...on the body. It is the study of the geometry of motion without consideration of the causes of motion. Kinematics deals only with relationships among the position, velocity, acceleration, and time. Kinetics deals with both forces and motion. 2. PARTICLES AND RIGID BODIES Bodies in motion can be considered particles if rotation is absent or insignificant. Particles do not possess rotational kinetic energy. All parts of a particle have the same instantaneous displacement, velocity, and acceleration. A rigid body does not deform when loaded and can be considered as a combination of two or more particles that remain at a fixed, finite distance from each other. 3. COORDINATE SYSTEMS The position of a particle is specified with reference to a coordinate system. A coordinate can represent a position along an axis, as in the rectangular coordinate system or it can represent an angle, as in the polar, cylindrical, and spherical coordinate systems. In general, the number of degrees of freedom is equal to the number of coordinates required to completely specify the state of an object. If each of the coordinates is independent of the others, the coordinates are shown as holonomic coordinates. 4. CONVENTIONS OF REPRESENTATION For a given particle, position, velocity, and acceleration can be specified in three primary forms: vector form, rectangular coordinate form, and unit vector form. • The rectangular coordinate...
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...Steering Behaviors For Autonomous Characters Craig W. Reynolds Sony Computer Entertainment America 919 East Hillsdale Boulevard Foster City, California 94404 craig_reynolds@playstation.sony.com http://www.red.com/cwr/ cwr@red.com Keywords: Animation Techniques, Virtual/Interactive Environments, Games, Simulation, behavioral animation, autonomous agent, situated, embodied, reactive, vehicle, steering, path planning, path following, pursuit, evasion, obstacle avoidance, collision avoidance, flocking, group behavior, navigation, artificial life, improvisation. Abstract This paper presents solutions for one requirement of autonomous characters in animation and games: the ability to navigate around their world in a life-like and improvisational manner. These “steering behaviors” are largely independent of the particulars of the character’s means of locomotion. Combinations of steering behaviors can be used to achieve higher level goals This paper divides motion behavior into three levels. It will focus on the (For example: get from here to there while avoiding obstacles, follow this corridor, join that group of characters...) middle level of steering behaviors, briefly describe the lower level of locomotion, and touch lightly on the higher level of goal setting and strategy. Introduction Autonomous characters are a type of autonomous agent intended for use in computer animation and interactive media such as games and virtual reality. These agents represent a This stands...
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...Worksheet Kinematics 1. A body starts from rest and reaches a speed of 5 m/s after travelling with uniform acceleration in a straight line for 2 s. Calculate the acceleration of the body. 2. A body starts from rest and moves with uniform acceleration of 2m/s2 in a straight line. a. Calculate the velocity after 5s. b. Calculate the distance travelled in 5s. c. Find the time taken for the body to reach 100m from its starting point. 3. An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance traveled before takeoff. 4. A car starts from rest and accelerates uniformly over a time of 5.21 seconds for a distance of 110 m. Determine the acceleration of the car. 5. Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far will he fall? 6. A race car accelerates uniformly from 18.5 m/s to 46.1 m/s in 2.47 seconds. Determine the acceleration of the car and the distance traveled. 7. A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s2. Determine the time for the feather to fall to the surface of the moon. 8. Rocket-powered sleds are used to test the human response to acceleration. If a rocket-powered...
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...1. This problem is hard to define because with today’s technology it would not be that difficult to complete. Major problem components would be not knowing the GPS way points, the RDDF, or the speed limits until two hours prior to the start. It will be a definite obstacle to make sure that during that two hour period that the information is correctly entered into the computer to guide the autonomous vehicle. 2. On average the vehicle would have to travel at seventeen and one half miles per hour (MPH). Although, at times that speed will have to be adjusted to a higher rate of speed for times when slower speeds are necessary. 3. Considerations for the average speed would be the narrow roads, the cliff drop off, as well as other landscape obstacles. Whenever possible, the speed would need to be adjusted to more than seventeen and one half miles per hour (MPH) to allow for the times that the average speed cannot be achieved. 4. Strategies to avoid obstacles would include large all terrain tires and a computer monitoring system which would include views of the outer vehicle. An over- ride system would be in place to allow a person to operate the vehicle, by remote, in case of emergency. 5. The disadvantages of this vehicle driving the route are numerous. This includes, but is not limited to, narrow roads, sharp turns, and dangerous cliff drop offs. The biggest disadvantage will be the loss of the GPS signal. 6. Strategies to prepare...
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...brings it to a stop. The horizontal component of gravity is zero. 2. What is the acceleration of a car that moves at a steady velocity of 100km/hr for 100 seconds? Explain your answer, and state why this question is an exercise in careful reading as well as in Physics. The acceleration is 0. There is no change of velocity in those 100 seconds time interval. The word you have to pay attention to is “steady” that is why is can exercise in careful reading and in Physics because you would try to do the math but at the end the answer would be wrong because the car never accelerated. * Problems 1,5,8 and 10 1. Find the net force produced by a 30-N force and a 20-N force in each of the following cases: a. Both forces act in the same direction. 30+20= 50N b. The two forces act in different directions. 30-20=10N 2. A vehicle changes its velocity from 100 km/h to a dead stop in 10 s. Show that the acceleration in stopping is -10 km/h x s. VF-Vi= 0-100 VT/t = (0-100)/10s = -10 km/h x s 3. A ball is thrown straight up with enough speed so that it is in the air for several seconds. c. What is the velocity of the ball when it reaches its highest point? Velocity is 0 at highest point. d. What is its velocity 1 s before it reaches its highest point? 9.8m/s e. What is the change in its velocity during this 1-s interval? -9.8m/s...
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...AP Physics – Waves Ain’t Gone, Alas - 4 Thee Hee?________________________________________________________________________Per__ School days, I believe, are the unhappiest in the whole span of human existence. They are full of dull, unintelligible tasks, new and unpleasant ordinances, brutal violations of common sense and common decency. -- H.L. Mencken 1. A 7.50 kg ball is thrown. It has an initial velocity of 8.468 m/s. It travels a horizontal distance of 7.3 m in 1.25 s. Find: (a) The weight of the ball. (b) The initial kinetic energy of the ball. (c) The angle of the ball’s initial velocity with the horizontal.(73.5,74.9,46.4) 2. You are on a train traveling at 55.0 km/h. You approach a bell. The actual frequency of the bell is 725 Hz. What frequency do you hear? (759) 3. Draw a picture of a pendulum showing its swing. Label the following points: (a) point of maximum velocity, (b) point of minimum velocity, (c) point where the potential energy is greatest, (d) point where kinetic energy is greatest, (e) if the period of the pendulum is 0.750 seconds, what is its length? (f) What is the speed of the pendulum at the bottom of its swing if the angle that the thing makes at its maximum displacement is 11.0 ?(.14,.225) 4. A pipe is 18.5 cm long and open on one of its ends. (a) What are the frequencies of the first three harmonics that resonate in the pipe? (b) What is the wavelength of the third harmonic?(1st466 2nd 1300 3rd 2330, .148) 5. An FM radio station’s basic...
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...Acceleration of free falling metal ball Brian Ahn November 11, 2013 Raw Data <Table of time taken for ball to reach ground in different heights> Height (m) ± 0.005 m | Time taken (s) ± 0.01 s | | Trial 1 | Trial 2 | Trial 3 | 0.5 | 0.35 | 0.35 | 0.33 | 1.0 | 0.45 | 0.43 | 0.40 | 1.5 | 0.53 | 0.44 | 0.47 | 2.0 | 0.56 | 0.56 | 0.53 | 2.5 | 0.72 | 0.64 | 0.72 | 3.0 | 0.75 | 0.76 | 0.79 | 3.5 | 0.77 | 0.84 | 0.78 | Processing Data <Table of average time taken for ball to reach ground in different heights> Height (m) ± 0.005 | Average time taken (s) | 0.5 | 0.34 ± 0.01 | 1.0 | 0.43 ± 0.03 | 1.5 | 0.48 ± 0.05 | 2.0 | 0.55 ± 0.02 | 2.5 | 0.69 ± 0.04 | 3.0 | 0.77 ± 0.02 | 3.5 | 0.80 ± 0.04 | Average of the time taken is (t1 + t2 + t3) ÷ 3 Uncertainty for the time taken is (tmax– tmin) ÷ 2 Average of the time taken in height 1 is (0.45 + 0.43 + 0.40) ÷ 3 = 0.42667 ≅ 0.43 (to two significant figures) Uncertainty for the time taken in height 1 is (0.45 – 0.40) ÷ 2 = 0.025 ≅ 0.03 (to one significant figure) <Table of average time taken squared by dropping an object in different heights> Height (m) ± 0.005 | Average time taken squared (s2) | 0.5 | 0.12 ± 0.007 | 1.0 | 0.18 ± 0.03 | 1.5 | 0.23 ± 0.05 | 2.0 | 0.30 ± 0.02 | 2.5 | 0.48 ± 0.05 | 3.0 | 0.59 ± 0.03 | 3.5 | 0.64 ± 0.06 | Uncertainty for average time taken squared is 2 × (percentage uncertainty) × (time taken) 2 Uncertainty...
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...1) The following problems are representative of the type problems that will be on the 1st semester exam. Exam will cover Chapters 1 - 5. 2) Please solve/answer each of these - pay particular attention to the “type” solution required for each one. 3) You will not be given ANY additional material - any and all equations and/or constants that YOU think you will need must be placed on either a 3x5 or 5x8 index card. This card must be submitted to me during the exam review days and approved by me. The “approved/signed” cards may be used during the exam. 4) YOU MUST HAVE YOUR CARD, CALCULATOR and PENCILS WITH YOU WHEN THE BELL RINGS TO START THE PERIOD. YOU WILL NOT BE PERMITTED TO GO GET ANYTHING AND/OR BORROW ANYTHING FROM ANYONE!!!! 1. One year is about ____ seconds while one day is exactly ____ seconds. a) | 3.16 x 107, 86 400 | b) | 5.26 x 105, 86 400 | c) | 3.16 x 107, 8 640 | d) | 1.04 x 106, 36 000 | 2. The proton contains which of the following combination of quarks? a) | two up quarks and one down quark | b) | one up quark and two down quarks | c) | one top quark and two bottom quarks | d) | two top quarks and one bottom quark | 3. On planet Z, the standard unit of length is the foose. Ann the Astronaut is 5.90 feet tall on earth. She lands on planet Z and is measured to be 94 foosi tall. Her partner Rachael is 88 foosi tall. How tall is Rachael on Earth? a) | 5.2 feet | b) | 5.5 feet | c) | 5.8 feet | d) | 6.3 feet | 4....
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...ABDUL RAHMAN |Centre |: Centre for Foundation Studies (CFS) |Unit Code |: FHSC1014 | |Course |: Foundation in Science |Unit Title |: Mechanics | |Year/ Trimester |: Year 1 / Trimester 1 |Lecturer | | |Session |: 201605 | | | Additional Tutorial 2: Vector and translational kinematics. 1. Find the x and y-components of: (a) a displacement of 200 km, at 30.0o. (b) a velocity of 40.0 km/h, at 120o; and (c) a force of 50.0 N at 330o. [(a) 173 km, 100 km, (b) -20.0 km/h, +34.6 km/h, (c) 43.3 N, -25.0 N] 2. Three forces are applied to an object, as indicated in the drawing. Force [pic] has a magnitude of 21.0 Newton (21.0 N) and is directed 30.0° to the left of the + y axis. Force [pic] has a magnitude of 15.0 N and points along the + x axis. What must be the magnitude and direction (specified by the angle ( in the drawing) of the third force [pic] such that the vector sum of the three forces is 0 N? [18.7 N, 76o] 3. A 200 N block rests on a 30o inclined plane as shown in figure below. If the weight of the block acts vertically downward, what are the components of the weight down the plane...
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...Drop Drag And Spray Models Abstract This paper reviews and critiques the published work of Liu et al, “On modeling the effect of drop drag and breakup on Fuel Sprays”. A dynamic drop drag model (DDM) has been coupled to the (TAB) and (KH) spray models. The interaction the (DDM) with these models provides insight into the phenomenon of drop drag and the atomization process. Due to the interaction of the parent drop during interaction with the spray, it is shown that the KH model must be adjusted to account for drag. The (TAB) model, however, remains unaffected by drag given the formulation of its breakup mechanism. The (DDM) also shows that the standard drag model underestimates drop size. And lastly, a critique of the ineffectualness of drop drag on penetration is presented. Introduction Recent studies estimate that twenty-five percent of the world’s energy comes from fuel spray combustion [4]. Given the impact of sprays on the energy industry, spray optimization is crucial to supply the growing demand for energy. Spray and atomization science developed from the ideas prominent scientist like Rayleigh, Kelvin and Helmholtz who were studying liquid jet break-up mechanisms. All modern models incorporate their work in some way. The field is a conglomerate of studies and insights built on break-up mechanisms, drop dynamics, and spray characteristics but a unified theory of atomization still escapes scientist and research engineers. An often neglected phenomenon is drag...
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...What is the difference between speed and velocity? * Speed is how fast you’re going * Velocity is how fast you’re going but you need to add direction of the way you’re going in. What are different parts of a distance-time graph? * Flat sections up – steady speed * Flat line – stopped * Curved line up – accelerating * Line curving off – decelerating * Straight line down – steady speed in other direction How do you calculate speed from a distance time graph? * Vertical / horizontal = speed What is acceleration? * How quickly the velocity is changing * The change in velocity can be a change in speed, or direction or both How to calculate acceleration? * Acceleration = change in velocity / time taken What is each part of a velocity time graph? * Straight line up – accelerating * Straight line – constant speed * Curved line up – increasing acceleration * Straight line down – decelerating How to find the distance travelled on a velocity time graph? * It is equal to the time interval underneath an area of a graph What is mass and weight? * Mass Is the Amount of matter that makes up an object * Weight is the force which pulls a object to the ground What is weight measured in? * It is a force measured in newton’s (N) What is the resultant force? * The sum of all the forces acting on an object What happens to an object if the resultant force is zero? * It will remain...
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...Theory: The free fall is a known example or the most common example of a uniformly accelerated movement, with an acceleration a = -9.8m/s2 (vertical axis pointing vertically upward). If you choose the vertical axis pointing vertically downward, the acceleration is taken as + 9.8m/s2. The kinematic equations for a rectilinear movement under the acceleration of gravity are the same as any movement with constant acceleration: (1) v = vi - gt velocity as function of time. (2) y - yi = ½(vi + v)t displacement as function of time (3) y - yi = vit - ½gt2 displacement as function of time (4) v2 = vi2 -2g(x - xi) velocity as function of displacement The sub index i denotes initial quantities, g the gravity acceleration and t, the time. But for this type of motion, the displacement of the object as a function of time is described mathematically as: (5) ∆y=Vot + ½gt2 where Vo is the initial velocity of the object. If object if just drop velocity, Equation (5) becomes (6) ) ∆y=½gt2 Methodology Procedure: * A digital balance was used to measure the masses of the small and big steel balls. * A set-up of the free fall sensor was followed on the book. * The color-coded cables was connected to its color-coded socket. * Coach 6 free fall activity was clicked in the desktop of the computer. * The small steel ball was attached to the free fall sensor. * The steel ball was released...
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...UMUC NSCI 101/103 Lab 2: Types of Forces INSTRUCTIONS: On your own and without assistance, complete this Lab 2 Answer Form electronically and submit it via the Assignments Folder by the date listed on your Course Schedule (under Syllabus). To conduct your laboratory exercises, use the Laboratory Manual that is available in the classroom. Laboratory exercises on your CD may not be updated. Save your Lab 2 Answer Form in the following format: LastName_Lab2 (e.g., Smith_Lab2). You should submit your document in a Word (.doc or .docx) or Rich Text Format (.rtf) for best compatibility. Experiment 1: Friction Table 1: Applied Force Required to Slide Cup |Cup Material |Force Applied F1 |Force Applied F2 |F1 / FN1 |F2 / FN2 | | |m1 = 300 g water |m2 = 150 g water | | | | | | | | | | | | | | | |Plastic | | | | | | ...
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...Virtual Lab: Stopping Distance of a Car Question: How can we determine the deceleration rate of a virtual car? How does reaction time affect the stopping distance of a car? Go to this website: http://higheredbcs.wiley.com/legacy/college/halliday/0471320005/simulations6e/index.htm?newwindow=true and on the left side of the screen select “Stopping Distance of a Car” Introduction: In this virtual experiment, a yellow sports car is coming to a stop from some initial velocity. On the left of the screen below the car you see a position vs. time and velocity vs. time graph of the motion. On the right of the screen below the car you are given lots of information about the car’s motion: time, distance covered, speed, distance traveled before braking, distance traveled after braking, and total stopping distance. Follow the instructions for the lab and answer questions as you proceed. Instructions: 1. Load up the Java Lab from the website shown above. 2. On the left side of the screen select “Stopping Distance of a Car” 3. Before you start recording data for the lab, “play” around with the buttons at the bottom of the screen and see what they do. (Play, pause, reset, step back, step forward.) 4. When you feel comfortable, hit the “clear trace” button and go on to procedure 1. Procedure-Part 1 Reset/clear trace and have the initial speed is set at 80 km/hr, the reaction time is 0.10 s, and the coefficient of friction is equal to 1.00. Answer the...
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