A little bit of science on the occasion of a college graduation

This weekend I was out of town to attend a graduation. The night before the ceremony the family was gathered, visiting, and the graduate shared a recent event from her physics class. The professor described a scenario, asked the members of the class to make a prediction of the outcome, told them that they were all wrong, but was unable to explain why they were wrong.

Here is a scenario: a container of water has an ice cube floating in it, and a pebble sits on the ice cube. The ice cube melts. The pebble drops to the bottom of the container. Does the water level in the container rise, fall, or remain the same?

Along with most of the other family members, I predicted that the water level would rise. I had pictures of Archimedes running through the streets shouting “Eureka!” after realizing that the volume of a solid object could be measured by dropping it into a container of water and measuring the displacement of the water. Moreover, it seems that the water level should rise because of the melting of the ice. The graduate said all the members of the class had made the same prediction and it was wrong, but she still did not understand why.

One family member, an engineer, said that the professor was correct, and he explained why. The explanation puzzled most of the family members, although I caught on after a couple times through the scenario. The engineer wanted to produce a mathematical explanation with paper and pencil, but the rest of the family assured him that would not be necessary. We did try to experiment by creating the scenario with a measuring cup, an ice cube, and a pebble, but we could not find the right size ice cube or pebble to conduct the experiment.

The next day there was a party in the same house after the graduation ceremony. In addition to family members, several fellow graduates and other college students were present. To fill a lull in the conversation, I reintroduced the scenario from the physics class. One of the college students, a mathematician, insisted that the water level would rise. The engineer again countered that it would drop. This time the two of them did resort to pencil, paper, a laptop computer, and information from the internet, including the density of water and ice. The engineer was able to convince the mathematician that the water level would indeed drop.

It happens that the classic form of this scenario involves a boat and an anchor rather than an ice cube and a pebble. When the anchor is removed from the boat and dropped into the water, the water level drops, even though it seems that it should rise. The reason for the counterintuitive answer is that the boat with the anchor in it displaces some of the water in the pond. When the anchor is removed from the boat, the boat rises and the water level falls. When the anchor is dropped into the water, some water is displaced and the water level rises, but not to the height that it had been when the anchor was in the boat. The reason this happens is that the anchor sinks because it is denser than the water. (If the anchor floated and did not sink, it would not be an anchor, said the engineer.) Because of its density, the anchor displaces less water than its weight alone displaced when it was in the boat, being supported by the water.

By the same token, ice floats because it is less dense than water. As it floats, it displaces some of the water. When it melts, the volume of the water that was previously frozen is less than the volume of water displaced by the floating ice. Therefore, the pebble-ice cube combination displaced more water when the ice was frozen and floating, supporting the pebble, than the pebble displaced after the ice melted; even the melted ice did not add enough water to raise the water level to the height it had been when the ice was still frozen.

The rest of the weekend, including the graduation, was also nice. J.

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Weekend repairs; or, flies in the ointment

The weekend was good and I don’t wish to complain… but I will anyhow. There were three flies in the ointment that kept the weekend from being perfect. Murphy’s Gremlins were not interested in leaving the family alone all weekend.

The first of the flies arrived Friday night, as a puddle of water began to flow from under the refrigerator. I pulled the refrigerator away from the wall, expecting to find a leak in the hose that connects to the ice maker. At first I found no such hole, and I began to suspect that the leak was coming from the dishwasher. Since the dishwasher was not running at the time, I put some green food dye in a glass of water and poured it into the dishwasher drain. When the puddle under the refrigerator did not turn green, I rechecked the hose and finally found a small leak. For a short-term solution, I turned off the water line to the icemaker, hoping that we had enough ice to make it through the weekend.

Of course Murphy’s Gremlins act on a Friday night, not in the middle of the week. And of course they choose a weekend when family from out of town is coming to visit. At least I was able to visit with more talented do-it-yourself relatives about the needed repair. From the internet, I had gathered that I needed either to replace the entire hose or to cut the leaking section and attach the two pieces of hose with a connector. My relatives recommended a connector and also suggested that I take the removed section of hose with me to the hardware store to be sure to get the right size connector.

Murphy’s Gremlins visited again Saturday afternoon when the spring on the garage door broke. I’ve reattached broken springs on that door before, but this time the spring managed to break at both ends. A fair amount of trial and error was required to get the entire system working again (and I have several unattractive and painful scrapes and cuts on my hands from the repair), but after about an hour (and with some assistance from my daughter when two hands were not enough), I got the door working again.

Sunday, Murphy’s Gremlins got some help from Mrs. Dim. After returning from church, family members decided to take some pictures of each other in front of the house. One part of the family had flown in from out of town and rented a car at the airport. When we came back from church, they parked in the street, since they would be the first to leave after our cookout. Of course they parked on the very patch of pavement where Mrs. Dim likes to leave her trash bags of cut grass and other lawn maintenance residue. (The city ordinance forbids putting such trash on the pavement-it’s supposed to be left on the lawn within six feet of the pavement. But Mrs. Dim doesn’t want to risk hurting her carefully-tended lawn, so she usually puts her bags on the pavement.)

So, while we were involved in family photographs, Mrs. Dim began dragging her trash bags right to the property line. The first she placed directly on the line; the others were more on my side than her side. (Yes, they were on the grass.) I think my out-of-town family assumed that I exaggerate when I describe Mrs. Dim’s petty and childish behavior. Now they got to see it for themselves. When we were on the other side of the house, I whispered to my sister, “This is SO going on the internet.”

All of these problems were relatively small. No one crashed while traveling, and no one was taken to the hospital from my house.  The weather was virtually ideal, everyone got enough to eat, and we enjoyed each other’s company. It would take a genuine curmudgeon to find any reason to complain about the weekend-but a curmudgeon is exactly what I am. J.

Holy Saturday

According to the book of Genesis, when God created the world, he did so in six days. By the power of his Word he called into existence everything that exists, aside from God himself. Then, on the seventh day, God rested. Even before sin entered the world, God commanded his people to rest on the seventh day of each week. He created a weekly holiday so people would have a break from their usual work and would have time to celebrate fellowship with God and with each other.

In the Ten Commandments, God reaffirmed this commandment to rest on the seventh day of the week. Through the prophets he repeated the message that his Sabbath Day was to be respected. God never told any of the prophets that he was going to change his mind about that commandment (although he did reveal to Jeremiah that a new covenant was coming). Jesus debated with his opponents about the meaning of the Sabbath Day, saying that it was appropriate to do good and helpful things on that day. But Jesus did not signal that he was going to change God’s weekly holiday.

The vast majority of Christians in the world today worship God on Sunday. Sunday morning is treated as the weekly anniversary of the resurrection of Jesus. Christians are free to move their time of rest and worship from Saturday to Sunday, or to Wednesday night, or any other time they please. The apostle Paul wrote to the Colossians, “Let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath. These are a shadow of the things to come, but the substance belongs to Christ.” Kosher rules no longer apply, because they were related to the animals sacrificed on the altar, and Jesus has fulfilled the substance of which they were a picture. Christians are free to hold a Seder and observe the Passover week if they wish, but most choose instead to celebrate Holy Week and Easter, since Jesus has fulfilled the substance of which Passover is a picture. Christians do not have to make a Sabbath rest every Saturday, because Jesus has fulfilled the substance of which the Sabbath is a picture.

In the week of creation, God rested on the seventh day. In Holy Week once again, God rested on the seventh day. The body of the Son of God rested the rest of death, buried in a borrowed tomb. The soul of the Son of God rested in Paradise, in the hands of his Father. Whenever a Christian dies, that Christian rests the same way—the body buried or otherwise resting on earth, the soul with Jesus in Paradise.

But the rest of Jesus was short. When the Sabbath ended, a new day began, and Jesus no longer rested. The substance of the Sabbath was fulfilled, as the substance of Passover and of animal sacrifices was fulfilled in the death of Jesus. Christians are free, not only from sin and death, but also from the burden of the Law. “Let no one pass judgment on you,” for God has already judged you worthy of eternal life in his Kingdom. J.