После долгого дня она машинально улыбнулась, а я попытался её ободрить.

Because после always requires the genitive case.

• день → genitive singular дня
• долгий → genitive singular masculine/neuter долгого

So:

• после дня = after the day
• после долгого дня = after a long day

This is a very common pattern in Russian:

• после работы = after work
• после урока = after the lesson
• после долгой поездки = after a long trip

Машинально means something like automatically, without thinking, out of habit, or mechanically.

In this sentence, it suggests that her smile was not especially emotional or deliberate. She smiled almost by reflex.

A close English sense would be:

• she smiled automatically
• she gave an absent-minded smile
• she smiled mechanically

So it is not about literal machines; it describes a person's action done without conscious thought.

The verb is улыбнуться / улыбаться = to smile.

In this sentence, Russian uses улыбнулась, which is:

• past tense
• feminine
• perfective
• reflexive verb form

Why this form?

1. Past tense feminine
   The subject is она, so the past tense ends in -а / -ась / -лась-type feminine forms.

   • он улыбнулся
   • она улыбнулась

2. Perfective aspect
   улыбнулась presents the smile as a single completed action: she smiled once.

3. Not улыбала
   улыбать is generally not the verb you want here. The common verb for to smile is улыбаться / улыбнуться.

4. Why not улыбалась?
   улыбалась would be imperfective, suggesting an ongoing or repeated action:

   • она улыбалась = she was smiling / used to smile

Here the sentence describes one momentary smile, so улыбнулась fits better.

The -ся (or -сь after a vowel) marks a reflexive verb.

The dictionary form is:

• улыбнуться
• улыбаться

Russian uses reflexive forms for many actions that English does not mark as reflexive. Улыбнуться simply means to smile.

So you do not translate улыбнулась literally as smiled herself. It just means smiled.

You will see this often:

• смеяться = to laugh
• бояться = to be afraid
• надеяться = to hope
• улыбаться = to smile

Both а and и can often translate as and, but they are not identical.

• и usually simply adds information: and
• а often sets up a contrast, comparison, or a shift of perspective: while / and meanwhile / whereas / and as for

In this sentence:

• она машинально улыбнулась, а я попытался её ободрить

The speaker is not just listing two actions. There is a mild contrast between what she did and what I did.

A natural sense is:

• She smiled mechanically, and I tried to cheer her up
• or even She gave an automatic smile, while I tried to encourage her

So а helps separate the two participants and their actions.

Попытался comes from попытаться = to try / make an attempt.

This form is:

• past tense
• masculine
• perfective
• reflexive

What it tells us:

1. Past tense: the trying happened in the past.
2. Masculine: the speaker я is male.
   If the speaker were female, it would be попыталась.
3. Perfective: it presents the attempt as a single completed attempt.

So:

• я попытался = I tried / I made an attempt
• я пытался = I was trying / I tried (with more process, duration, or repeated effort)

Here попытался sounds natural because it describes one attempt to cheer her up.

In Russian, the past tense agrees with gender and number, even in the first person.

So with я:

• if the speaker is male: я попытался
• if the speaker is female: я попыталась

This happens with many past-tense verbs:

• я устал / я устала = I got tired / I was tired
• я родился / я родилась = I was born
• я улыбнулся / я улыбнулась = I smiled

English does not do this, so it often feels unusual to learners.

Because ободрить takes a direct object in the accusative case.

Here, the person being cheered up is the object:

• ободрить кого? = cheer up whom?

So:

• её = her (accusative/genitive form)
• ей = to her (dative)

In this sentence, the meaning is to cheer her up, not to something-to her, so Russian uses её.

Compare:

• Я увидел её. = I saw her.
• Я помог ей. = I helped her.

Different verbs require different cases.

They are different case forms of она.

Common forms:

• она = she
• её = her
  
  • accusative: I saw her
  • genitive: without her
• ей = to her / for her / by her, depending on context
  • dative: I gave her
  • instrumental/poetic? no, instrumental is ею / ей in some contexts

In this sentence:

• её ободрить = to cheer her up

So accusative is needed.

Ободрить means to encourage, to cheer up, to hearten, to raise someone's spirits.

It is the perfective verb. The imperfective partner is ободрять.

• ободрить = to cheer someone up once / to make an encouraging attempt with a result in view
• ободрять = to be cheering someone up / to encourage repeatedly or in general

In this sentence, её ободрить means the speaker tried to make her feel better emotionally.

It is a good fit because the earlier part suggests she is tired or emotionally drained after a long day.

Both are possible.

Russian word order is flexible, and the difference is mostly about focus and flow, not basic grammar.

• попытался её ободрить sounds neutral and natural.
• попытался ободрить её puts a bit more emphasis on её or can sound slightly more deliberate/stylized depending on context.

Russian often places short pronouns like её before the infinitive quite naturally:

• я хотел его увидеть
• она пыталась меня понять
• мы решили их пригласить

So the word order in the sentence is standard and idiomatic.

Because а is joining two clauses, each with its own subject and verb:

1. она машинально улыбнулась
2. я попытался её ободрить

In Russian, when coordinating two full clauses with а, you normally use a comma.

So the comma is required here.

Russian would likely use imperfective verbs instead.

Current sentence:

• она машинально улыбнулась, а я попытался её ободрить

This describes two completed events:

• she smiled once
• I made one attempt

If you wanted more of an ongoing/process sense, you might get something like:

• она машинально улыбалась, а я пытался её ободрить

That would suggest:

• she was smiling in that automatic way, or kept doing it
• I was trying to cheer her up over some period of time

So aspect changes how the scene feels:

• perfective = bounded event
• imperfective = process, duration, repetition, or background action

It could go elsewhere, but putting it first is very natural because it sets the scene.

Original:

• После долгого дня она машинально улыбнулась, а я попытался её ободрить.

Possible alternatives:

• Она после долгого дня машинально улыбнулась, а я попытался её ободрить.
• Она машинально улыбнулась после долгого дня, а я попытался её ободрить.

These are grammatically possible, but the original sounds the most natural if you want to establish the context first.

Russian often puts time expressions early in the sentence:

• Утром я пошёл на работу.
• После ужина мы гуляли.
• Вчера она мне позвонила.

Here is the stress:

• после
• до́лгого
• дня
• машина́льно
• улы́бнулась
• а
• я
• попыта́лся
• её
• ободри́ть

A few useful notes:

• её is pronounced roughly yi-YO
• улыбнулась has the stress on -лы́-
• ободрить has the stress on the last syllable: ободри́ть

Stress matters a lot in Russian, so it is worth learning words together with their stress.

It can be translated as mechanically, but you should be careful.

In Russian, машинально often means:

• automatically
• absent-mindedly
• without thinking
• by force of habit

English mechanically can work, but sometimes it sounds a bit stiff or overly literal. Depending on context, automatically or absent-mindedly may sound more natural.

So in this sentence, the emotional nuance is more important than the literal image: she smiled without really meaning to, or without much conscious emotional engagement.