Put a cork in it

Definition: Be quiet

Could you please put a cork in it?!
Tom, put a cork in it! I can't hear what Mary is saying

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Put down

Definition: criticize someone

Jack put him down and he hasn't been the same since.
Don't put me down
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Put someone away

Definition: put in prison

They put him away for twenty years.
Jason was put away for life in prison

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Put the finger on someone

Definition: identify someone

The victim put the finger on the criminal.
She put the finger on her boss for the crime
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Put the heat / screws on someone

Definition: pressure someone to do something

He's putting the heat on me to finish the report.
Janet's really putting the screws on her husband to get a new car.