For an annual fee of $79, Amazon.com AMZN, +1.45% offers customers free two-day shipping on most of its inventory — a business model that defies conventional wisdom and, perhaps, the laws of gravity.

One doesn’t have to be Sir Isaac Newton to know that the heavier an item is, the more energy it takes to hoist it off the ground and transport it around the country. But the online retailer sets few limits, if any, on the weight of the items it ships for free.

While sending off something as a light as an 0.8-ounce pack of feathers doesn’t cost the company much, analysts say Amazon may lose hundreds of dollars covering the cost of lugging around heftier items, such as 149-pound sofabeds or 300-pound treadmills. Shoppers, on the other hand, can more than make up for that $79 Amazon Prime enrollment fee with a single purchase.

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“It’s really an amazing deal,” says Amazon spokeswoman Pia Arthur, even if the heaviest items sometimes have to be handled by “specialty shippers” instead of UPS or FedEx and can’t always be delivered within the usual two-day time frame. See Amazon’s policy for shipping large items.

So what’s the heaviest item Amazon will ship for free? The company declined to say, but the makers of a 1,509-pound safe (shipping weight: 1,672 pounds) claim the prize for biggest bang for one’s 79 bucks. See Cannon Safe CO54 Commander Series Premium 90 Minute Fire Safe

These days, if Wile E. Coyote wanted a safe to drop on the Road Runner, he would be better off ordering from Amazon than Acme, which probably charged for shipping.

The Cannon Commander Series 54 is designed by Cannon Safe to hold up to 48 guns, but can also be used to protect jewelry and important documents. It stands 6-feet tall, features a 5.75-inch thick steel door with 13 locking bolts and sells for $3,486.57 on Amazon.

“We charge customers around $700 to ship this safe, but when they buy it through Amazon they get it shipped for free,” says Pasquale Murena, marketing manager for Cannon Safe. “As a result, we get orders through Amazon every day.” In fact, Amazon will pick up the tab for shipping the safe even for non-Prime members, if they are willing to wait a few extra days for delivery. Like many items priced over $25, it qualifies for “Super Saver Shipping,” which usually take five to eight days to arrive.

Amazon would not comment on its shipping costs. And that, analysts say, is the elephant in Amazon’s mail room. “Amazon discloses almost nothing about the economics of Prime, not even how many Prime members there are,” says Colin Gillis, an analyst with BGC Partners. The company has also been criticized for a similar lack of transparency about the economics of its e-reader and tablet business. “If I were an investor paying a multiple premium for Amazon, I’d want a little more information about this,”Gillis says.

What investors do know is this: The company reported $636 million in shipping losses in the quarter ended Sept. 30 ($2.8 billion in the past year) — that’s represents 4.6% of its sales. Amazon reported a net $274 million loss that quarter, but “they would have earned a hefty profit were it not for the costs of free shipping,” says Gillis. In fact, free shipping reduces Amazon’s profit margin on any one item to about 1%, compared with the 5% retailers earn typically, he says.

CEO Jeff Bezos insists its shipping costs are a calculated risk. “It’s not like we didn’t do some arithmetic ahead of time,” he told AllThingsD in September. “Despite what some have said from time to time, Amazon is a for-profit business. So, we looked at some numbers, and we believed that this would be a good program for customers and for Amazon.” See Making Money While Keeping Prices Low: Amazon CEO Jeff Bezos Explains It All (Mostly)

Gillis and other Wall Street analysts say Bezos is betting that Prime customers will become so loyal to the service that they won’t shop around at rivals’ sites. And for his part, Gillis says the strategy appears to be working. “I buy everything from Amazon now — even my underwear,” he says.