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

James Prescott Joule's apparatus. Credit: Harper's New Monthly Magazine, No. 231, August 1869 By Andrew Bennett For many years, people did not understand the nature of temperature. In an experiment that combined measurements of motion (and the energy associated with it) and temperature, James Prescott Joule established that the energy associated with motion and position is the same as the energy associated with heat. Richard Feynman had a great way of describing how all this works at the atomic level. Check out an interview where he describes atoms "jiggling" and how we perceive it as temperature. How Do We Apply the Results of Joule's Experiment? This establishes some key ideas for our investigations of processes involving compressing, expanding, heating, and cooling of gases. At the end of this video, we work through a conservation of energy problem that has energy entering or leaving the system both as work and as heat. If viewing via ema

Photo Credit: Public Domain By Andrew Bennett Fluids in motion show some interesting properties. In fact, some behaviors are so far impossible to predict exactly. In a first-year high school physics class, we tend to limit our discussion of moving fluids to the simpler cases, involving incompressible, nonviscous fluids with consistent flow rates. Water moving through pipes is a great example of this, so we end up doing a lot of problems about water in pipes of different shapes and sizes. Continuity Equation and Volume Flow Rate With these assumptions, we can conclude that in some amount of time, the same amount of water must pass one point in the pipe as passes another nearby point in the pipe. If anything else were true, we would have water appearing or disappearing between the two points. This idea can be expressed by the continuity equation, which reads: The product of the cross-sectional area and the fluid speed is equal to the "volume flow rate" of the wate

Photo Credit: Public Domain By Andrew Bennett What Is Absolute Pressure? Absolute pressure is the force applied per unit of area ( see my previous post on pressure ). What Is Gauge Pressure? The pressure in a fluid is caused by the particles in the fluid colliding. As long as there is fluid present, there is pressure. So, why does my gauge read zero pressure when I have a flat tire?  Is there a perfect vacuum inside my tire? We often measure what is known as "gauge pressure" (rather than absolute pressure), which simply subtracts atmospheric pressure from absolute pressure. Frequently, what we care about is actually the difference in pressure between what is in a container and what is outside the container (often atmospheric pressure), so gauge pressure is a convenient measurement. When the gauge reads zero, it simply means that the pressure inside the tire is equal to the pressure outside the tire, which is very close to "atmospheric pressure." Gauge

Illustration Created Using Public Domain Photos By Andrew Bennett Forces and Pressure in Physics Problem Which would be worse: Having your foot stepped on by an elephant or by a woman wearing stiletto heels? Although the force from the elephant will certainly be larger, it might also be worth considering the amount of pressure on your foot. By this measure, you might be better off with the elephant! **Important warning: Do not tell any woman you know that you'd rather have an elephant step on your foot than her. No amount of physics will get you out of a mess like that!** Forces and Pressure in Fluids When we move from solid objects to fluids (liquids and gases), all of the same rules of physics still apply. We sometimes have some work to do to convert those rules to a form that we can make calculations and predictions with. What Is Pressure? When dealing with solid objects, it was easy to identify individual forces that act at single locations.  With fluids, howeve

Credit: Public Domain By Andrew Bennett Most of us are familiar with gravity as the force the pulls things down toward the ground, but it turns out to be much broader than that. All objects exert gravitational forces on each other. We notice the one from the Earth so much more than from any other object because it is so big and close. We also don't notice the effect of ourselves exerting a gravitational force on the Earth. This is because such a small force doesn't do anything noticeable to something the size of the Earth. What Is Newton's Law of Universal Gravitation? Newton's Law of Universal Gravitation says that for any pair of objects, the size of the gravitational forces they exert on each other depends on their masses and the distance between them. In this video, you will learn about the basic idea of gravitational attraction. Then, you will learn how the Newton's Law of Universal Gravitation equation works. Finally, you will learn how to solve an e

Credit: Public Domain By Andrew Bennett Making models to describe the world around us is a huge part of science. One way to model something is to write an equation that describes it. For example, we can write equations that describe the position of objects in simple harmonic motion. Since a simple harmonic oscillator (such as a pendulum or a mass on a spring) goes back and forth again and again, we need to model this using a function that does the same thing. As long as the requirements for simple harmonic motion are met, the motion can be modeled with a sine or cosine function. (SHM is periodic motion caused by a restoring force that is proportional the object's distance from equilibrium. See this post for more information.) Simple Harmonic Motion Equation If we were to graph Y = sin( x ) and Y = cos( x ), we would see that both functions have a maximum value of 1, a minimum value of -1 (so the amplitude of each function is 1), and a period of 2ℼ radians (360 degrees).