Work up an appetite

Work up an appetite

According to a dictionary, It means "gradually become hungry, develop an appetite.

I've heard this expression a lot in some of the most popular American dramas like "Friends", "The big bang theory".

Now work up alone as a verb phrase means

Work up (phrasal verb)

1. to arouse the feeling of, excite.
2. to cause to grow are develop.

And from the dialogs I've heard I can infer that besides developing an appetite or gradually becoming hungry it also means "doing something that increases your hunger" like if you are already hungry but you get even hungrier after you see something delicious or mouth-watering.

Let's have a hypothetical situation in which the meal isn't ready yet but Sara is hungry, she asks Catherine for something to eat.

Sara: I am hungry, can you get me something to eat.
Catherine: There are some nuts and fruits in the upper cabinet, they will work up your appetite.

So does it mean eating nuts and fruit will increase Sara's appetite after the meal is served?
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Does work up an appetite also mean to get a little excercise to develop an appetite. Like is there any relation between work up and workout?

You get up in the morning and go for a run. That is "working up an appetite."

If you eat a snack shortly before a meal, that's "spoiling your appetite".