Bennett Science Blog

Photo Credit: Zátonyi Sándor/Wikimedia Commons By Andrew Bennett In this blog post, you will learn how to model an object's position as it undergoes simple harmonic motion using sine or cosine functions. Simple Harmonic Motion Refresher Simple harmonic motion is defined as periodic motion caused by a restoring force that is proportional to the object's displacement from equilibrium. This definition might seem arbitrarily complicated, but there are good reasons for separating this type of motion. For this post, it is important to note that the position, velocity, and acceleration of any object undergoing simple harmonic motion can be described using the sine and cosine functions. We might not be able to model other types of repeated motions with simple equations like this. Sine Function for SHM A general form frequently used here for the sine function is: x ( t ) = A *sin (ꞷ t ) Where: x = the position at some moment in time A = the amplitude of the motion...

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...

Photo Credit: Public Domain By Andrew Bennett What Is Heat Mean in Physics? Heat is a bit of a tricky term to work with in science. In everyday use, we typically use heat as a verb to mean "make warmer." We also use it as a noun in reference to the furnace, as in, "turn up the heat."  In science, heat refers specifically to the processes in which thermal energy (kinetic energy for individual atoms) moves from place to place. All objects are doing this all the time, but we find that heat transfers from warmer objects happen faster than from cooler objects, meaning that there is a net flow of energy from warmer to colder objects or locations. As a result, putting a hot cup of tea in your cold hands will always result in the tea getting colder and your hands getting warmer. Heating Methods There are three methods of heating: conduction, convection, and radiation. Frequently, we find situations involving heating where all three of these are going o...