つける
tsukeru
Same picture, your hand on it: つける
The picture Your own hand pressing something onto a surface so that it stays. つける is your hand sticking it on; つく is it sticking on by itself.
Where the picture shows up in つける
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flip it on and it stays on
暑いのでエアコンをつけてください。
atsui node eakon o tsukete kudasai
Could you turn on the AC? It's hot.
Pressing the switch so the current sticks to the air conditioner and stays
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spread it on
パンにバターをつけて食べます。
pan ni batā o tsukete tabemasu
I eat my bread with butter on it.
Lifting butter on a knife tip and spreading it onto the face of the bread
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stick your attention to it
気をつけて帰ってください。
ki o tsukete kaette kudasai
Take care on your way home.
Taking your scattered attention and sticking it onto the road at your feet
気をつけて works as a parting greeting; take it whole, not word by word.
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keep sticking entries down
毎日、家計簿をつけています。
mainichi, kakeibo o tsukete imasu
I keep a household budget every day.
Sticking today's spending onto the notebook one line at a time
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pin it on you
名札を胸につけてください。
nafuda o mune ni tsukete kudasai
Please put the name tag on your chest.
Holding a name tag to your chest and pressing it on with your palm
All of it in one picture
つける is the picture of your own hand pressing something onto a surface so it stays. The switch sticks the current to the machine; the knife sticks butter onto the bread; 'take care' sticks your attention onto the road ahead; the budget book sticks today's numbers onto the page, one line at a time; the tag gets pressed onto your chest. Only what you stick changes — current, butter, attention, a record, a badge. So つける is the same picture as つく, with one difference: the hand doing the sticking is yours.