Recreating this experiment to confirm universal gravitation would be awesome. Construction of the experimental apparatus should be well within an intelligent 8-year-old’s abilities—all you need to provide/acquire is the idea and the more specialized equipment (e.g. lead weights). You can go shopping together for the more common stuff (nylon monofilament, etc.).
Finding a suitable location is probably the trickiest part, but the reward would be well worth it—this is a real scientific experiment, the Cavendish experiment, which wasn’t carried out until after Newton’s lifetime. It is also something that nobody ever does in school, because our schools are lame and boring.
The level of precision, patience, and understanding in that experiment would make me estimate a slightly higher age range than 8 years old for it. I would have guessed around 12 as the appropriate minimal age.
Nineteen centuries elapsed between the death of Archimedes in 212 B.C. and the publication of Newton’s Principia in 1687. Given the philosophical implications of Newton’s theory, it’s interesting to speculate what might have happened had Archimedes discovered the universal nature of gravitation.
To do this, he would have had to suspect that attraction was universal, suggest an experiment to confirm this, and perform that experiment, with results validating the hypothesis. Here is information in Archimedes’ possession which might have suggested the universality of gravitation.
The main problem with this experiment for an eight year old is that one has to leave the room when it operates. That’s a big deal.
Now suppose you’re crouching down in order to move the test masses, with your centre of gravity one metre from the closer test mass, and that you weigh 65 kg. Plugging these numbers into the calculator shows that your own gravitational attraction on the nearer end of the beam is 0.000147 dynes, 1.7 times as great as that of the test mass. Your actual influence on the motion of the balance arm is less, however, since what matters is the difference in force exerted on the masses at the two ends of the balance arm. Since your centre of gravity is more distant than the test masses, the difference is less.
Let’s work it out. Assume the centres of gravity of the two masses on the balance arm are 25 cm apart, and that you’re crouching so the arm makes a 45° angle with your centre of gravity, one metre from the centre of the arm. The nearer mass is then 17.68 cm closer than the more distant one and the difference in gravitational attraction (or tidal force) on the two masses is the difference in attraction on a mass 91.16 cm distant and one 108.84 cm away. The calculator gives the attraction on the near end of the arm as 0.0001764 dynes and the far end as 0.0001238 dyne, with a difference of 0.0000527 dynes. Now recall that the force exerted by the test mass was 0.000085 dynes, only 1.6 times as large, so even taking into account the reduced tidal influence due to your greater distance, the force you exert on the balance cannot be neglected. This makes it essential to remotely monitor the experiment so your own mass doesn’t disrupt it.
In practice, air currents due to your motion and resulting from convection driven by your body’s temperature being above room temperature may exert greater forces on the balance arm than the gravitational field generated by your mass. In any case, it’s best to let the experiment evolve on its own, observed from elsewhere.
Fourmilab’s version is bogus… given the masses involved, a calculation using f = GmM/r^2 shows that it should take a lot longer for the moving mass to reach the test mass than it does in the video. The most likely explanations for what is seen in Fourmilab’s video are static electricity or outright fraud. (Incidentally, my father actually did build a workingCavendish experiment in our basement; it uses much larger fixed masses and a thinner wire, and it does indeed move much more slowly. It turned out to be very difficult to get it to work; the effects of ordinary air currents tend to overwhelm the gravitational attraction.)
As long as we made sure none of the objects we were experimenting with were magnetic or electrically charged (easily arranged, assuming they are conductive, simply by bringing them into contact so all excess charges equilibrate)
But you’re right, I would consider it much more convincing if the experiment were set up so that everything was connected by conductors.
The other thing is that in the video, the bar is initially nearly perpendicular to the external masses. In this configuration, not only are the bar’s masses far from the external masses, but the torques are almost balanced. I don’t see any mention of this.
The video appears to indicate that it takes 3 minutes for the bar to rotate around and make contact with the external masses. I wrote a quick sketch of a program to figure out how long it should take, and I got over 3 hours. Specifically, I used the favorable assumptions that the foam bar is massless, that the setup is frictionless, and I calculated what would happen with one external mass of 740g and an initial separation of 17 cm, until the separation decreased to 2 cm. The initial separation isn’t clearly stated anywhere—there is a vague mention of “at the 14 cm distance when the beam is at the midpoint between the masses”. The bar diameter is clearly given as 30 cm, and I believe I’m getting the basic trig right when I calculate that an angle of 70 degrees would result in a 17 cm separation. Finally, I’m considering only one bar mass and one external mass (utterly neglecting the near-symmetrical torque is highly favorable, producing a time estimate that will be shorter than reality) and because I didn’t want to write the trig, I’m working with linear movement in free space, instead of the actual rotation. (I used Boost.Units to ensure that I didn’t screw up my math even further than these simplifications.)
(It would be quite possible to modify this to do a fully “realistic” simulation, with the two pairs of masses and the rotation. That’s more work than I want to do at 1 AM, though.)
Recreating this experiment to confirm universal gravitation would be awesome. Construction of the experimental apparatus should be well within an intelligent 8-year-old’s abilities—all you need to provide/acquire is the idea and the more specialized equipment (e.g. lead weights). You can go shopping together for the more common stuff (nylon monofilament, etc.).
Finding a suitable location is probably the trickiest part, but the reward would be well worth it—this is a real scientific experiment, the Cavendish experiment, which wasn’t carried out until after Newton’s lifetime. It is also something that nobody ever does in school, because our schools are lame and boring.
The level of precision, patience, and understanding in that experiment would make me estimate a slightly higher age range than 8 years old for it. I would have guessed around 12 as the appropriate minimal age.
Yeah, you’re probably right.
I love that write up for this:
The main problem with this experiment for an eight year old is that one has to leave the room when it operates. That’s a big deal.
It occurs to me that you could probably build a box around it with a plastic window, to isolate it from air currents.
That’s what I deserve for not rereading the page after a decade, sigh.
Fourmilab’s version is bogus… given the masses involved, a calculation using f = GmM/r^2 shows that it should take a lot longer for the moving mass to reach the test mass than it does in the video. The most likely explanations for what is seen in Fourmilab’s video are static electricity or outright fraud. (Incidentally, my father actually did build a working Cavendish experiment in our basement; it uses much larger fixed masses and a thinner wire, and it does indeed move much more slowly. It turned out to be very difficult to get it to work; the effects of ordinary air currents tend to overwhelm the gravitational attraction.)
Static electricity was mentioned:
But you’re right, I would consider it much more convincing if the experiment were set up so that everything was connected by conductors.
The other thing is that in the video, the bar is initially nearly perpendicular to the external masses. In this configuration, not only are the bar’s masses far from the external masses, but the torques are almost balanced. I don’t see any mention of this.
The video appears to indicate that it takes 3 minutes for the bar to rotate around and make contact with the external masses. I wrote a quick sketch of a program to figure out how long it should take, and I got over 3 hours. Specifically, I used the favorable assumptions that the foam bar is massless, that the setup is frictionless, and I calculated what would happen with one external mass of 740g and an initial separation of 17 cm, until the separation decreased to 2 cm. The initial separation isn’t clearly stated anywhere—there is a vague mention of “at the 14 cm distance when the beam is at the midpoint between the masses”. The bar diameter is clearly given as 30 cm, and I believe I’m getting the basic trig right when I calculate that an angle of 70 degrees would result in a 17 cm separation. Finally, I’m considering only one bar mass and one external mass (utterly neglecting the near-symmetrical torque is highly favorable, producing a time estimate that will be shorter than reality) and because I didn’t want to write the trig, I’m working with linear movement in free space, instead of the actual rotation. (I used Boost.Units to ensure that I didn’t screw up my math even further than these simplifications.)
I agree—something is extremely fishy here.
Showing my work:
The final velocity is about 9 inches per hour.
(It would be quite possible to modify this to do a fully “realistic” simulation, with the two pairs of masses and the rotation. That’s more work than I want to do at 1 AM, though.)