Ask Mr. Science
page 21

 
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Making a wooden cyclotron?

You need two D's, half-circular dishes. A marble starts near the center, and needs to be accelerated every time it crosses the gap. You do this by moving the D's up and down such that when the marble arrives at the gap, it is higher than the opposing D. You need a ramp across the gap. Because the marble is accelerated, the radius of the orbit in the dish will be bigger every time, and eventually the marble will leave the accelerator. In a cyclotron, the time it takes to make one revolution is constant, and in order to achieve this in the wooden model, the slope needs to increase with radius as follows (balance gravity with the centrifugal force):
4*pi^2*r
-------- =  tan(alpha)
g*T^2
where r is the radius, g is the acceleration of gravity, T is the (fixed) time for one revolution, and alpha is the angle of the surface at radius r. So for an orbit time of 1.5 seconds, and a dish of about 2' diameter, the angles would be like this:
r (cm) angle (degrees)
xxx xxxxxxx xxxxxxx xxxxxxxx xxxxxxxxx xxxxxxxx xxxxxxx xxxxx
0 0
5 5.1
10 10.2
15 15.0
20 19.7
25 24.1
30 28.2

Since the slope (tangent) is linear in r, the shape of the bowl is a parabola. Here is a table of orbit time, dish depth, maximum velocity, for a dish of 60cm diameter.

orbit time (s) dish depth (cm) max velocity (m/s)
1.0
1.5
2.0
One of these ramps needs to be attached to each of the dish halves. The drop is equal for all radii, and the drop is s-shaped so that it smoothly matches the surface of the dishes.
To operate, crank the handle up and down. There should be stops (not shown) so that the surfaces line up nicely in both the up and down positions.

The D's ride up and down on vertical 1" dowels mounted on the base, over which plastic sleeves ride smoothly. (also not shown.

A little chute near the center with a latch/release launches the marble with just the right velocity onto its first orbit. Then you crank until the marble gets accelerated right out of the top edge of the dish. If you surround the dish with a rim that prevents the marble from flying off in a random direction, and which has one hole in it so tha marble can escape in a pre-defined direction, you can aim at a gong. This would loudly announce when you have successfully achieved full acceleration. Bingo!

1 April 2005

 

Why do you get carsick?

Your brain gets different inputs on where your body is, if it is straight up, upside down or sideways, if you are accelerating, rotating or sitting still. It gets these inputs primarily from 3 sources:
  1. your eyes
  2. your muscles, bones etc
  3. your inner ear
Clearly your eyes give you primary input about how you are moving and how you are oriented in space. Nerve cells in your muscles and bones also can feel things about your orientation, acceleration and all that. This is called proprioception: the perception of yourself. Finally a small organ in your inner ear also can sense if your head is rotating or accelerating.

The trouble starts when there is a conflict between the different inputs. For example, if you are reading a book in a car that is driving on a winding road, your inner ear and your proprioception tell your brain that you are moving and turning, but your eyes are looking at the book which is not moving in front of you. The different messages reaching your brain can make you carsick. Most times, if you start feeling bad, and then stop reading and look out the window, you'll get better because your eyes now agree with what your inner ear and your body are saying about your movements.
A similar thing can happen on a ship, or more rarely, in an airplane.

I made a model of the balance organ of the inner ear out of 1" (ID) tubing, bent in circles and joined with a short coupling. I made three of these, tied together with twist ties at right angles to each other. I filled 2 with water, in which I also put some washed-out coffee grounds, representing otoliths, and xxx (more to come)

 

A Heliostat

A heliostat is a device that lets you project a sunbeam onto the same spot for a long time, even as the sun moves across the sky. Devices like this were used in labs at a time when bright light sources were not easy to come by. Some models date back to the 1700's [verify this].

My friend Peer had given me one. Records showed that it was bought by te Lab in the 40's, for $250. The way it works is that there is a primary mirror which is slowly rotated by a clockwork mechanism to compensate for the rotation of the earth. This first mirror sends the sunlight in the direction of the North Star. A second mirror then sends the sunbeam to wherever you want. To set this up, first you align the base along a north-south axis, and make sure it is level. Then the main axis of the mechanism is tilted up to point at Polaris, which is an angle equal to the latitude wher you are. Next, tilt the primary mirror such that the sunbeam points along the There is supposed to be a scale mounted on the fork that holds the primary mirror, such that you can set the mirror at the correct angle. [This angle would be 45° on the days of the spring and fall equinoxes, and deviate from that by up to 23° depending on the time of year]. On my instrument, the second fork and mirror were missing, so I fabricated them (the shiny Aluminum parts, obviously).

1 April 2005






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