- #1

HWGXX7

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I got into a very little and simple problem which I should understand. But I don't..

Look at this picture:

The mass naturally will move downwards from the hill. Oke, no problem. Analysing the external forces applied to this mass: gravity and friction.

Gravity, independent of time.

[tex]F_{g}=m.g[/tex]

Friction force, depents on the speed the mass is moving down.

[tex]F_{w}=k.\frac{dx}{dt}[/tex]

This I do understand.

Aply Newton second law: [tex]\sum F=m.a[/tex], this is a vectorial equation.

Means that the orientation of the forces is important, you also know this offcourse.

Now the tricky part I can't understand: I know de speed of the mass is getting smaller en smaller because de mass is slowing down because of friction.

Acceleration is defined as :[tex]a=\frac{dv}{dt}[/tex], in this case the derivative is negative.

So [tex]m.a[/tex] is also negative and must orient in the negative x direction...

I know I'am wrong but I can't find a decent reason in my logic for it..

gratefull for help