simulations

Description/Notes

Bart Simpson rides an elevator, standing on a scale.  You can choose the initial velocity and acceleration and then observe the effect on what the scale reads.  You also get the graphs of his motion so you can use this simulation just to explore the kinematics.

Here's another look at kinematics graphs:  you can choose the initial conditions and then run the simulation.  The rocket sled tracks along the bottom of the screen and its position and velocity graphs show above.  (There are websites that do this also, but the ones I found did not let you use negative initial velocities.)

This is a simulation of the ballistics cart but with added twists:

1.  You can change the reference frame from an outsider to a passenger.  (That's why there are "trees" in the background.)  This shows that one viewers parabola is another's straight line motion.

2.  You can press on a brake or accelerator to show that this only works at constant velocity.  But then you can view this one from the passenger's reference frame as well and introduce the idea of "virtual" force.  I call it "sideways gravity" -- setting the stage for later discussions of centrifugal force

BONUS:  You also see the car rotate as it moves linearly.  Where did this rotation come from?  It was already "rotating" as it "revolved" around the center of the track.  Time the rotations and you will see that they match the period of the original orbit.

Boat crossing a river:  you can choose the boat speed, current and heading and then time the crossing...

Here is an activity that guides students as they play with this simulation: River-Crossing-Mania

Students will discover that if they aim straight across, the current won't affect the crossing time.  And they will learn how to aim to compensate for the current.

One object travels in a circular path while two objects undergo the corresponding simple harmonic motion in the x and y directions.  The goal is to show that SHM is just circular motion projected along one dimension.

BONUS:  you can change the relative frequencies of the x and y components and generate some really hypnotic Lissajous figures.  Save this one for the last few minutes of class and set the frequency at something like a 0.85 ...no one will want to leave the room until the figure closes!

This was posed as a problem in Quantum Magazine a long time ago:  A uniform beam rests on two cylinders which are spinning toward each other.  The beam is initially placed off-center.  Describe the motion that ensues...

A tank of water sits on an electronic balance.  A 1-liter mass is suspended above from a rope.  You can vary the specific gravity of the mass.  Then, while the simulation is running, you can lower the mass into the water.

Things to watch:

As you lower the object, the tension in the rope decreases and the reading on the electronic balance increases.  If the chosen  specific gravity is less than one, the tension goes to zero and the object floats partially submerged (depending on the ratio of the specific gravities).  Also, if you lower the object quickly (or lower it before you press start) it will display damped simple harmonic motion.

These two are designed to be used together.  The first shows an object at the bottom of a finite well, hoping to "jump" with sufficient energy to escape.  Potential energy is measured from the top of the well and g is assumed to be constant (so U = mgh).  You can monitor the energy totals and the position of the object as it escapes (or doesn't).

Now, the object is at the bottom of an infinite well -- at the surface of a planet.  (The mass of the planet is 100 kg, its radius is 3.45 meters and in this universe G = 7 Nm2/kg2.)  Again, you can vary the launch velocity and monitor the energy totals.

When I use these two simulations, I give my students a framework for taking notes.  If you'd like a copy, click here.  It will show you how these go together.   Note:  the gaps in the document are intentional.  They are for the parts of the development that I want my students to do for themselves or at least to take notes themselves.

By this time in the course, students should know that retro-rockets can make you go faster if you are already moving backward.  But what if you are moving forward in circular orbit?  Again, retro-rockets will increase your speed as you fall to a lower orbit. This simulation lets you explore that counterintuitive situation.

A 1-kg rocket orbits a 25-kg planet with an orbital radius of 7 meters in a universe where G = 7 Nm2/kg2 .  The initial speed of 5 m/s puts the rocket in a circular orbit.  You can then fire the forward or retro-rockets to change your orbit while monitoring speed, mechanical energy and work done by the rockets.

Also note that to establish a larger circular orbit requires two separate "burns" -- the initial burn and then a second one at the apogee of the resulting elliptical orbit.  Students can then research how a communications satellite gets from low-Earth- to geosynchronous orbit. 

I used to teach chemistry and I would use this one when we discussed Rutherford's gold foil experiment.  We didn't do any mathematical analysis, but this one is just fun to watch.

A box is dropped onto a stationary sled.  The box has initial horizontal velocity.  Momentum is conserved, but explore what happens along the way...

The original question:  a bowling ball is released with some horizontal velocity, but zero rotational velocity.  When will it stop sliding and start rolling, At what speed?  After what distance?

Then come the variations:  back spin?  Overspin?  Up a ramp?  

This simulation is designed to show that two springs attached in parallel will oscillate like a single spring with a constant equal to the sum of their separate constants.  So parallel springs "add" like capacitors: keq = k1 + k2

9/6/13

A mass hangs from a pair of two springs in series with each other.  You can vary the constants of each of the two springs.  Then you can vary the constant of a single spring attached to an equal mass.  When the masses oscillate with the same frequency, you will see that the single spring has the constant predicted by the "one over" rule, like capacitors in series: 1/keq = 1/k1 + 1/k2

9/6/13

This simulation was inspired by a number of items on the Force Concept Inventory.  You choose a speed and direction for an object.  Then you choose a size and direction for the force you wish to apply.  But the force is only applied when you are pressing the button.  So you can apply a force in the same direction as the motion, the opposite direction, perpendicularly to the initial motion (but not necessarily perpendicularly to the CURRENT motion).  In each case, the tracking reveals the effect of the applied force.  And when you remove the applied force, the object then continues at constant speed in the direction it was moving.

9/6/13

This is designed to introduce some very basic notions about electric fields and field strengths.  Using this, I hope my students will learn:

1.  That a field is a property of a place

2.  That a charge in an electric field will experience a force

3.  That the force will be bigger if the charge is bigger but that the f/q ratio of a given field remains constant

4. That the direction of the force depends on the sign of the charge.

None of these things seem obvious to my students when we begin.  Here is a document I give them to guide them as they play with the simulation.  As always, I welcome your feedback...

9/6/13

This was inspired by all of those kinematics problems where one thing is chasing another.  Here you have a motorcycle and a police car.  You can give either one a head start and assign initial velocities and accelerations.  Then, when you run it, you also get position and velocity graphs on the screen.

I use these to try to convince my students that using the velocity graphs directly is often easier and more elegant than using the kinematics equations.

9/20/13