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When I first learned about forces and motion I was taught F=ma in terms of apply a force to a mass and the acceleration of that mass = x. I was quite clear about how something moved ie apply a force to a mass - it moves or tends to move.

But then I came onto the D' Alembert variation of F-ma=0 ie everything in equilibrium.

Very useful it is too.

In terms of F= ma so ma = F and F-F = 0. So the I thought well how can things move then? I was told by many that the insertion of inertia into the equation so that F-ma = 0 is just a mathematical trick and useful for resolving forces and moments in a mechanical system.

However to me at least inertia is real and easily proved. You can't apply a force unless an equivalent force pushes back.

So I decided that motion is caused by the transfer of kinetic energy of momentum in the direction of the force applied. In terms of conservation of momentum, so that even though there is equal and opposite inertial force there is not equal and opposite momentum and the motion carries on in the direction of the force.

But I cant quite resolve that concept! Since the force applied to the mass does work on the mass as it accelerates therefore (in my mind) the inertial force must do equal and opposite (negative) work to the applied force. As Ek = 1/2mv^2 and work = fd theta and this becomes W = 1/2mv^2theta then Ek of applied force should equal negative Ek of inertial force.

So how do things move??

Can anyone explain? have I got my concepts mixed up?

Thanks Dave Smith