Different grammatical usages of もの
The formal noun もの can have a few different meanings and usages. The "Fun with Grammar" initiative by the Japan Foundation distinguishes two cases concerning もの, the first case explains the usage of もの at the end of the sentence, whereas the second case explains the usage of もの in the middle of sentence. Since your question falls within the first category, where もの is used at the end, I will only talk about that category.
1. Four main usages of もの at the end of a sentence
As pointed out in l'électeur's answer, using もの at the end of the sentence is often used to express these four distinct nuances:
- To describe the true nature or an ideal state of something (l'électeur: cold facts)
- To express advice, warning or admonition (l'électeur: common sense)
- To express admiration or strong feelings for something in general (l'électeur: deep emotion)
- To express nostalgic feelings when looking back at life (l'électeur: recollection)
People don't easily change.
The speaker may be speaking from personal experience, noticing a pattern.
Students should study more.
The speaker might be a teacher who has noticed a decline in marks over time.
Life is beautiful.
The speaker carefully assessed their opinion on life, and perhaps concluded that the positive aspects of life greatly outweigh the negative ones.
Back in the day, every household would brew their own sake.
The speaker was alive back then, and happens to remember that fact.
2. Further nuances
While l'électeur's answer touches on the same four usages as the Japan Foundation's web page, another implied nuance is that the speaker (who uses もの) is addressing the topic in a more distantiated and indirect way. This in turn implies that the speaker is trying to be objective. The speaker might have the relevant expertise to make certain claims, or they might have assessed a certain topic very carefully before forming an opinion about it. In order not to repeat the same examples, I have attempted to explain why each example can be considered objective above in italic.
According to the Japan Foundation, here's when and why もの would be appropriate:
- The speaker has significant experience or knowledge about a topic
- The listener is not experienced OR the speaker is talking to themselves
- The speaker is talking indirectly and/or objectively about the topic
- The speaker takes their time to form an opinion, rather than expressing a casual opinion
3. To answer your question
This もの（だ・です） construction has a rather serious and reflective tone, which does not easily lend itself to casual conversation. In the first conversation between the student and their mother, this tone is appropriate. The mother, much like any parent, wants to make sure her child studies hard and admonishes them when she fears that her child will not do well in school.
For the second example, I'm assuming you're reflecting about how you think your life would be if you had a lover. This is also an appropriate scenario to use もの. However, if you were casually talking to someone about being in a relationship, then that same sentence could come off as cold or even as patronising.
As an aside, when you're talking to yourself, you don't have to use the polite form です or the particle よ.
Hope this helps!