Download Exercise 5

Astronomy 102
Name:
Exercise 5: Propulsion
The ring launcher
In 1865, James Clerk Maxwell published an article titled “A Dynamical Theory of
the Electromagnetic Field” in the Philosophical Transactions of the Royal
Society of London. In the article, he described a set of equations that unified the
until-then separate forces of electricity and magnetism as one force called
electromagnetism. Eventually, his equations were distilled into the four
Maxwell’s Equations of Electromagnetism. Because the phenomena were
discovered long before Maxwell’s time, the individual equations are known by
other scientists’ names.
In particular, Faraday’s Law (Maxwell Equation 3) suggests that a changing
magnetic field induces an electric field. If there is a conductive material, like a
wire, in the field, an electric current will be set up in the material. Ampère’s Law
(Maxwell Equation 4) states that an electric current generates a magnetic field.
A good illustration of these principles is found in the ring launcher. The launcher
is simply a coil of wire attached to an electrical cord – when plugged into the wall
socket, the alternating current (AC) of a standard building power supply will
generate an alternating direction electric current in the coil, which in turn will
generate an alternating direction magnetic field within the coil and an alternating
direction electric current and magnetic field in any ring of material placed around
the coil. The two magnetic fields (inside the coil and inside the ring of material)
will repel and move the ring up.
Actually, the generation of force is still not that well explained; check out a recent
attempt at explanation by a physics professor:
http://www.wired.com/wiredscience/2014/01/physics-of-the-electromagneticring-launcher/
This doesn’t mean that we can’t at least discover some empirical relationships
about the force that propels.
Needed: Ring launcher, various material and size rings, iron core extender, bulb
1. Place the coil attached to the bulb circuit on the ring launcher and briefly turn
on the launcher. What happened to the bulb? Explain this phenomenon, using
the word “induction” or “induced”.
2. Now carefully launch (or attempt to launch) various rings of different materials
and sizes. Record the information in the table below; with the height the ring
goes up, you can be approximate.
Ring material
Ring height
(cm)
Ring mass (g)
Maximum
movement height
(cm)
The rings are all machined to be the same thickness and diameter, so when a ring
is double the mass of another ring of the same material, it is twice the height of
the other ring.
3. a. The conductivity of a ring depends on the area though which the current
will move – for the rings, the area is the inside of the ring. So if one ring is twice
the mass of another ring of the same material, what can be said about the ring’s
area (compared to the other ring’s area)?
b. So what is the mathematical relationship between ring height and ring
conductivity, roughly?
c. Test this theory: copper has about twice the conductivity of aluminum. Look
at the data for the aluminum and copper rings of the same height. Which would
you predict would have a greater maximum movement height, and why? Was
your prediction true? How confident are you about the ring height/conductivity
connection in part b?
4. How did the “split” ring do? Explain the result in terms of Maxwell’s
Equations.
5. Place the iron core snugly in the middle of the coil, then launch a ring. Record
the maximum movement height in centimeters and compare this number to the
movement height of the same ring without the iron core. Why does the iron core
improve the maximum movement height?
The reaction motor
As noted in previous lectures, all rockets these days use Newton’s Third Law
as the basis of their motion and thus are called “reaction motors”. The rocket
equation will describe the rocket’s velocity as a function of its exhaust velocity,
the fuel mass and the spacecraft mass.
Needed: rechargeable carbon dioxide fire extinguisher, wheeled cart, reasonably
long corridor with low friction surface, video recorder, tape measure
𝑚!
∆𝑣 = 𝑣! ln
𝑚!
where ∆v is the change in velocity of the spacecraft, ve is the exhaust velocity, m0
is the initial total mass and m1 is the final total mass. In this experiment, we are
going to try to calculate the exhaust velocity of the carbon dioxide fire
extinguisher, by determining how fast the extinguisher will propel a cart.
Set up the cart in the corridor and the fire extinguisher nozzle as straight as
possible away from the back of the cart (and opposite the direction of motion).
Make sure the front of the cart is at some kind of recognizable mark. Set up the
video recorder at right angles to the path of the cart and make sure that regularlyspaced markings are visible to the video recorder.
6. Record the mass of the cart plus fire extinguisher plus astronaut (note units,
too). Which variable in the equation is this?
Begin recording the video. Carefully remove the ring on the fire extinguisher
handle and depress the fire extinguisher handle for ten seconds at full blast. It
will be very loud but don’t release the handle until ten seconds are up.
Stop the video recording.
7. Determine the final speed of the cart, using the last few seconds of video and
the distance markings (write down the setup of the calculation). What was the
cart’s initial speed? So calculate ∆v. Be careful about units, here.
8. Meanwhile, reweigh the astronaut, spent fire extinguisher and cart, and
record the mass.
9. Calculate the exhaust velocity of the fire extinguisher. Pay attention to units
and show your setup!
Repeat the experiment if there is enough pressure left in the fire extinguisher.
10. We tried to use a “reasonably” friction-free surface, but of course, it was not
really friction-free. If the floor were really friction-free, how would that have
affected the experiment? In other words, which measurement(s) would have
changed, and how (larger, smaller?)? Run through the exhaust velocity
calculation and determine if the exhaust velocity would have been greater, lesser
or about the same.