The Third Rule about Modifiers

Rule 3:  Make the connection between clauses clear

Some words have a very special role in a sentence.  For example, because let's you know that the sentence is about cause and effect.  When let's you know that two things happened at the same time.  If we forget these words it might make the sentence confusing.  Here are a few examples of confusing sentences:

Getting a good night sleep, the day is always easier.
Running out of money, the refrigerator was empty.
Carrying the heavy bag all day, my back was very sore.

As you can see, making small changes to these sentences would make them much clearer.  These sentences need actors, and they also need words to show the relationship between each clause.  How would you change my sample sentences?