A Physics Problem

Thanks everyone for the input! My preliminary answer based on sjstuart’s method is . . . more than 15 pennies. That’s all I had, and it wasn’t enough to sink the snorkel with both ends taped. I didn’t try to dunk the snorkel 3 cm into the water and then tape it, because I thought the tape wouldn’t stick. Likewise, to avoid having to dry the snorkel off before taping additional pennies to it, I used a plastic baggie to hold the pennies, which I then to the attached tightly to the snorkel with hair elastics. I thought I could squeeze all the air out of the baggie and keep the pennies dry, but it became obvious that that did not work, so I held the bag underwater to zipper it shut so that no air remained in it. My plan had been to measure the number of pennies I needed to make the snorkel neutrally buoyant, then multiply that by 95 percent or so, to account for the percentage of snorkel above the water, and then round up to the next penny to account for that portion’s weight. I have obtained more pennies and will report back after my next round of experimentation. To predict how many pennies it might require, I took Arthur’s suggestion and filled my snorkel with water and measured it. I must have originally estimated the snorkel’s dimensions on the low side—it actually holds right at 7 ounces of water, or 207 mL. Wikipedia says that pennies weigh 2.5 grams each, so it would take nearly 83 pennies to neutralize the buoyancy of that much air. When the weight of the snorkel itself is factored in, it wouldn’t actually take that many pennies, but wowsers--it still sounds like it might require more than I want to duct tape to the snorkel. And Steve, it is entirely possible that I have a delicate forehead! I have seen entire teams of age-groupers using these contraptions with neither complaint nor snorkel adaptation (or forehead injury, as far as I know). Maybe I should just accept that the snorkel pushes the head up slightly (thereby giving me more than 3 cm clearance for taking on water, which seems a very small margin of error to me, too, now that I think about it), and rest my head on it like a pillow rather than worrying about pushing it back down. Or—aha—maybe I should just pad the snorkel headpiece so it actually becomes more like a pillow, and bothers my forehead less. My plan right now: tape a dozen pennies to the snorkel to weight it a bit and see how that feels, experiment with more pennies in the baggie to see how many it actually takes to make the snorkel neutrally buoyant (because now I’m curious), and brainstorm what I could use to pad the piece that sits on my forehead.

Thanks everyone for the input! My preliminary answer based on sjstuart’s method is . . . more than 15 pennies. That’s all I had, and it wasn’t enough to sink the snorkel with both ends taped. I didn’t try to dunk the snorkel 3 cm into the water and then tape it, because I thought the tape wouldn’t stick. Likewise, to avoid having to dry the snorkel off before taping additional pennies to it, I used a plastic baggie to hold the pennies, which I then to the attached tightly to the snorkel with hair elastics. I thought I could squeeze all the air out of the baggie and keep the pennies dry, but it became obvious that that did not work, so I held the bag underwater to zipper it shut so that no air remained in it. My plan had been to measure the number of pennies I needed to make the snorkel neutrally buoyant, then multiply that by 95 percent or so, to account for the percentage of snorkel above the water, and then round up to the next penny to account for that portion’s weight. I have obtained more pennies and will report back after my next round of experimentation. To predict how many pennies it might require, I took Arthur’s suggestion and filled my snorkel with water and measured it. I must have originally estimated the snorkel’s dimensions on the low side—it actually holds right at 7 ounces of water, or 207 mL. Wikipedia says that pennies weigh 2.5 grams each, so it would take nearly 83 pennies to neutralize the buoyancy of that much air. When the weight of the snorkel itself is factored in, it wouldn’t actually take that many pennies, but wowsers--it still sounds like it might require more than I want to duct tape to the snorkel. And Steve, it is entirely possible that I have a delicate forehead! I have seen entire teams of age-groupers using these contraptions with neither complaint nor snorkel adaptation (or forehead injury, as far as I know). Maybe I should just accept that the snorkel pushes the head up slightly (thereby giving me more than 3 cm clearance for taking on water, which seems a very small margin of error to me, too, now that I think about it), and rest my head on it like a pillow rather than worrying about pushing it back down. Or—aha—maybe I should just pad the snorkel headpiece so it actually becomes more like a pillow, and bothers my forehead less. My plan right now: tape a dozen pennies to the snorkel to weight it a bit and see how that feels, experiment with more pennies in the baggie to see how many it actually takes to make the snorkel neutrally buoyant (because now I’m curious), and brainstorm what I could use to pad the piece that sits on my forehead.