Mass on a spring through oscilloscope eyes

A few days ago I bought PicoScope 2204A, a digital oscilloscope that uses a computer as a screen. I started to play with it from usual experiments like AC current graph, a voltage on AC/DC converter etc. I showed it to my colleagues, and our department head asked me where I can use it in my course. I teach AC current to my AP physics 2 class after the exam, and that is what I told her. Then I started to think where else I can use it. Here is my first idea.

https://drive.google.com/file/d/1_vQKBDmhTlwgEKOXeYjwbJusjDO4vm41/view?usp=sharing

This instrument, unlike old scopes, can show stable signals of low ( less than 1 Hz) frequencies. I put a few round magnets on a spring and placed them inside a big diameter coil connected to the scope. When I started mass-on-a-spring oscillations, the result was almost a perfect sine graph. Changing springs and a number of round magnets in a stack, we can easily find how frequencies change depending on the system parameters. Or we can find a spring constant and compare it with direct measurements done using Hooke’s Law. I believe that this idea has some good potential for the experimental problems and labs. What do you think?

Remark 1. This scope does not have a stable software for Macs.

Remark 2. After this post was written I saw the great author of the blog Teach.Brian.Teach. Brian Frank’s tweet with another method of mass-on-a-spring oscillations lab using Vernier probes. I really like it.

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“Mysteries” of an apparent weight.

A couple of days ago I was working on my notes/plans/lessons for the upcoming school year, and the topic of weight-apparent weight came up. Every year it bothers me how to make it more clear for students. Finally, I decided to dig in. Many textbooks avoid defining apparent weight. Regular weight is defined as the force of gravity on the object. ISO definition (ISO 80000-4:2006, Quantities and units – Part 4: Mechanics) :

Fg = mg, where m is mass and g is a local acceleration of free fall.

Remark: When the reference frame is Earth, this quantity comprises not only the local gravitational force but also the local centrifugal force due to the rotation of the Earth, a force which varies with latitude.

Ok, almost clear 🙂

Now, apparent weight. Out of all strange definitions in different sources, the only one that works for me is the operational one:

Apparent weight is what the scale shows.

Great. It means that it is the force that applies to the scale. That is what I always tell my students. This definition also works well if the buoyancy force is involved as well as if something is weightless.

I just have to remember to tell my students not to read a Wikipedia article on this topic. The definition there is

apparent weight is a property of objects that correspond to how heavy an object is.

Force is “a property of objects”. How about ‘heavy’ in weightlessness. Ok, let’s forget it. I have real questions that bother me.

  1. If a rollercoaster cart or a plane makes loop-the-loop, is an apparent weight of the driver or the pilot directed down?
  2. If a car accelerates horizontally, is apparent weight directed at the angle arctan(a/g) to the vertical?
  3. If the object is in a centrifuge, is apparent weight directed at the angle arctan(v^2/rg) to the vertical?

To me, the answers to all these questions are the same: Yes. What do you think?

Always believe in the laws of physics

Yesterday on Facebook someone posted a picture of a hammer “floating” on the edge of the table with the help of a ruler. One of the comments was “It is possible only theoretically, the picture is a photoshop. I decided to check and prove that physics always works. Here is a picture (not a great angle, but you can get the idea).

IMG_2862.JPG

Only one inch of the ruler is on the table, but it is enough for the system to stay at equilibrium. You can try it at home, it takes 30 seconds to set up. It is a perfect illustration of a static equilibrium, even better than a bird made of a potato, two forks, and a toothpick. Next year I will give my classes a lab problem to find a position of the center of masses of this system.

Can you recommend your favorite experiments?

Twins Paradox and Special Relativity

This post is a bit off topic to my blog, but there are some things in popular science that really bother me. One of the groups that I follow on Facebook posted a clip on Twins Paradox in Special Relativity. Again! There is no such thing as Twins Paradox in Special Relativity. In order to compare the ages of the twins, you need to return them to the same point.  You have to accelerate (decelerate) at least one of them, making his/her frame of reference a non-inertial one. This means we cannot longer use Special Relativity. Only General Relativity has non-inertial frames of reference. For detailed explanations one can look at the famous Landau & Lifshitz book.

To me, it was always a criterium of a good vs bad book on Special Relativity: if there is a chapter on Twins Paradox, I would never buy a book.

Equipotential color-coding

Last week on Twitter  posted a picture on equipotential color-coding for electric circuits.

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I liked it, and a short discussion followed.   directed us to PASCO CASTLE kit where this idea is described. Please, be aware that their description has a physical error: using hydrodynamic analogy, they claim that all points of the same color have the same static pressure. This is not true. Just drop their explanation completely and use equal levels of gravitational potential energy instead.

Today I tried this method in my classes for review of electric current. It did work well, and many students liked the idea.  I added energy diagram that also clarified some details and, hopefully, will help me, when it comes to atomic energy levels.

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Overall, I believe that this method works for establishing in students’ heads universal energy/ law of conservation of energy idea.

Sink or swim

Sink or swim – a topic as old as our civilization. Everything about it is well known since Archimedes.

https://www.youtube.com/watch?v=0v86Yk14rf8

What can be added to a lesson on this subject to make it interesting and unusual? I decided on everyday vegetables and fruit. Carrots? Sink. Radishes? Sink. Onions? Swim. Apples? Swim. Lemons? Swim.

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Ok, let’s peel this lemon.

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Now it sinks! Why? Let your kids explain it.

Side note: a peeled lemon always sinks. If you try the same experiment with an orange or tangerine, the result is unpredictable and depends on the variety, size etc of the orange. If you want predictable results, use a lemon.