...oscillation depended on the effective mass of the spring and the period of oscillation. Students recorded basic information such as the position of the mass before the spring is charged, the path of the mass, the peak of the oscillation, as well as the force the mass and the spring exert on each other. Data studio and a force sensor, and a position sensor was used to get accurate measurements of these values. Goal The purpose of this laboratory is to characterize the oscillation of a simple spring-mass system. Theory If a spring is stretched or compressed a small distance from its equilibrium position, the spring will exert a force on the body given by Hooke's Law, where is known as the spring force. The constant, , known as the spring constant, and is the displacement from the equilibrium position. The spring constant is a clue of the spring's strength. A large value for indicates that the spring is strong or stiff. A low value for means the spring is weak or flexible. Springs with large values can balance larger forces than springs with low values. The negative sign in indicates that the direction of is always opposite the direction of the displacement. The spring force is a restoring force. In other words, the spring force always acts to return the weight or body to the equilibrium position regardless of the direction of the...
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...! ! ! ! ! ! ! ! ! A Boxer’s Punch A Senior Project presented to the Faculty of the Physics Department California Polytechnic State University, San Luis Obispo ! ! ! In Partial Fulfillment of the Requirements for the Degree Bachelor of Science, Physics ! ! by ! ! ! Jacob A. Ekegren ! April 2014 ! ! Advised by Dr. Matthew Moelter ! © 2014 Jacob A. Ekegren ! ! Table of Contents ! Pg. # Introduction and Setup 3 Theory Applied 4 Experimental Procedure 5 Results and Analysis 5 Conclusion! 10 References 11 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 2 Introduction and Setup For over a year now, I have been interested in the sport of boxing. This fascination led me to explore what occurs to a human head upon impact from a boxer’s punch. It is known that a knockout occurs when blood circulation to the brain is compressed. This compression results from the sudden acceleration and deceleration of the head[1]. Therefore, the primary focus of this experiment explores the relative effort necessary to cause significant movement to a head about a neck. Figure 1 - Picture of modeled head and spine secured to a table ! To achieve this, a simplistic mechanical model of a human head, a socket, and a spine was built. A volleyball was used to simulate a head. A garage door spring with a diameter of 4.0 ± .05cm was used as a spine. Lastly, a small wooden...
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...plane should have flown better than a 100,000 lb. metal object. It wasn’t until I was older and had my first physical science class that I really started to get a grasp on what was really going on to make something that large liftoff and continue to fly. There are two names that stand out when speaking about the physics of flight: Sir Isaac Newton and Daniel Bernoulli. Without them there would be far less understanding of the forces of flight and the physics behind the art of flying. Sir Issac Newton was a mathematician and physicist who transformed the scientific world in 1666 with the development of the theories of gravitation at the young age of 23. Twenty years later in 1686, Newton published Principia Mathematics Philosophiae Naturalis, Latin for “Mathematical Principles of Natural Philosophy”, which detailed his work in mathematical physics and presented his three laws of motion. His first law is commonly known as the law of Inertia, and it states “A body in motion at a constant speed will remain in motion at that speed unless acted upon by outside force; A body at rest will remain at rest unless acted upon by...
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...For each mass, there is a force on a spring that acts on it from both left and right side of the masses. The following list of equations, that will be written in a linear system of differential equations, represents the forces acting onto each mass: m_1 〖x_1〗^''=〖-k〗_1 x_1+k_2 (x_2-x_1 ) m_2 x_2^''=〖-k〗_2 (x_2-x_1 )+k_3 (x_3-x_2) m_3 x_3''=-k_3 (x_3-x_2 )-k_4 x_3 m_1 〖x_1〗^''=x_1 〖(-k〗_1-k_2)+x_2 (k_2) m_2 x_2^''= x_1 (k_2 )+x_2 (〖-k〗_2 〖-k〗_3 )+x_3 (k_3) m_3 x_3''= x_2 (k_3 )+x_3 (〖-k〗_3 〖-k〗_4) [■(x_1''@x_2''@x_3'')]= [■((〖-k〗_1 〖-k〗_2)/m_1 &k_2/m_1...
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...MEASUREMENT OF THE SPRING CONSTANT TWO METHODS COMPARED ABSTRACT A spring is an elastic object, which can be extended and contracted by forces with a constant elastic coefficient. This report assesses two methods for determining the spring constant of a specific spring. One method uses the length that the spring extends and the masses that are attached to the spring. The other method measuring the spring constant is based on the harmonic motion. INTRODUCTION Spring constant is an instinct property of a spring. The magnitude of a spring constant depends on the material of the spring but not the lengths it extends or contracts or the forces that are applied to the spring. Hook’s law predicts that the length the spring extends or contracts is directly proportional to the force applied by the coefficient of the spring constant. The aim of this experiment is to compare the two measures of finding the value of the spring constant of a spring. MATERIALS AND METHODS METHOD A The spring is hanged on an iron stand. The lengths of the spring, L, are measured when the spring is attached to different masses, M, of metals vertically. The lengths are measured by using a ruler with scales, while the mass attached to the spring can be read from the metal. For better accuracy, five masses are attached during this method. METHOD B The spring is hanged on an iron stand. Different masses, m, attached to the spring can be read from the metals and the time period, t, of the spring...
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...Holt Physics—Chapter 5: Work and Energy Price I. Section 5.1—Work A. Definition of work 1. Work does not mean the same thing in Physics as it does in the everyday sense of the word. 2. Work is defined as a force causing a displacement. Work = force x displacement W = Fd 3. Work is NOT done on an object unless the displacement is greater than zero 4. The only forces that are considered to do work are those that are parallel to the displacement. 5. For this reason we use our trigonometric functions to calculate forces applied at an angle. Insert Fig 5-2 6. Note that Θ is the angle between the applied force and the displacement. 7. Work is described in Newtons x meters (force x displacement). The unit of work is the Joule (J) 8. 1 Newton meter = 1 Joule 9. Work is a vector with both direction AND magnitude. This means WORK CAN BE NEGATIVE! 10. Negative work is most commonly used to slow an object down or decrease its velocity. II. Section 5-2: Energy A. Kinetic Energy 1. Kinetic energy is associated with an object in motion. 2. Kinetic energy depends on speed and mass Kinetic Energy = ½mv2 3. Kinetic energy is a scalar and will use Joules as...
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...ASSAM EARTHQUAKE AND OUR BUILDINGS Md Ali Akbar MOLLICK* Introduction An earthquake of magnitude 8.7 on the Richter Scale (8.1 on the Moment Magnitude Scale) occurred on 12th June 1897 at 5.11pm in the Assam Basin, some 250 kilometers (km) north from Dhaka, 130 km north-west from Sylhet and 70 km north from today's Bangladesh and Indian border. The epicenter was 26o (N) and 91o (E) and focal depth was 32 km. The shaking was felt over an area of 650,000 square-kilometer (sq-km) and destruction was taking place over an area of 390,000 sq-km. Many masonry buildings including temples, over the destructive area such as Dhubri, Goalpara, Guwahati, Kuch Bihar, Agortola, Kolkata and other cities inside India, either totally or partially damaged due to this earthquake. The earthquake created general panic in Dhaka and other areas of today's Bangladesh including Rangpur, Dinajpur, Sylhet, Rajshahi, Natore, Mymensing, Dhaka, Chittagong, Comilla, Noakhali, Jamalpur etc. A total number of 1542 persons were killed due to this earthquake out of which five were from Dhaka including two foreigners. Three buildings such as Shaheen Medical Hall, Temple Nazi's Shabagh Math and house occupied by Mrs Stansbury were totally damaged and the government houses for commissioner, collector, judge and civil surgeon were partially damaged in Dhaka, which were rebuilt. The total cost for the rehabilitation was 150,000 taka. The intensity of shaking in Dhaka was VIII+ on the Modified Mercili Intensity (MMI)...
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...some interesting ideas about various types of motion along a single direction. We gain some valuable insights and tools so that when we generalize to study the motion of objects in the real three-dimensional world we are well prepared for that undertaking. The case studies in this chapter include motion when the net force is constant (we study the local gravitational force near the Earth), one-dimensional motion of an object in a fluid (where we show that there are frictional forces that vary with time), and the oscillatory motion of an object attached to a spring. After learning something about springs, we next consider the deformation of an elastic solid and the phenomenon of viscoelasticity. This is a topic of special interest in the study of structural biomolecules such as bone and blood vessels. We conclude the chapter with a discussion of the structure and dynamics of macromolecules, specifically illustrating how to apply Newton’s second law to the difficult problem of determining the molecular motions (here in one dimension) of the constituent atoms of a protein. 1. THE CONSTANT FORCE Very frequently in dealing with mechanics problems, we know the forces acting on an...
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...Design of Body Slip Angle Observer Based on Nonlinear Tire Model for Electric Vehicle Stabilization Control with In-Wheel Motors Geng Cong, Hori Yoichi (The University of Tokyo) Abstract: Body slip angle is important for electric vehicle stabilization control with in-wheel-motors. However，as sensors to measure body slip angle are very expensive, it needs to estimate β from variables measurable. The most difficult forβestimation is that the strong non-linear characteristics of vehicle, especially non-linear characteristics of tire force makes vehicle model parameters change greatly as vehicle running in nonlinear conditions. This paper proposes an observer based on nonlinear tire model which can describe the tire lateral force in its nonlinear region. Simulation and experimental analysis demonstrate the observer’s effectiveness, especially when the vehicle running in nonlinear cornering regions. Key words: electric vehicle, vehicle stabilization control, body slip angle, nonlinear observer, nonlinear tire model 1. Introduction In recent years, considering environmental protection and energy conservation, electric vehicles (EVs) are intensively developed. Due to the improvement of motor design and control technology, modern configurations are developed for EV. One of the latest configurations is motor-in-wheels, which means motors can be fitted into all the driving wheels of EV independently. For vehicle chassis control, such configuration brings much more advantages...
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...o n b, a, C. C a r a m e l l a a Oepartment of Pharmaceutical Chemistry, University of Pavia, Viale TarameUi 12, 27100 Pavia, Italy b Department of Pharmacy, De Montfort University, The Gateway, Leicester LE1 9BH, UK Received 10 October 1994; accepted 9 December 1994 Abstract The mechanical resistance of gel systems was measured by means of a gel strength tester. Measurements were performed using a standard sample holder and probes of different geometry (conical, spherical and cylindrical). The systems tested were a K-carrageenan aqueous gel and a semisolid hydrophilic colloidal solution of hydroxypropylmethylcellulose. Blank measurements were also carried out using distilled water in order to take into account the buoyancy effect of the probe. The conical probe exerts mainly shear stresses on the gel, whereas the spherical and, to a greater extent, the cylindrical probe mainly exert compression stresses. Analysis of the shapes of the force-displacement curves has led to isolation of the shear and compressive deformation occurring in the systems and this, in turn, has enabled the differentiation between the structure and performance of the two semisolids. Keywords: Gel system; Gel strength test; Probe shape I. Introduction Gels are commonly used as vehicles for pharmaceutical and cosmetic preparations in many types of applications (dermatological, ophthalmic and intramuscular injectable). Gel formation is also involved in drug release from hydrophilic swellable...
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...Motion Of Train Control System Syed Zulfiqar Haider Bukhari(11TC51)1,Syed Noor-ul-Hassan Bukhari(11TC63)2 Department of Telecommunication Engineering, University College of Engineering & Technology, The Islamia University of Bahawalpur, Pakistan. engr.szhb@gmail.com1, syednoorulhassanbukhari@gmail.com2 Abstract— This project Automatic Street Light Control System aims at designing and executing the advanced development in embedded systems for energy saving of street lights by using light dependent resistor (LDR). Nowadays, human has become too busy and he is unable to find time even to switch the lights on or off. This can be seen more effectively in the case of street lights. The present system is like, the street lights will be switched on in the evening before the sun sets and they are switched off the next day morning after there is sufficient light on the roads. But the actual timing for these street lights to be switched on are when there is absolute darkness on the roads. This project gives the best solution for electrical power Keywords—: Small Toy train system (STTS), Small Toy Train System-Railway Track(STTS-RT) I. INTRODUCTION rain system has become very popular means for transportation of passengers and exchanging goods from one place to another in this modern era. Every developing country use the train system for these purposes. Thousands of people travel by the train system hundreds of miles far from one destination to another destination in a day. Even that...
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...electrostatic force is given by 1 0 tV 2 Fe 2 d The total driving force acting on gripper for ( n capacitors 2 sides) is F 2n Fe n 0 tV 2 d For numerical values, F n 0tV 2 d 200 8.55 10 12 50 10 6 140 2 0.335 mN 5 10 6 b) From the motion equation, F m x B x Kx x B K F x x m m m By taking state variables x1 x and x2 x , and F as input variable, the state space equations are given by x1 x x2 x2 x B K F x2 x1 m m m The transfer function for the system when B is assumed to be zero: X ( s) 1 1 K /m 2 2 n 2 2 F ( s) ms K K s K / m s n 2 Thus, the resonant frequency can be calculated as follows, n and f n 1 2 K , m K 1 m 2 51 2.48 kHz 2.110 7 Question 2 Solution a) When V 0 kx0 mg , where x0 is the initial stretching distance of the spring. When V 0 , the spring stretches an additional displacement x x0 x due to an additional electric energy storage AV 2 . We have the following force 2x balance equation at equilibrium: k (x x0 ) mg AV 2 2x2 1 V2 A 2 k ( x0 x) 2 x for 0 x x0 2kx2 ( x0 x) V . A Alternatively, this voltage can be obtained from the co-energy W A 2x V 2 and the net force: F F k ( x0 x) W A k ( x0 x) 2 V 2 k ( x0 x) . ...
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...Overhang Mike Paterson † ∗ ‡ Uri Zwick arXiv:0710.2357v1 [math.HO] 12 Oct 2007 Figure 1: A harmonic stack with 10 blocks. 1 Introduction How far off the edge of the table can we reach by stacking n identical, homogeneous, frictionless 1 blocks of length 1? A classical solution achieves an overhang asymptotic to 2 ln n. This solution is widely believed to be optimal. We show, however, that it is exponentially far from optimality by constructing simple n-block stacks that achieve an overhang of cn1/3 , for some constant c > 0. The problem of stacking a set of objects, such as bricks, books, or cards, on a tabletop to maximize the overhang is an attractive problem with a long history. J. G. Coffin [2] posed the problem in the “Problems and Solutions” section of this Monthly, but no solution was given there. The problem recurred from time to time over subsequent years, e.g., [18, 19], [12], [4]. Either deliberately or inadvertently, these authors all seem to have introduced the further restriction that there can be at most one object resting on top of another. Under this restriction, the harmonic stacks, described below, are easily seen to be optimal. ∗ A preliminary version of this paper [14] appeared in the Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’06), pages 231–240. This full version is to appear in the American Mathematical Monthly. † DIMAP and Department of Computer Science, University of Warwick, Coventry CV4 7AL, UK...
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...Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.685 Electric Machines Class Notes 1: Electromagnetic Forces c 2003 James L. Kirtley Jr. September 5, 2005 1 Introduction Bearings Stator Stator Conductors Rotor Air Gap Rotor Conductors Shaft End Windings Figure 1: Form of Electric Machine This section of notes discusses some of the fundamental processes involved in electric machinery. In the section on energy conversion processes we examine the two major ways of estimating electromagnetic forces: those involving thermodynamic arguments (conservation of energy) and field methods (Maxwell’s Stress Tensor). But first it is appropriate to introduce the topic by describing a notional rotating electric machine. Electric machinery comes in many different types and a strikingly broad range of sizes, from those little machines that cause cell ’phones and pagers to vibrate (yes, those are rotating electric machines) to turbine generators with ratings upwards of a Gigawatt. Most of the machines with which we are familiar are rotating, but linear electric motors are widely used, from shuttle drives in weaving machines to equipment handling and amusement park rides. Currently under development are large linear induction machines to be used to launch aircraft. It is our purpose in this subject to develop an analytical basis for understanding how all of these different machines work. We start, however, with a picture of perhaps...
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...Simple Harmonic Motion Aston University Engineering and Applied Science – Physics Lab Report 01/11/2014 Determination by simple harmonic motion of the acceleration due to gravity Introduction: A system undertaking simple harmonic motion (SHM) can be restrained very accurately. The period of the SHM depends both on the mass of the system and the strength of the force tending to restore the system to its equilibrium state). Oscillations are a common part of life, for instance the vibrations of a musical instrument which helps make sounds or the foundations of a car suspension which are assisted by oscillations. The main aims of this experiment was to determine if the oscillation of a mass which hung vertically from a spring; this oscillating system was used to measure the acceleration of earth due to gravity and to determine the accuracy of experimental results precisely. (http://www.pgccphy.net/1020/phy1020.pdf Theory: | | | Acceleration due to gravity The value of 9.8m/s/s acceleration is given to a free falling object, directing downwards towards Earth. Any object moving solely under the influence of gravity is known as acceleration of gravity and this vital quantity is denoted by Physicians as the symbol g. (http://www.physicsclassroom.com/class/1DKin/Lesson-5/Acceleration-of-Gravity) Simple harmonic motion This is everyplace where the acceleration is proportional and opposite to displacement to the continuous amplitude from the position...
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