Bennett Science Blog

Photo Credit: YouTube Screenshot By Andrew Bennett The Cavendish gravity experiment requires us to be able to measure how much a hanging bar rotates when we place heavy weights nearby. In order to determine a reliable value for G, the gravitational constant, we must first measure the shift angle very precisely. In this video, I build a protractor with a 3-meter radius that can measure angular shifts of as little as one one-thousandth of a radian. That's less than 0.06   degrees or about 3.5 minutes of arc! How I Built My Protractor The design is pretty straightforward but is extremely labor-intensive to construct one this size. I start by making a circular wall to use as the surface of the protractor made of thin, white, flexible pressed wood. I glued some pieces of 2x4 to my garage floor and used a router to cut a groove that the wall will fit into. To make the groove along a circle, I first traced out the circle on the wood by attaching a marker to a long wire, which the...

Image Credit: Wikimedia Commons By Andrew Bennett As I'm using radians as my unit of measure for all angles in my Cavendish experiment, I thought some background might be useful for some of my readers. So, let's get right to it. What Is a Radian? Simply put, a radian is a unit for measuring angles. Imagine a big circle drawn on the ground in chalk. Use your chalk to draw a straight line from the center of the circle to the edge, and measure that line (the radius of the circle). Now, walk that same distance around the outside of the circle (if the circle has a radius of 5 meters, walk for 5 meters on the edge). Draw a new line from the edge of the circle where you are standing back to the middle. The two lines you've drawn have an angle between them that we define to be equal to 1 radian. Instead, if we had walked along the outside of the circle for a distance equal to 2 times the radius, then the lines we drew would have had an angle between them equal to 2 radi...

YouTube Screenshot (https://www.youtube.com/watch?v=eu_WRsxGnK0) By Andrew Bennett What Is the Law of Reflection? If you have ever played pool, you've probably done a little mental geometry that looks very similar to the Law of Reflection. This law simply states that whenever a wave hits a boundary and reflects, the angle it reflects at is equal to the angle at which it hit the boundary. Lining up a bounce shot in billiards requires the same thinking. What Is Specular Reflection?  Very flat surfaces (such as calm water, glass, and mirrors) make such clear reflections because every bit of light that hits the surface will encounter a surface at exactly the same angle. In physics, we describe this as regular or specular reflection. Specular reflection. YouTube Screenshot (https://www.youtube.com/watch?v=eu_WRsxGnK0) What Is Diffuse Reflection? Surfaces that aren't as polished (such as walls, clothes, or skin) have tiny bumps covering them.  When light h...

YouTube Screenshot (https://www.youtube.com/watch?v=E1lCjq4IzJw) By Andrew Bennett Cavendish Experiment Build Update At this point, the device itself is built except for plastic sheeting covering the whole thing. The next step is to set up the lasers and mirrors for making extremely precise measurements of angles. Cavendish Gravity Experiment FAQs I've received a lot of feedback and questions on my previous Cavendish videos . Here's a look at the frequently asked questions. "Doesn't his need to be done in a vacuum to eliminate air currents as a variable?"  This will not be conducted in a vacuum. As far as I can tell, that would make this nearly impossible.  Removing the air from the container requires a significant amount of air movement, which would get the torsional balance swinging. Since air resistance is really the only force slowing down that swinging, you'd be stuck with way too much movement to make a good measurement. I also don't...

YouTube Screenshot (https://www.youtube.com/watch?v=l-VRjwe_EHU) By Andrew Bennett What Is the Torsion Constant? The Cavendish gravity experiment involves a balancing of torques on the torsion balance . On the one hand, we have gravity from heavy objects placed near the ends of the balance trying to twist the whole thing in one direction. Opposing that, we have the wire trying to untwist. That "untwisting ability" is described by a number called the torsion constant of the wire . If we are to get a measurable deflection from the Cavendish experiment, we need to use a material for the wire with a very low torsion constant. Testing the Constant Using a Torsional Pendulum Testing for the torsion constant directly requires special equipment to measure very small torques. In this video, I test it indirectly by setting up a torsional pendulum (so that the bar on the wire twists back and forth repeatedly). I do this because the relationship between the period of a torsiona...

YouTube Screenshot (https://youtu.be/qqyxKSsXX7A) By Andrew Bennett In order to replicate the Cavendish gravity experiment and experimentally determine a value for the universal gravitation constant, I built a torsion balance. This revised design is longer than anything I've used before. It also gives me the flexibility to adjust the positions of the attachment points for the wire and the weights. What Materials Are Included? PVC pipe is used as the base for the brackets. I heated it with a heat gun, then molded it to the aluminum bar. The weights are currently dumbbell weights with a bottle cap turned into an adapter between the dumbbell mounting holes and the small bolts. If viewing via email, click here to see the video. What's Next in the Cavendish Gravity Demo Series? In the next video, I'll be using the torsion balance as a torsion pendulum to evaluate the torsion constant of the different string and wire options for the Cavendish experiment.  Please b...

YouTube Screenshot By Andrew Bennett After learning from a few previous versions of the Cavendish gravity experiment, I am carefully examining options for my third version. In the video below, we examine some of my options for materials. Choosing Wire with a Low Torsion Constant The big decision I need to make is what to use as the wire that the torsional balance hangs from.  Ideally, we want something with a very low torsion constant. This means that the wire presents very little resistance to twisting. Since the gravitational forces that will twist the pendulum are so small, the torque resisting that twist needs to be extremely small, as well. YouTube Screenshot The torsion constant seems to depend both on the material the wire is made of and the diameter of the wire. In the video below, we investigate some possibilities and discuss the material and diameter of each option. What's Next in My Cavendish Demo Project? I still have a question about whether the l...

YouTube Screenshot ( https://www.youtube.com/watch?v=19QbqZjKqJQ ) By Andrew Bennett Gravity Demo 3.0 Is Underway This video marks the beginning of my third dive into the Cavendish experiment . Before now, I've created devices that could potentially show the effects of gravitation between small objects. However, I have never eliminated enough sources of uncertainty to make that definitive or to derive a value for G. That is the goal of this summer's physics project. Math Behind Cavendish Experiment Explained In this video, I work through the math for determining G from the Cavendish gravity experiment. This math includes the Law of Universal Gravitation, equations for torque (from both a point force and a twisted string), the formula for the period of a torsional oscillator, and some equations for calculating rotational inertia. The end result is an ugly equation that will get us an important value: the Universal Gravitational Constant. More Info on My Newest Grav...

Cross-section drawing from Henry Cavendish's 1798 paper published in Philosophical Magazine. Credit: Public Domain By Andrew Bennett The Cavendish Gravity Experiment Explained In the late 1700s, a British scientist named Henry Cavendish developed a device to measure the gravitational force between two small objects. The data from his experiment was used to determine the mass of the Earth, as well as the value for the Universal Gravitational Constant, which appears in Newton's Law of Universal Gravitation. Nearly everyone is familiar with gravity as being the thing that makes us fall down toward the ground. The revelation that all objects (not just stars, planets, and moons) exert gravitational pulls on each other is fairly shocking for most of us. For small objects, like you and me and a rock, the size of this force is so small that we never notice it. Cavendish's experiment was the first time that anyone was able to measure the size of this tiny force. The unfor...