Category physics

1-D Motion with a force in Scratch

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I can’t remember how I found this, but [Scratch](http://scratch.mit.edu) is a graphical programming language developed at MIT. My kids love this. In order to make sure they don’t know more than I do, I created my own scratch program. I am sure someone from the scratch community will attack it for some reason, but I am ok with that.

The program shows a numerical calculation of the motion of a box with a constant force on it. You change the mass and the force. It “sort of” plots the position as a function of time. Don’t worry python, I still think you are the best.

Learn more about this project

Turn off daytime running lights, or reduce speed? Which saves more?

rhettallain 1 Comment

Which wastes more fuel? (and thus produces more carbon dioxide). This is a difficult to question to answer for a variety of reasons. The main reason is that a speed change from 71 mph to 70 mph is different than a reduction from 56 to 55 mph.

First, let me be clear that the question of how much fuel is wasted using daytime running lights (or DRL as they are called) has already been addressed. The first source I found was howstuffworks.com

**Assumptions**

  • The daytime running lights on a car run at about 100 watts (for the pair)
  • The energy density of gasoline is 1.21 x 108 Joules/gallon.
  • A car is 20% efficient at converting this energy to mechanical energy.
  • The alternator is 70% efficient at converting mechanical energy into electrical.
  • At highway speeds, air resistance is the dominating factor in fuel efficiency (this might be wrong)
  • The air resistance can be modeled as Fair = (1/2)?CAv2
  • I will assume an “average” car that has combined CdA of 9 ft2 or 0.84 m2 (where Cd is the coefficient of drag and A is the cross sectional area. Also ? is the density of air, about 1.2 kg/m2)
  • An average trip of 50 miles (I completely made this up).
  • My mythical “average” car gets 25 mpg when going 70 mph

Continue reading “Turn off daytime running lights, or reduce speed? Which saves more?” →

Basics: Free Body Diagrams

rhettallain 1 Comment

**Pre Reqs:** [Intro to Forces](http://blog.dotphys.net/2008/09/basics-what-is-a-force/), [Vectors](http://blog.dotphys.net/2008/09/basics-vectors-and-vector-addition/)

Hopefully now you have an idea of what a force is and what it isn’t. What do you do with them? The useful thing to do with forces is to determine the total force acting on an object. At the beginning of the introductory physics course, you will likely look at cases where the total force is the zero vector. This is called equilibrium. Even if you are looking at cases where the forces don’t add up to the zero vector (I say that instead of just “zero” to remind you that the total force is still a vector). Physicists like to represent forces on an object by drawing a Free Body Diagram. This is simply a representation of an object and a graphical representation of all the forces acting on that object.

Simply put, in a free body diagram, all the forces acting on the given object are represented as arrows. Let me start with a simple case, a box sitting on a table.

Continue reading “Basics: Free Body Diagrams” →

MythBusters: How small could a lead balloon be?

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On a previous episode of The MythBusters, Adam and Jamie made a lead balloon float. I was impressed. Anyway, I decided to give a more detailed explanation on how this happens. Using the thickness of foil they had, what is the smallest balloon that would float? If the one they created were filled all the way, how much could it lift?

First, how does stuff float at all? There are many levels that this question could be answered. I could start with the nature of pressure, but maybe I will save that for another day. So, let me start with pressure. The reason a balloon floats is because the air pressure (from the air outside the balloon) is greater on the bottom of the balloon than on the top. This pressure differential creates a force pushing up that can cause the balloon to float.

**Why is the pressure greater on the bottom?**
Think of air as a whole bunch of small particles (which it basically is). These particles have two interactions. They are interacting with other gas particles and they are being pulled down by the Earth’s gravity. All the particles would like to fall down to the surface of the Earth, but the more particles that are near the surface, the more collisions they will have that will push them back up. Instead of me explaining this anymore, the best thing for you to do is look at a great simulator (that I did not make)
[http://phet.colorado.edu/new/simulations/sims.php?sim=Balloons_and_Buoyancy](http://phet.colorado.edu/new/simulations/sims.php?sim=Balloons_and_Buoyancy)

![Page 0 Blog Entry 14 1](http://blog.dotphys.net/wp-content/uploads/2008/09/page-0-blog-entry-14-1.jpg)

Continue reading “MythBusters: How small could a lead balloon be?” →

Basics: What is a Force?

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**Pre-reqs:** None.

I intend to talk about forces and force diagrams, but there is a more fundamental question to address first. What is a force? Most texts define it as a push or a pull. That really isn’t a bad definition. Maybe a better (or maybe worse) definition would be “forces are things that change the motion of an object” (change being the key word). If I had to choose one definition of force, it would be something like this:

**Force:** *A force is an interaction between two objects. There are 4 known forces:*

  • Gravitational force: An attractive long range force between objects with mass
  • Electromagnetic force: An attractive or repulsive long range force between two objects with charge
  • Strong Nuclear force: An attractive short range force between particles like protons and neutrons
  • Weak Nuclear force: A short range force responsible for beta decay. *Yes, I know that is a confusing force – for introductory physics, you won’t use this force*

All forces are some form of the above forces.

**Important properties of forces**

  • Forces are an interaction between TWO objects. It is not possible to have a force on an object and not have another object involved.
  • Forces are vectors. They have magnitude and direction
  • The unit for force is the Newton. If you do a whole bunch of cool stuff, they will name something after you also.
  • Forces are NOT properties of an object like mass or speed or color. They are properties of an interaction between two objects. Yes, I already said that, but it is important.

There are some more things about force you will need to know. For now, this should be enough.

Comparison of quadratic curve fitting

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In a [previous post](http://blog.dotphys.net/2008/09/basics-making-graphs-with-kinematics-stuff-part-ii/), I talked about how to plot kinematics data with a spread sheet and how to fit a quadratic function to the data. In the back of my head I remember “Don’t trust Excel”. I seem to recall someone claiming that Excel did not do a proper fit. To test this, I collected some data and used several methods to fit the data:

  • MS Excel’s built in function fitting
  • Using the spread sheet (Excel) to manually calculate the best fit parameters
  • Vernier’s Logger Pro (version 3.6.1)
  • Plot 0.997 – http://plot.micw.eu/ – a program derived from Sci-Plot

I already discussed how to add a quadratic fit in Excel using the built in tools. Perhaps later I will also discuss Logger Pro and Plot. But how do you come up with a function to fit data? The basic idea is to create a quadratic function and vary the parameters such that the deviation of the actual data from the function is minimized. That is much detail as I want to go into except for the following two links that I used:

Continue reading “Comparison of quadratic curve fitting” →

Basics: Relative Velocity

rhettallain 1 Comment

**pre reqs:** [Vectors and Vector Addition](http://blog.dotphys.net/2008/09/basics-vectors-and-vector-addition/)

This was sent in as a request. I try to please, so here it is. The topic is something that comes up in introductory physics – although I am not sure why. There are many more important things to worry about. Let me start with an example. Suppose you are on a train that is moving 10 m/s to the right and you throw a ball at 5 m/s to the right. How fast would someone on the ground see this ball? You can likely come up with an answer of 15 m/s – that wasn’t so hard right? But let me draw a picture of this situation:

![Screenshot 15](http://blog.dotphys.net/wp-content/uploads/2008/09/screenshot-15.jpg)

The important thing is: If the velocity of the ball is 5 m/s, that is the velocity with respect to what? In the diagram, I listed the velocity of the ball as *vball-train* this indicates it is with respect to the train. There are three velocities in this example.

  • The velocity of the ball with respect to the train
  • The velocity of the train with respect to the ground
  • The velocity of the ball with respect to the ground

These three velocities are related by the following:

![relative v](http://blog.dotphys.net/wp-content/uploads/2008/09/relative-v.jpg)

**note**: The way I always remember this is to arrange it so that the frames match up on the left side. That is to say v(a-b) + v(b-c) – you can think of this as the “b’s” canceling and giving v(a-c).

Continue reading “Basics: Relative Velocity” →

Gravity, Weightlessness, and Apparent Weight

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In my classes, I like to bring up the question:

*Why do astronauts float around in space?*

The most common response to this question is that they float around because there is no gravity in space. Some people take this a small step further and say that there is no gravity in space because there is no air in space. This is why they claim there is no gravity on the moon (even though there is – more on this later).

I like to start off with the concept of gravity. Gravity is an attractive force between any two objects with mass. Your pencil and your dog both have mass so there is a force pulling your dog and your pencil (that is if you have a pencil) together. This force turns out to be extremely small. So small that you would never notice it. However, if one of the masses is very large, it is noticeable. An expression for the gravitational force was first determined by Newton. He came up with the following (turning off vector notation for simplicity).

![Page 25 1](http://blog.dotphys.net/wp-content/uploads/2008/09/page-25-1.jpg)

Where G is the universal gravitational constant, m1 and m2 are the two masses in the interaction and r is the distance between their centers. This force (as are all forces) is really a vector that points from one mass to the other.

Continue reading “Gravity, Weightlessness, and Apparent Weight” →

Basics: Making graphs with kinematics stuff part II

rhettallain 6 Comments

**pre-reqs**: [kinematics](http://blog.dotphys.net/2008/09/basics-kinematics/) *I don’t think you need [part I of this](http://blog.dotphys.net/2008/09/basics-making-graphs-with-kinematics-stuff/) if you don’t want*

So, you still want to make a graph with that kinematics data? You think that graphs on paper are too barbaric? Well, if you are ready, you can use a spreadsheet. But be careful. If you don’t know what you are doing, you can cause some damage (much like flying a 747 after reading a blog about it). Speadsheets allow you to do a couple of things.

  • make pretty graphs
  • fit mathematical functions to data

Of course they actually do much more – but you need [“clippy”](http://en.wikipedia.org/wiki/Clippy) to help you with that.

First, what software do you use? I think most people will immediately go for Microsoft Excel. I have to admit, this is what I use because I am so familiar with it. Many people already have this also. Truthfully, it is a good spreadsheet program (but not perfect). There are some free alternatives:

  • Open Office – I use the Mac OS X variant Neo Office
  • Online spreadsheet like Zoho) or Google Docs. Both of these are fairly useable.
  • Other – like Apple’s spreadsheet or other non-free stuff.
  • A final excellent option is Vernier’s Logger Pro. Although it is not free (nor perfect) it is not too expensive and can be covered by a school site license

For this tutorial, I will show explicitly how to make graphs using MS Excel. I was going to use open office, but in order to fit a polynomial to data, you have to do some more serious stuff. The basic idea is the same no matter what you use.

Continue reading “Basics: Making graphs with kinematics stuff part II” →

Unit for gravitational potential – the Golt

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Today I was talking about electric potential. My favorite analogy for electric potential energy is gravitational potential energy. But electric potential is something different. Electric potential (commonly called potential) can be defined as:

$$V=\frac{U_\text{electric}}{q}$$

So, V is the electric potential in units of Joules per Coulomb or Volts.

What about gravitational potential? I am sure some astrophysicist use gravitational potential. Maybe they even have some units for it, but I have never seen it. My students asked me if there was such a thing as gravitational potential. I said, sure. Here it is:

$$Y=\frac{U_\text{grav}}{m}$$

I picked the letter Y, why? Why not? The units for gravitational potential would be Joules per kilogram. I think this should be called the “golt”.