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In the above case, the normal force exerted by the elevator on the box would be = 10kg * g + 10kg*5m/s^2, assuming g = 10m/s^2, the elevator would exert a normal force of 150N on the box. But wouldn't the box exert an equal and opposite force on the elevator resulting in no motion? I know this is a really stupid question but I've not been able to understand where I'm going wrong.

Another related question: the box exert a force of mg = 10kg*g = 100N on the elevator, or, since the elevator is pushing on the box with 150N, it will react by pushing down on the elevator with 150N