Superhero Physics

The Physics of Pedals

There are essentially two kinds of pedals: clips and flat (oh sure, there is clipless, but that is the same as clips).

So, which should you use?  Let me start with clips.

Clips

Pros: These pedals are efficient.  They let you push AND pull on a pedal.  Cons: they aren’t hipster.

Flat

Pros: These pedals are hipster.  Cons: they aren’t as efficient and your foot could slip off the pedal and cause a boo boo.

 

Torque produced by balls in Fantastic Contraption

The fun part about exploring the physics of [Fantastic Contraption](http://fantasticcontraption.com/) is coming up with new setups to test ideas. Torque is not too difficult to set up. Here is what I did:

![Screenshot 04](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-041.jpg)

In this setup, I have a “turning ball” with a wood stick attached to the side. I increased the length of the stick until the ball does not turn. At this point, the torque from the gravitational force on the stick is equal to the torque from the ball. I can use [Tracker Video Analysis](http://www.cabrillo.edu/~dbrown/tracker/) to find the lengths of the two wood sticks. The torque from each stick will be its gravitational weight times the perpendicular distance to the center of the turning ball.

![Screenshot 05](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-053.jpg)

In order to calculate the gravitational force, I need the mass of each “stick”. [From my previous post](http://blog.dotphys.net/2008/10/physics-of-fantastic-contraption-i/), I found that the mass density per length for sticks was

![Screenshot 171](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-1711.jpg)

where mb is the mass of a ball and U is the diameter of a ball. I also need to find the horizontal distance from the center of the stick to the center of the ball. I will call the top stick 1 and the bottom 2. This gives:

![Screenshot 06](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-063.jpg)

Notice that stick 2 is connected at the same x-value as the ball, so I did not need to add the radius of the ball to its r value. Now I can calculate the total torque:

![Screenshot 07](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-073.jpg)

Although I do have an ok value for U in meters, I do not have a value for the mass of the ball, so no point in multiplying in the constant g. Anyway, let me test this. If this is true, how many balls could I hang right off the circle and lift? In that case, r would be 0.5 U (U is the diameter). So if the torque is around 3, I should be able to lift 6 balls (depending on the mass of string used). Let me try it.

![Screenshot 08](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-082.jpg)

I love it when a plan comes together. Actually, this was a little more than the weight of 6 balls, it also had the short length of water-sticks. But also, according to my calculation, this should not be able to lift 7 balls. Again, success.

Physics of Fantastic Contraption I

One of my students showed me this game, [Fantastic Contraption](http://fantasticcontraption.com/). The basic idea is to use a couple of different “machine” parts to build something that will move an object into a target area. Not a bad game. But what do I do when I look at a game? I think – hey! I wonder what kind of physics this “world” uses. This is very similar to [my analysis of the game Line Rider](http://blog.dotphys.net/2008/09/the-physics-of-linerider/) except completely different.

Fantastic Contraption gives the unique opportunity to build whatever you want. This is great for creating “experiments” in this world.

The first step is to “measure” some stuff. The game includes three types of “balls” and two types of connectors. The balls are:

  • Clockwise rotating
  • Counterclockwise rotating
  • Non-driven

Connectors:

  • wood lines – these can not pass through each other
  • water lines – these can pass through each other, but not the ground

First question: Do the different balls have the same mass? This can be tested by creating a little “balance”

![Screenshot 05](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-052.jpg)

Continue reading “Physics of Fantastic Contraption I”

Fetch with Ruff Ruffman uses a laser to measure temperature?

I am sorry to point this out, but I can’t help it. My kids watch this show “Fetch with Ruff Ruffman”. It’s mostly an ok kids show. However, there was a problem. In one episode, some kids were in the desert and measuring temperature with (they said it several times and it was even a quiz question at the end) – a LASER. Here is the device they used:

![Images](http://blog.dotphys.net/wp-content/uploads/2008/10/images.jpg)

This is an infrared thermometer with a LASER aiming system. The laser is only there to help you aim. The temperature is determined by measuring the infrared radiation from the object. You don’t even NEED the laser. Those ear thermometers work the same way, but they don’t have lasers.

I guess when a laser is involved, it just makes it so cool that it must be the most important thing. I am going to put a laser pointer on my computer – that way people can say “look, that computer runs on LASERS.”

A note about numerical calculations

[In a previous post, I talked about numerical calculations](http://blog.dotphys.net/2008/10/basics-numerical-calculations/). The basic idea is to use the momentum principle and the following “recipe”:

  • Update the position of the particle
  • Update the momentum of the particle
  • Update the force on the particle

Looks great, right? Well, it mostly is great. I want to give a couple of pointers about the last step, update the force on the particle. How and when can you do this? Really, in numerical calculations, you will see two types of forces:

  • Forces that you can calculate: That looks strange, but it’s true. Maybe you are thinking, can’t you calculate all the forces? – the answer is no. Yes, you can calculate the gravitational force and the electromagnetic force. Also, really all forces you are likely to see are one of those two. You can also calculate the force due to a spring(depends on position), the air resistance force (depends on velocity). These types of forces work well in the above numerical recipe.
  • Forces that you CAN NOT calculate: These are all the other forces. Typically, these are forces of constraint. Suppose a block slides down a plane. Yes, you can calculate the force the plane exerts on the block, but it depends on things other than just the position of the block. The force the plane exerts on the block is such as to keep the block on the plane. You can not calculate this in the same way as the previous category of forces. Yes, technically the force the plane exerts on the block IS the electromagnetic force. If you want to calculate this force between all the atoms in the two objects, I encourage that.

So what does this all mean? This means that you can not use the above “recipe” for whatever you want. Sorry.

(I have a trick I will show you later)

Word Police: Use of the word pressure

I know I should just let go, but this is what makes me, me. I understand that there are terms in physics (like for instance ‘pressure’) that are used in all sorts of ways in common language. The problem is when someone tries to explain something scientifically and misuses a word. Pressure means something. It is the average force per area due to collisions of a gas or liquid on a surface. Really, you can see a good animation of this, I have a link and explanation when [I talked about MythBuster’s Lead Balloon](http://blog.dotphys.net/2008/09/mythbusters-how-small-could-a-lead-balloon-be/).

So, what is my problem? I was reading this interesting article on [Scientific American.com about solar refrigerators](http://www.sciam.com/article.cfm?id=solar-refrigeration). Here is a small quote:

*The key is the energy exchanged when liquids turn to vapor and vice versa—the process that cools you when you sweat. By far the most common approach, the one used by the refrigerator in your house, uses an electric motor to compress a refrigerant—say, Freon—turning it into liquid. When the pressure created by the compressor is released, the liquid evaporates, absorbing heat and lowering the temperature.*

“Pressure created by the compressor” isn’t too bad (although it might be interpreted by some that pressure is some substance). My biggest problem is the “When the pressure created by the compressor is released” part. How do you release pressure? Yes, you could allow the particles in the gas to stop colliding with the wall and thus “release” them. But aren’t you releasing the particles not the pressure?

I don’t mean to pick on this particular case because it’s not that bad. There are many other cases where the word pressure is used in a really incorrect manner.

On a side note, about the above article, I find cooling to an extremely interesting problem. It is funny how easy it is to heat something up, but so difficult to cool it off.

**PS:** I also don’t like how the article says “absorb heat”. This also implies that heat is a substance. I don’t really like the word “heat”.

Basics: Work Energy

**Pre Reqs:** [What is a Force](http://blog.dotphys.net/2008/09/basics-what-is-a-force/)

[Previously, I talked about the momentum principle](http://blog.dotphys.net/2008/10/basics-forces-and-the-momentum-principle/). Very useful and very fundamental idea. The other big (and useful) idea in introductory physics is the work-energy theorem. Really, with work-energy and momentum principle, you will be like a Jedi with a lightsaber and The Force – extremely powerful.

Well, what is work? What is energy? How are they related? In [another post, I talked about energy.](http://blog.dotphys.net/2008/10/what-is-energy/) I think it is interesting to look at how most textbooks define energy:

*Energy is the ability to do work*

This is really a stupid definition. Kind of circular logic, if you ask me. In the post I mentioned earlier, I claim there are two kinds of energy, particle energy and field energy. At low speeds (not near the speed of light), particle energy can be written as:

![Screenshot 53](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-53.jpg)

Where *m* is the mass of the particle, *c* is the speed of light. So, if you just look at a particle, that is it for the energy. Now, what about the “work” portion? Work is defined as:

![Screenshot 54](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-54.jpg)

Where *F* is the net force on the particle, ?r is the vector displacement of the particle. The “dot” in between F and ?r represents the “dot product” operation between vectors (also known as the scalar product). In a [previous post](http://blog.dotphys.net/2008/09/basics-vectors-and-vector-addition/) I showed that you could multiply a scalar quantity by a vector quantity. Here I need to do “something” with two vectors. You can’t multiply two vectors in the same sense that you multiply scalars. A general definition of the dot product for two vectors:

![Screenshot 55](http://blog.dotphys.net/wp-content/uploads/2008/10/screenshot-55.jpg)

That looks a little more messy than I wanted, but it can not be helped. Really, it is not that complicated. The dot product is simply the projection of one vector on the other. Let me explain in terms of work.

Continue reading “Basics: Work Energy”