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I was in an elevator the other day and I began to think about the forces acting on me and the elevator during my ascent and I became very confused.

Let's say for example that my mass and the elevator's mass combined is 100kg so this weighs 98N. When the elevator is at rest I figured that we would weigh 98N, but if the elevator began to acclerate, I think I might weigh more because there is now a net force on me and the elevator that is causing us to accelerate up at let's say 3m/s^2.

Fnet = ma

= 100kg (3m/s^2) = 300N of net force

If the opposing force is the weight of the elevator and my weight combined which is -98N, then the applied force is 398N right?

Is this 398N the tension in the rope? Or is 300N the tension in the rope since 98N is already the reaction force of the pull of weight? My main question is I understand that one pair of action reaction forces is the -98N of weight and the normal force of 98N but if the rope is pulling the elevator up for a net force, would the elevator not pull the rope down and cancel this net force? Why does the object accelerate?

Thank you!!