Teachers are often hung up on grading policies, especially those for late work. We tend to model our approach after that of the English department: typically, an English teacher might subtract a letter grade for each day late. So we do something similar, creating a sliding scale of credit, a scale whose complexity sometimes rivals that of the tax code, and adjusting the policy over the years in response to complaints and lawyerly arguments.
What is the overriding goal, the most important purpose, of your homework "policy"? You want your students to do their homework carefully, and to turn it in on time. That's because well presented homework leads to learning physics well, which leads to success on tests, which leads to happy and smart students.
When you're structuring your homework "policy", then, don't think in terms of "what is a fair consequence for late work?" Think instead about how to best accomplish the goal of receiving timely, well-done problems.
I don't think the English department is the best model for us as physics teachers. English essays are -- usually -- assigned days or weeks in advance, and are due only occasionally. If an essay is due every fourteen days, and won't be graded for another week after it's turned in, then one day doesn't really make so much of a difference. In fact, I've had English teachers explain they'd much rather have a three-day-late but good essay than a poor essay turned in on time.
Physics is different. I assign work every day at my boarding school. At the day school, problems were due twice a week. Problems are returned within a day or two in order to provide continual feedback, showing students where they do and don't understand new material. Unlike the typical English teacher, I would prefer finished work to correct work. The point of homework is to engage with the material, not to show mastery. The goal of my homework "policy" is to produce that engagement.
A story... Can't cite it, but read it in (I think) the Wall Street Journal: A daycare service in a large city was having trouble with clients picking up their kids well after the appointed pickup time. Employees had no choice but to stay late, sometimes very late -- you can't just leave a 4-year-old on the doorstep and say "Mommy will be here soon, sit tight, bye now."
The service revised their policies to provide monetary penalties for late pickups. That didn't help. They made the fines for late pickup ever bigger... and yet, the rate of late pickups continued to increase.
Finally, the service tried something different -- they ELIMINATED MONETARY PENALTIES for late pickup. Instead of a page in their handbook listing crimes and punishments (Late 5-20 minutes = $50, late 20-60 minutes = $200, etc.), they merely wrote that daycare employees expected to leave promptly in order to join their own families for the evening. Repeated lateness was not considerate of the employees, and would not be tolerated.
Hah! Late pickups were virtually eliminated. The article I read speculated that by fining parents for late pickup, they had in the parents' minds created "late pickup" as an economic good which could be bought and sold. The parents would do a cost-benefit analysis... is picking my kid up late worth the fine? If so, I'll just pay the fine. I can afford it. And why are the employees so grouchy at me when I show up two hours late? I'm paying them a bloody fortune for the late pickup, they should be happy for the money.
But without the fine, late pickup became not a saleable good, but a sin. The frowning from the employees was no longer interpreted as ungratefulness for the opportunity to earn overtime pay; instead, the late parents were embarrassed and apologetic. "I'm so sorry I took time away from your own family. This won't happen again. Please continue to watch my child and take care of him with love... I promise to respect your time in the future."
I think of homework the same way as late daycare pickup. If I assign a sliding scale of grade penalties, I'm encouraging students to weigh the cost against the inconvenience of actually doing the work. If a student is happy to settle for a C, he can decide to do just enough for that grade.
However, if I present missing homework as a sin, awarding no credit and requiring the homework to be done in any case, the rate of completed homework skyrockets. Even half-arsed problem sets allow a student to engage with the material, and improves that student's understanding. Since I've gone to some version* of "no credit for late work, period" I've had few complaints, and very few late assignments.
* In upper level classes, I allow two no-excuse-necessary extensions per marking period.
Anecdote from Burrito Girl: Some physics teachers will say that they couldn't possibly give no credit for late work, because they'd have to deal with so many complaints from students, parents, colleagues, and administrators. My wife and sidekick Burrito Girl used to teach English. She took points off for late work according to a sliding scale. She says that she got way more complaints about her policy than I ever get about mine. Students, parents, and colleagues argued that the grade penalty shouldn't be as steep for a particular assignment, or that the policy should be adjusted, or that extenuating circumstances should apply...
In other words, you're going to have perpetual arguments whether you take off 10% or 100% for a late assignment. Why not give a shot to the method that is most likely to convince students to engage with their physics problems on a regular basis?