Isaac Newton (1643-1727) proved mathematically that Galileo was correct. Newton's law of universal gravitation states that the attraction between two objects M and m placed a distance r apart (from center to center) is given by F = GMm/r2 , where G is the gravitational constant. But Newton's second law states that the force (F) on an object (m) is related to it's acceleration (a) by F = ma. Combining these two equations we get F = GMm/r2 = ma, or a = GM/r2. Thus, the gravitational acceleration of an object is only dependent on the mass of the Earth (M), it's distance from the Earth's center (r), and the gravitational constant G. We call this acceleration due to gravity g to distiguish it from acceleration due to some other force. The precise value of g varies with location and the local Earth density, but standard gravity is defined as g = 9.80665 m/s2.
Newtons third law states that forces exist in equal and opposite pairs. This means that for a given force F1 acting on a small mass m resulting in an acceleration a1, the Earth also experiences a force F2 on its mass M resulting in an acceleration a2. The total acceleration of the Earth and the small mass m is just the sum a1 + a2 = G(M + m)/r2. However, the mass of the Earth (5.98 x 1024 kg) is many many orders of magnitude greater than the small mass m so M + m is essentially M and a2 is essentially 0. If the mathematics are hard to read here, check out the Wikipedia articles on Universal Gravitation and Earth's gravity.
This experiment has even been performed on the moon by Apollo 15 Commander David Scott using a 1.32 kg geological hammer and a 0.03 kg falcon feather (Falcon was the name of the lunar module). Because there's no atmosphere on the moon, the hammer and the feather landed on the lunar surface simultaneously. This was broadcast live in 1971 and a link to the video is below.
On a historical note, the guinea was the British gold coin first used in this experiment and in the US it's sometimes called the Penny and Feather. Many current versions use a piece of ordinary metal instead of a coin, and a piece of paper instead of a feather.
Please note that the title picture is from the PIRA 200 demonstration list and is copyright 1993 by the University of Minnesota and the Physics Instructional Resource Association. According to this webpage, the title image is released for nonprofit educational use only. All pictures used for other nonprofit purposes, need to retain the signature of their creators...
Step 1: Motivation for a New Apparatus
Typically, the Guinea and Feather demonstration consists of a transparent tube containing two different masses and a method of attaching a vacuum pump. The tube is held vertically with both objects at the bottom, and then quickly flipped upside down. This is a fast and reliable way of starting both objects falling from close to the same height at close to the same time.
Several companies sell Guinea and Feather demonstrations, placing both objects together in the same tube. The problem with this configuration is that, at atmosphere, the heavy object can push the light object down underneath it, so it appears that they are falling at the same rate. Another major problem with the commercial models is that the tube diameter does not permit large objects. This means that someone sitting in the back of a large lecture hall may not be able to see the full effect of the demonstration. Finally, some single tube models are designed so that it is impossible to replace the objects within. While it may not be necessary to replace the objects, it's nice to at least have that option.
A far more instructive demonstration places the two objects, each in their own tube, next to each other for a direct comparison. This eliminates the possibility of the heavier object being situated above the light object and interferring during free fall.
There are a few pictures of dual tube variations online at other universities, but as far as I know, they are not commercially available. We used the dual tube apparatus below until it fell off the table and became a one-time-only demonstration of the exact same principle. The two problems with the old dual tube apparatus were: (1) The shortened tube length did not permit a long enough fall time, and (2) It was impossible to replace the light object (dried up and disentigrating masking tape).
Step 2: Before We Begin
I designed everything in AutoCAD 2000 and a detailed drawing will be available at the end of this instructable. All of the machining was done on manual (non CNC) shop equipment and any well equipped machine shop should be able to reproduce any of these parts without too much trouble. At the very least, you'll need a milling machine and a lathe with both 3-jaw dependent and 4-jaw independent chucks (a collet chuck helps too), a band saw for rough cuts, taps, and a wide assortment of end mills and drill bits.
The stock material needed for this includes acrylic, aluminum, and 303 stainless steel.
Before we use any power tools, let's take a moment to talk about shop safety. Be sure to read, understand, and follow all the safety rules that come with your power tools. Knowing how to use your power tools properly will greatly reduce the risk of personal injury. And remember this: there is no more important safety rule than to wear safety glasses.
Step 3: Top O-ring Block
This was the first part that I designed and machined for the new apparatus. The through hole is 2.25" and the counterbore is a few thousandths larger than 2.5". Later on, the acrylic tubes would be cemented to both this part the bottom o-ring block.
The O-rings are 2 7/8" ID x 3 1/4" OD x 3/16" wide, McMaster-Carr P/N 9452K56. The through hole, counterbore, and O-ring grooves were machined on a lathe using a 4-jaw chuck. To cut O-ring grooves you can either buy parting/grooving tools, or grind your own from high speed steel tool blanks. I ground my own from a 3/16" HSS tool blank.
There are eight untapped through holes in this piece, the top cap block, and the counterweight for 1/4"-20 x 3" long stainless steel socket head cap screws.
Step 4: Top Cap Block
My original plan was to have the top O-ring block and the top cap block fastened together without the counterweight (next step).
The second picture is a section view showing the top two blocks and the O-rings. The scaled image is dim and hard to see, but it looks better enlarged (click on the i in the upper left corner).
Step 5: Counterweight
A big slab of aluminum to balance out the weight of the brass fittings on the bottom. It doesn't have the best surface finish but you'll only see the sides when everything is assembled.
Step 6: Top Assembly
Everything is held together by eight 1/4"-20 socket head cap screws.
Step 7: Bottom O-ring Block
Like the Top O-ring block, this part has a 2.25" through hole with a 2.5" counterbore as well as the O-ring grooves. Additionally though, it has two 1/4"-18 holes for the right angle brass fittings, eight 1/4"-20 holes to mount the bottom cap block, and six #10-32 holes to mount Al channel brackets.
Step 8: Bottom Cap Block and Object Platforms
The Bottom cap block is also similar to the Top cap block except for two 1/4"-20 bottom-tapped holes to mount the object landing platforms. The objects in the two vacuum tubes will land on these platforms, just above the top face of the Bottom O-ring block. Without the platforms, the objects would land out of sight below the right angle brass fittings. The platform outside diameters are smaller than the 2.25" tube inside diameter and they are drilled through the top and sides to allow air to be pumped out of the tubes.
Step 9: Bottom Two Blocks and Object Platforms
Step 10: Vacuum Hardware
Two short pieces of Aluminum channel are used as brackets to mount toggle valves. These pictures were taken before I sanded the aluminum with some 100 grit sandpaper.
Another piece was used to mount a simple manifold.
See the complete assembly pictures to see how the tubing will connect the two tubes to the vacuum pump.
Step 11: Pivot Block
The two tubes are clamped and held in place by the pivot block. The whole assembly rotates about the 303 stainless steel dowel pins which are in turn clamped to the aluminum support tubes. After I took these pictures, I drilled a hole in the front face for a 1/4"-20 set screw to prevent the dowel pins from rotating without the pivot block. I also milled a flat surface on the dowel pins for the set screw to hold on to.
Before inserting the dowel pins, cut two short lengths of tube and turn two aluminum donuts to provide support. Acrylic can be brittle and could break if too much pressure is applied when pushing in the dowel pins.
Step 12: Bearings, Bearing Blocks, and Aluminum Support Tubes
The ball bearings are 3/8" x 7/8" x 7/32" wide, McMaster-Carr P/N 60355K14. The bearings sit in a 2" aluminum block with a 0.876" counterbore.
There are two 2" square aluminum support tubes with 1/8" thick walls. There are four more holes and another slot on the opposite parallel face. The bearing support blocks are screwed to the aluminum support tubes so that the screw heads are completely hidden from the outside.
Step 13: Base Plate and Support Tubes
Originally, the new Guinea and Feather apparatus was going to be bolted to a table during use and then removed and placed on a shelf for storage. The large knurled knobs and handles were going to make it easier to setup and disassemble. We later found a perfect sized typing cart so it became a permanent assembly. The large knobs were replaced by a smaller screw assembly, but the handles remained. Also, I bought black anodized handles because the original idea was to paint all of the aluminum parts black.
The short posts are 1.76" square with a 0.025" chamfer to accomodate the inside radius of the 2" square tubes. They're mirror opposites of each other and are screwed to the base plate from the bottom. The support tubes are screwed to the posts from the side and back by 1/4"-20 socket head cap screws.
The base plate is fastened to the table by two 1/2"-13 x 3 1/2" socket head cap screws. There's a short piece of aluminum with the same hole location and thread pattern underneath the top of the cart.
Step 14: Dowel Extensions, Handles, Bolts
The dowel pin stops in the middle of the 2" support tubes. The dowel pin extensions and the 2" square dowel pin clamping blocks extend the dowel pin outside the support tubes and allow a long handle to be attached. The dowel pin extensions extend about 0.01" past the face of the clamping blocks. When the handles are screwed to the clamping block, the friction is enough to turn the whole apparatus.
Instead of flipping the apparatus upside down by hand, possibly breaking the brittle acrylic, people turn the handles quickly to rotate the apparatus.
The threaded hole on the handle lines up with the through hole in the sides of the support tubes. The locking bolt holds the whole apparatus in the upright and locked position during storage and transport.
Step 15: Vacuum Pump, Gauge, and Cart
The vacuum gauge was purchased off eBay. Standard atmospheric pressure is 76 cm of Hg (or 760 mmHg which is also called 760 Torr), and the gauge reads the pressure relative to atmosphere. For example, if the gauge reads -70 cm Hg, that's 76 - 70 cm Hg = 6 cm Hg (or 60 Torr). Some mechanical pumps can get down to a few millitorr, which is more than sufficient to remove the air resistance in this experiment.
Step 16: Objects
At first I was planning to use a replica of a British guinea but they're only about an inch in diameter and that's too small to be very visable. The aluminum disk was originally the guinea from the old dual tube apparatus shown earlier. I simply reused it when the old apparatus broke.
I was also going to use real feathers, but there was too much static cling between them and the acrylic tubes. The bright pink and green paper is much more visable anyways.
Both the aluminum and paper disks have a diameter of 1.75" (the tube ID is 2.25"), but the mass of the aluminum disk is over 60 times greater. This combination of the metal and bright paper disks works quite well because the metal makes a loud thud as it hits the bottom of the tube, and the paper is large enough to be seen fluttering down. When the air is pumped out, you can still hear the aluminum disk land, but you can see that the paper lands at the same time. Just watching the paper, it can appear as if the paper is making the loud thud even though it's really the aluminum disk landing at the same time.
The electronic scale was surplus equipment which is why it has a Do Not Use sticker. It still works fine and is accurate even if the calibration isn't official.
Step 17: Complete Apparatus
Here is the complete Guinea and Feather apparatus from top to bottom. There is a one meter stick (white) in front of the cart, and a two meter stick (brown) in front of the left support tube. The total height is approximately 252 cm (8 feet, 3 inches) tall.
After some sanding, the aluminum parts look pretty good.
To demonstrate the different fall times at atmosphere, all three toggle valves are opened. The hose is then connected and the pump is turned on. After sufficient vacuum is reached, the valves are closed and the hose is disconnected. Most of the air has now been removed, and the gauge still reads the pressure in the tubes.
Step 18: Operation and Video
Free fall in atmosphere
1) Open all three toggle valves and disconnect the hose from the manifold.
2) Unscrew both of the locking bolts. The apparatus is now free to rotate.
3) Grasp one of the handles and quickly rotate the whole apparatus 180 degrees.
4) Watch and listen for the thud as the aluminum disk lands first while the paper floats down.
5) Repeat a couple times to show that air resistance always causes the paper to land second.
Creating the vacuum
It helps to screw in one of the locking bolts to keep the apparatus in place during this stage.
1) Connect the hose to the vacuum manifold.
2) Turn on the vacuum pump.
3) Watch the vacuum gauge change as the air is removed from both tubes.
5) Wait until the gauge reads -76 cmHg. Remember, this is relative to atmosphere (76 cmHg) so the actual pressure in the tubes is close to (but still slightly above) 0 cmHg.
6) Close all three toggle valves, turn off the vacuum pump, and disconnect the hose from the manifold.
Because the vacuum gauge is on the low pressure side of the cart/base plate toggle valve, it will read the same pressure as the tubes.
Free fall in vacuum
1) Unscrew the locking bolt that kept the apparatus upright. The apparatus is again free to rotate.
2) Grasp one of the handles and quickly rotate the whole apparatus 180 degrees.
3) Watch and listen as both objects always land simultaneously.
4) Repeat a couple times to verify the effect.
Repeat at atmosphere
1) Open the toggle valves to the tubes and listen to the air rush back in. Watch as the rushing air blows the paper disk upwards.
2) Repeat the experiment at atmosphere. The paper again lands second.
When completely finished, screw in both locking bolts to secure the apparatus and open the cart/base plate toggle valve.
Step 19: CAD Files
I originally designed this in 2D using AutoCAD. I've since been playing around with the free 3D CAD program Alibre Design Xpress and I made models of most of the parts (I don't have an assembly file yet). You can download my original .DWG and a .ZIP of the Alibre parts if you want.
Step 20: Support Amazon.com
Step 21: The End
About Me (Shameless Self Promotion)
Luke Luck isn't my real name of course, it's really Steven. I probably have the coolest job ever as a full time lecture demonstrator for the University of WashingtonDepartment of Physics. We provide demonstrations for undergraduate physics classes on everything from basic mechanics, electromagnetism, thermodynamics, quantum mechanics, and everything in between. Essentially, I get to play with toys (uhh I mean teaching tools) all day, as well as design and build new demonstrations. This new Guinea and Feather apparatus took about a year to design and build (working off and on, in between regular classes and other projects) and was just completed recently.
Thank you reading this instructable. Please post any questions and comments and I'll try to reply in a timely manner.
University of Washington Department of Physics