According to Linguapress:
The commonly repeated "rule" that you can "only use 's with people" is
quite wrong. It is a very broad generalisation, and there are lots of
In cases of real possession, where someone possesses an object, 's is most common. For example:
Mary's dress was very pretty. (correct)
The dress of Mary was very pretty. (wrong)
When a real person possesses a quality, attribute or action, 's is probably more common, but you can often use either. When you use 's, it emphasizes the possessor. When you use of, it emphasizes the quality or attribute. For example:
The Queen's reputation is remarkable. (emphasizes the Queen)
The reputation of the Queen is remarkable. (emphasizes the reputation)
However, the more intangible the possessor, the more common of is used. For example:
The cost of a ticket was outrageous. (correct)
The ticket's cost was outrageous. (very awkward)
The rear bumper of the car was damaged. (probably more common)
The car's rear bumper was damaged. (perfectly fine)
You must use of when you express that something is a part or proportion of a whole or the unit of a group:
A majority of the people prefer the incumbent.
The rest of the cake was left uneaten.
The top of the mountain is in the clouds.
The collection of paintings is astonishing.
There are a lot of rules and many exceptions. I'm afraid that sometimes it comes down to how it sounds and the structure of the sentence.
There's no reason not to use 's to indicate possession in an essay of any type. You might be thinking of a convention with contractions, where you might avoid using contractions in essays because they are too informal:
We discovered that a student cannot learn as quickly if he is hungry. (more formal)
We discovered that a student can't learn as quickly if he's hungry. (informal)