...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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...by a multitude of independent kinematic chains. Generally it comprises two platforms which are connected by joints or legs acting in parallel. In recent years, parallel kinematic mechanisms have attracted a lot of attention from the academic and industrial communities due to their potential applications not only as robot manipulators but also as machine tools. The dream of all developers in Machine Tools has always been to combine the flexibility and envelope of the robots with the accuracy and stiffness of traditional Machine Tools. In the last 20 years the focus of this development has been Parallel Kinematics Machines so called PKM. This technology means that the motions in X, Y and Z are performed by three or more parallel axis that gives an outstanding stiffness and accuracy with a maintained flexibility and envelope. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behavior. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. 1.2 OUTLAY OF PROJECT REPORT Objective of our major project is to model, design and fabricate a 2-axis Parallel Kinematic Machine and to test the same...
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...Lecture 3 Kinematics Copyright © 2010 Pearson Education, Inc. Units of Lecture 3 Position, Distance, and Displacement, Average Speed and Velocity, Acceleration Motion with Constant Acceleration Freely Falling Objects Motion in Two Dimensions Relative Velocity Copyright © 2010 Pearson Education, Inc. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin and a positive direction. Copyright © 2010 Pearson Education, Inc. Position, Distance, and Displacement The distance is the total length of travel; (Example - if you drive from your house to the grocery store and back, you have covered a distance of 8.6 mi). Displacement is the change in position. (Example - If you drive from your house to the grocery store and then to your friend’s house, your displacement is 2.1 mi and the distance you have traveled is 10.7 mi). Copyright © 2010 Pearson Education, Inc. Distance is the length of Displacement is the the actual path taken by an object. straight-line separation of two points in a specified direction. Distance, s is a scalar Displacement, D is a quantity (no direction) Contains magnitude only and consists of a number and a unit. Example: (20 m, 40 mi/h) vector quantity Contains magnitude AND direction, a number, unit & angle. Example: (12 m, 300; 8 km/h) Consider travel from point A to point B in diagram below: Consider travel from point...
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...UNIVERSITI TUNKU 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...
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...com SDC CATIA V5 Tutorials in Mechanism Design and Animation 4-1 Chapter 4 Copyrighted Slider Crank Mechanism Material Copyrighted Material Copyrighted Material Copyrighted Material 4-2 CATIA V5 Tutorials in Mechanism Design and Animation Introduction In this tutorial you create a slider crank mechanism using a combination of revolute and cylindrical joints. You will also experiment with additional plotting utilities in CATIA. 1 Problem Statement A slider crank mechanism, sometimes referred to as a three-bar-linkage, can be thought of as a four bar linkage where one of the links is made infinite in length. The piston based internal combustion is based off of this mechanism. The analytical solution to the kinematics of a slider crank can be found in elementary dynamics textbooks. In this tutorial, we aim to simulate the slider crank mechanism shown below for constant crank rotation and to generate plots of some of the results, including position, velocity, and acceleration of the slider. The mechanism is constructed by assembling four parts as described later in the tutorial. In CATIA, the number and type of mechanism joints will be determined by the nature of the assembly constraints applied. There are several valid combinations of joints which would produce a kinematically correct simulation of the slider crank mechanism. The most intuitive combination would be three revolute joints and a prismatic joint. From a degrees of freedom standpoint, using...
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...and obtain solutions to fundamental problems in engineering and physics. A course in kinematics and kinetics of particles and rigid bodies with applications of Newton's second law and the principles of work-energy and impulse momentum. Course Objectives: * Learn the fundamental concepts of engineering Dynamics. * Learn a sound methodology to solve engineering problems that is applicable to all future courses and work. * Develop in the engineering student the ability to analyze any problem in a simple and logical manner. * Analyze the dynamics of particles and rigid bodies with applications * Appreciate that the governing equations in Dynamics are differential equations. Course Outcomes: * Establish coordinates, sign conventions, variables, and parameters that quantify physical conditions or states. * Draw clear and rigorous Free Body Diagrams that accurately describe physical systems, maintaining consistency with assumptions and quantifiers. * Write equations (in vector form) that govern the behavior physical systems, and check that the equations are well-posed. * Determine the solutions using mathematical techniques that are appropriate to their level. * Determine the solutions using software’s that are appropriate to their level. * Check solutions for dimensional consistency and appropriate order of magnitude. * Distinguish kinematics principles from kinetics principles. * Distinguish forces from accelerations. ...
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...Motion of Freely Falling Objects Objectives: * To study the motion of free falling objects * To determine the acceleration due to gravity, g. * To derive quantities from the slope and intercept of graphs * To determine if the motion of a falling object changes by varying its mass 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. ...
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...* 000000 Motion * Acceleration * Velocity Keywords * Motion * Acceleration * Velocity * Circular Motion * Vectors * Harmonic Motion * Kinematics * Rotational Motion * Linear Motion Sample Learning Goals * Is the velocity vector blue or green? How can you tell? * Is the acceleration vector blue or green? How can you tell? * Explain why the velocity and acceleration vectors behave as they do for the preset motions (linear acceleration I, II, circular motion, & harmonic motion). Tips for Teachers The teacher's guide (pdf) contains tips created by the PhET team. Teaching Ideas Title | Authors | Level | Type | Updated | 2D Motion | Patrick Foley | HS | Lab | 9/20/12 | Rotational Motion | Sarah Stanhope | HS | Lab | 1/27/11 | 1 Dimensional Motion - Kinematics and Graphing | Sarah Stanhope | HS | Lab | 1/27/11 | Introduction to rotational motion | Sarah Stanhope | HS UG-Intro | CQs | 2/24/10 | 2D Motion Activity | Drew Isola | HS | CQs | 1/11/09 | Vectors Phet Lab | Chris Bires | HS | Lab | 8/4/10 | Modeling a linear simple harmonic oscillator | Mark Kelly | UG-Intro | Lab | 4/7/08 | Motion in Two Dimensions | Gretchen Swanson | HS | Lab | 9/18/07 | You can submit your own ideas and activities. Translated Versions: Language | Language (Translated) | Simulation Title | | | Arabic | العربية | الحركة في بعدين | Run Now | Download | Arabic, Saudi Arabia | العربية (السعودية) | الحركة...
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...net force is equal to the product of the object's mass (a scalar quantity) and the acceleration. For example, when a car starts from a standstill (zero relative velocity) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the car changes direction there is an acceleration toward the new direction. When accelerating forward, passengers in the car experience a force pushing them back into their seats. They experience sideways forces when changing direction. If the speed of the car decreases, this is acceleration in the opposite direction, sometimes called deceleration.[4]Mathematically, there is no separate formula for deceleration, as both are changes in velocity. In everyday use and in kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar quantity.[1] The average speed of an object in an interval of time is the distance travelled by the object divided by theduration of the interval;[2] the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Like velocity, speed has the dimensions of a length divided by a time; the SI unit of speed is the metre per second, but the most usual unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour. For air and marine travel the knot is commonly used. The fastest possible speed at...
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...To predict, sketch and test acceleration vs. time kinematics graphs To review predicting and sketching distance vs. time and velocity vs. time kinematics graphs PROCEDURE: Begin by making charts like the one below for each of the following a-d a. The man walks slowly to the house from the origin. Position –Time Graph The moving man starts at a position of -8 meters and is accelerating at 1 m/s 2. He starts with a velocity of 0 m/s. After 1 second, he will be going 1 m/s (remember acceleration is 1 m/s per s so velocity will change by +1 m/s with each second that elapses). So after 2 seconds, he will be going 2 m/s, etc. If you carry this motion out with moving man, you see it will take him 4 seconds to get to the origin (a position of 0 meters), or equivalently to move +8 meters from where he started. At 4 seconds, he will have a velocity of 4 m/s On the Position-Time graph, the line is a positive consistent rise. This is because his position is going in a positive direction as well as the time is going in a consistent positive direction. Explanation for graph’s appearance –after actually performing the activity. Velocity-Time Graph On the Velocity-Time graph, the line is straight across at 2 m/s because the velocity does not change because of the consistent speed of the man walking to the house. Since the velocity is constant the acceleration is zero. Explanation for graph’s appearance - after actually performing the activity. Acceleration –Time Graph On the Acceleration-Time...
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...UNIVERSITI TUNKU ABDUL RAHMAN Centre | : | Centre for Foundation Studies (Kampar) | | Course Code | : | FHSP1014 | Programme | : | Foundation in Science | | Course Title | : | Physics I | Year/ Trimester Session | :: | Year 1 / Trimester 12016/05 | | Lecturer | : | | Additional Questions 3: Kinematics 1. A balloon is 30.0 m above the ground and is rising vertically with a uniform speed when a coin is dropped from it. If the coin reaches the ground in 4.00 s, what is the speed of the balloon? Solution:- Initial velocity of coin = speed of balloon, v. by using the equation [Answer: 12.1 ms–1] 2. A car and train moves together along two parallel paths at 25.0 m s–1. The car then undergoes a uniform acceleration of -2.5 m s–2 because of a red light and comes to rest. It remains at rest for 45.0 s, then accelerates back to a speed of 25 m s–1 at a rate of +2.5 m s–2. How far behind the train is the car when it reaches the speed of 25 m s–1, assuming that the train’s speed has remained constant at 25 m s–1. Solution:- For the car to stop we used the equation v2=v02 + 2as and v = v0 + at m and s For the car to speed up again, m and time taken, s Total distance moved by car in that time = 125 m + 125 m = 250 m. Total distance travelled by the train = 25 × (10+45+10) = 1625 m Therefore the car is (1625 – 250) = 1375 m behind the train. [Answer:...
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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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...Acceleration Due to Gravity Introduction In this lab you will measure the acceleration due to gravity near the earth’s surface with two experiments: first, by determining the time for a steel ball to fall a known vertical distance (free fall), and then second, by measuring the velocity of a cart at various points as it glides down a slightly inclined and nearly frictionless air track (slow fall). Equipment Part 1: Free-Fall • Free-fall apparatus (steel plate, drop mechanism) • Electronic Timer • Steel Ball Part 2: Slow-Fall • Air Track • Electronic Timer (may be different brand/model than in Part 1) • Gliding Car • Laser Photogate Background: Free Fall Acceleration Under the constant acceleration of gravity near the Earth’s surface, g, the vertical position, y, of a falling object is related to the time it has fallen by 1 y = y 0 + v 0 t " gt 2 2 where y0 and v0 are the initial position and velocity, respectively. The distance fallen after a time, t, has elapsed is: ! 1 y 0 " y = gt 2 " v 0 t 2 If you release the object from rest, v0 = 0, the equation simplifies to ! y0 " y = 1 2 gt 2 By varying the distance the ball drops and measuring the corresponding transit times, we can determine the acceleration of gravity from a best fit line to a linear graph of the experimental data. ! ! Procedure: Free-Fall Acceleration A diagram of the experimental apparatus is shown in Figure 1. When the ball loses contact with the release mechanism, the timer starts counting. It stops...
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...the same. Check Worksheet #2 for a good example: the girl going around the carousel has zero displacement and thus zero average velocity, but certainly went at a nonzero average speed as she went around the circle. 13. To her, the ball looks like it drops straight down, despite the train’s speed (vBT is the same as a normal falling ball). But to someone standing still on the earth outside, they see the ball moving in a curved parabolic path, as if it’s launched with an initial velocity of vBE = (175 mph, 0), because it’s “boosted” by the train. WP Answer Equation and quick explanation 14. 4.87 m/s2 v = v0 + at 15. 4.77 m/s v2 = v02 + 2aΔx 16. 4.35 m/s avg speed = total distance / total time 17. 4.4 m Use the projectile kinematics equations, with Δx = 48m to solve for t (it’s 2.44 seconds), then use t in the y equation to find Δy 18. a) v = v0 – gt Eq. 1 b) Δy = v0t – ½ gt2 Eq. 2 c) Δy = v02 / (2g) Eq. 3 19.1,116 m The goal is to find the total time Amy spends going 74 m/s while Bob is slowing down and speeding up. The easiest way to do this is with the average velocity equation, (v+v0) / 2 = Δx / t. Find the two times it takes Bob to slow down and speed up, add those to the 7.5 s, to get the total time. 20. a) v0 = 8.82 m/s Use Δy = 0 (starts and ends on the ground) along with...
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...Assignment: * Exercises 3 and 29: 1. When a ball rolls down an inclined plane it gains speed because of gravity. When rolling up, it loses speed because of gravity. Why doesn't gravity play a role when it rolls on a horizontal surface? While rolling level a ball does not roll with or against the vertical force of gravity, it neither speeds up nor slows down. The rolling ball maintains a constant speed; this happens because friction overcomes the ball’s inertia and 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...
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