good, hard, sharp
All it needed was a good tug.

firm
gentle, little, slight, small
quick, sudden

give (sth)
feel

with a tug
She started the engine with one tug of the starter rope.

tug at
She felt a sharp tug at her sleeve.

tug on
She gave a little tug on the rope.

gently, lightly
He tugged lightly at my wrist.

hard
He tugged harder, but it was caught fast.

nervously
She nervously tugged at her long brown hair.

playfully
She playfully tugged at his shirt.

at
She tugged at his arm to get his attention.

by
He tugged me by the sleeve.

on
Alexis was up in a flash, tugging on his arm.

Tug is used with these nouns as the subject:
hand

Tug is used with these nouns as the object:
beard, rein