

3. The attempt at a solution

I think this would be correct because the minus is telling us the direction in which the force is being applied, but i really am not sure, any advice would be appreciated?

2. Oct 19, 2011

### Ahmedbasil

A force is a vector, it cannot have a negative magnitude. Although what you see as -3000 newtons is really just a contradiction of the direction. The 3000 newtons is acting in the direction opposite to the one you assumed it's acting in.

F=ma, should actually be |F|=m|a|, or $$\vec{F} = m \vec{a}$$

EDIT: Sorry, just read your attempt at solution. You're right, it corresponds to the direction.

3. Oct 19, 2011

### zoezoehzoe

Hi, thank you for your reply. So if i were to write the answer as -3000 newtons would that be correct? Or should it be 3000?

Many thanks.

4. Oct 19, 2011

### sankalpmittal

Hiii zoezoehzoe !

Force is a vector quantity but that doesn't even mean that it has to be negative. However I came across some text books which claim the answers in -500 N etc. It is not a big deal but this is not correct. It is wrong ! As Ahmedbasil said that force is vector because of direction. It has magnitude as well as direction.

|F| = m x |a| ---> This is a correct representation.

Cross product of vector(acceleration) and scalar(mass) is always vector(force).

Vector quantity : Direction + Magnitude + can be negative or remain absolute OR only magnitude but negative ; Example: Displacement , acceleration , velocity etc .

Scalar quantity :Only Magnitude ;and only positive . Eg. Distance , speed , mass etc .

In F=ma , acceleration has nothing to do with direction even. It just tells increase or decrease in velocity per unit time. Force is dependent on direction. Example : Centripetal force in centre due to constant change in direction.

___________________________________________________________
Ahmedbasil , you are correct to say that -X N means force is applied in opposite direction but you must not say that it is because it is causing retardation in opposite direction. Retardation = -(-Acceleration).
Positive and negative sign in acceleration just tell that whether speed is increasing (velocity for particular) or decreasing.

Always feel free to ask questions. Well done !

Last edited: Oct 19, 2011
5. Oct 19, 2011

### zoezoehzoe

Thank you both very much for your help :)