See, when you stand on those gym scales in an accelerating lift, it's not just your mass—it's the push of the acceleration too! If the lift zooms up, the scale shows more than your usual 'mg', because it's fighting your weight *plus* giving you that upward speed. I learned this when the gym lift at my apartment rushed upwards and my weight showed an extra two kilos—felt like a cheat day I didn't even have, yaar! So, for that moment, the normal force had to be greater, simple.
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