The execution of a prisoner serves several purposes. One, obviously, is punishment for the condemned person's crimes. The executed person will never commit such an act again.
The execution also warns others of the consequence of committing such acts. The third is to show the people they are well-protected by their governing body.
The hanging with a short drop addresses all of these. The condemned has her hands bound behind her back to prevent her from grabbing at the rope she will be hanged from. Another rope has a noose or loop fashioned on one end, When the stool is kicked from beneath her feet, the weight of her body will pull the noose against her neck until she is dead.
Of course she will struggle as she is strangled by the noose, but in the end her own weight kills her.
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The crowd can look at the drool dripping from her mouth that she could not swallow and know justice was done...