Newton’s Law of Cooling!

This post is to give information to my Alaska Math Consortium classmates and teachers. In the first two videos, we have the data collection via digital infrared thermometers and a video.

In the second two videos, the calculus students present their equations and graphs of their results to the class.

To gather your own data from the videos, make a table of values, then start in!


Stove Data

Newton’s Law of Cooling states that the rate of change in the temperature of an object is proportional to the difference between the object’s temperature and the temperature of the surrounding medium. The differential equation that arises from this is: y’ = k(Y-t)



Laser Printer

This is a short video and the paper drops from 176 degrees to 75.5 degrees in about 2 minutes.


Mug Data Video

Video is spliced together from 4 videos and is quite long. One would want to pick an interval to use like, say 5 minutes. (very long: 56 minutes!) Turns out, a cup of water takes much longer to cool down than a piece of paper.


Chris & Blake do a rap up. The battery on the camera died before the end.


Chris and Blake do a find job in this video. Unfortunately, the battery died before the end of their presentation.


Hunter and Abby do their presentation.

Abby and Hunter have a nice wrap-up here.

Red Box

P1030734One of my favorite discoveries during Spring Break was Red Box video rentals. There are none of these in SE Alaska. Juneau has none, Sitka has none, and Ketchikan has none. I was amazed by the them. I believe that Anchorage has 33 of them and Fairbanks has something like 8.

Basically, they are vending machines that require a credit card to rent a video and all rentals are $0.99 per day. If you turn the video in by 9 PM the next day, you are only charged $0.99 for the rental, if you fail to return the video by 9 PM, your card is charged an additional $0.99 until a maximum of 25 days, at which time, the fees stop, and you have in essence purchased the video. 

You typically see these Red Box machines at the entryways to Wal-Mart stores or QFCs, or other retailers that have a large volume of foot traffic. You can rent a maximum of five videos at a time. When you rent or return a video, a confirmation is automatically sent to your email address so you can make sure that their records agree with yours.\

As seen below, the disc comes in a little plastic protective case. What makes all of this possible, is that the case has gaps in it that allow a reader inside the machine to identify the DVDs individually.

P1030739In the Seattle area, there are hundreds of these vending machines, and you can rent a video from any one of them, and you can return the video to any one of them as well. To simplify things, you can search them online to find out which machines have which videos plus you can reserve a video and rest assured that it will be available when you show up to the machine.

P1040442At one store, a machine was broken down and I got to peak inside at the inner workings. There is a large carousel inside that spins as well as an arm that disperses and retrieves the videos.

The coolest thing about the Red Boxes is that they have all the latest releases available for a $1.00. Every week, the new releases come out and, if you live near one, you can get them in a heart-beat.

If you’ve used Netflix, you’re familiar with searching an online video data base to pick your favorite movies. Red Box has a similar website that doesn’t use ratings, favorites, or queues, but is nevertheless easy to use and fun to peruse.

On the website, there are vague instructions on how to purchase a Red Box franchise, but I don’t think I have time for that, nor does Haines have the population base to properly support one.

On the one hand, it’s sad to see all the Blockbuster Video and Hollywood Video shops with lights out and For Lease signs all over them, but on the other hand, how do you compete with $1 rentals? I think some places continue to rent videos: Safeway has its own rentals, and other convenience shops will probably always have their own rentals.