How Many Straight Pins can be Added to a Full Glass of Water

One of my students is doing a science project with a problem stated as follows: "How many straight pins can be added to a full glass of water before it will overflow. We’ve done the experiment twice,and so far our water has not overflowed. The last time we added 700 pins one at a time. I believe this has something to do with the surface tension of the water, but I’m not able to explain this to my student. Can you help me?
- Barbara Rush
Maplesville, AL USA

Barbara, The reason it’s hard to overflow a glass of water by adding pins to it is that each pin takes up very little room. I just measured the size of a pin and found the "long" part of it was about 26mm in length and 0.29 mm in radius. The head of the pin was about .89mm in radius and .51mm thick. Figuring out the total volume of this pin I get only about 8.1 cubic millimeters. This is the same volume of water that the pin will displace when you put it into a glass of water, or in other words adding one pin has the same effect as adding only about 8 cubic millimeters of water. The volume of 700 pins is therefore only about 5600 cubic millimeters, which is the same as 5.6 cc, or just under two tenths of an ounce. This is a pretty small change in the water level, which is why you were not able to overflow the glass. You would need about 3700 pins to increase the level of water in the glass the same amount as adding one ounce of water. So we have learned two interesting things: 1) The volume of a pin is very small. 2) The glass you thought was full to begin with was really not…you can add more water to it without it overflowing, or as you have found out, lots of pins. The reason for this is, as you said, surface tension. The level of the top of the water in the glass can actually be a slightly above the rim of the glass since the surface tension of the water acts as sort of a "skin" to keep it from overflowing. You can actually get chemicals that will reduce this tension…this is what you put in many newer dishwashers and is probably available at the grocery store. If you add a few drops of this to the water before doing your experiment you may have better luck overflowing the glass. (An easier and better way might be to just start with more water in the glass). MS Follow-up: I just want to say a big thanks for helping me out with the pin problem. We did try it again the next day. This time we filled the glass until it was well above the rim. It took 1160 pin to make one drop trickle down the side. Barbara Rush Isabella School Maplesville, AL USA

(published on 10/22/2007)