Chapter 10: Linear Kinematics of Human Movement

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Chapter 10: Linear Kinematics of Human Movement"

Transcription

1 Chapter 10: Linear Kinematics of Human Movement Basic Biomechanics, 4 th edition Susan J. Hall Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University

2 Objectives Discuss the interrelationship among kinematic variables Correctly associate linear kinematic quantities with their units of measure Identify & describe effects of factors governing projectile trajectory Explain why the horizontal and vertical components of projectile motion are analyzed separately Distinguish between average & instantaneous quantities & identify circumstance which each is a quantity of interest

3 Linear Kinematic Quantities Kinematics: describes appearance of motion Kinetics: study of forces associated with motion Linear kinematics: involves the study of the shape, form, pattern and sequencing of linear movement through time Qualitative: major joint actions & sequencing Quantitative: Range of motion, forces, distance etc.

4 Distance & Displacement Measured in units of length Metric: meter, kilometer, centimeter, etc. English: inch, foot, yard & mile Distance: Scalar quantity Linear displacement: Vector quantity: length & direction (compass directions, left, right, up, & down, or positive & negative

5 Speed & Velocity Speed = length (or distance) change in time Velocity (v) = change in position = Δ position change in time Δ time v = displacement = d change in time Δ t

6 Speed & Velocity Velocity = position 2 - position 1 time 2 - time 1 Velocity is a vector quantity direction and magnitude of motion Laws of vector algebra

7 10-2

8 Acceleration Acceleration (a) = change in velocity = change in time Δv Δt a = v 2 - v 1 Δt When acceleration is zero, velocity is constant

9 Positive/Negative Acceleration

10 Average & Instantaneous Quantities Instantaneous : Instantaneous values Average: Average velocity = final displacement total time

11 Velocity Curve for Sprinting

12 Velocity Curves for Two Sprinters

13 Kinematics of Projectile Motion Bodies projected into the air are projectiles Horizontal & Vertical Components Vertical is influenced by gravity No force (neglecting air resistance) affects the horizontal Horizontal relates to distance Vertical relates to maximum height achieved

14 Kinematics of Projectile Motion Influence of Gravity Major influence of vertical component Not the horizontal component Force of Gravity: Constant, unchanging Negative acceleration (-9.81 m/s 2 ) Apex: The highest point in the trajectory

15 10-6

16 Kinematics of Projectile Motion Influence of Air Resistance In a vacuum, horizontal speed of a projectile remain constant Air resistance affects the horizontal speed of a projectile This chapter, velocity will be regarded as constant

17 Factors Influencing Projectile Trajectory Trajectory: Angle of projection Projection speed Relative height of projection

18 10-9

19 Factors Influencing Projectile Trajectory Angle of Projection General shapes Perfectly vertical Parabolic Perfectly horizontal Implications in sports Air resistance may cause irregularities

20 10-10

21 Factors Influencing Projectile Trajectory Projection speed: Range: Relative Projection Height:

22 10-14

23 Optimum Projection Conditions Maximize the speed of projection Maximize release height Optimum angle of projection Release height = 0, then angle = 45 0 Release height, then angle Release height, then angle

24 Range at Various Angles

25 Analyzing Projectile Motion Initial velocity: Horizontal component is constant Horizontal acceleration = 0 Vertical component is constantly changing Vertical acceleration = m/s 2

26 10-17

27 Equations of Constant Acceleration Galileo s Laws of constant acceleration v 2 = v 1 + at D = v 1 t + ½at 2 V 2 2 = v ad d = displacement; v = velocity; a = acceleration; t = time Subscript 1 & 2 represent first or initial and second or final point in time

28 Equations of Constant Acceleration Horizontal component : a = 0 v 2 = v 1 D = v 1 t V 2 2 = v2 1

29 Equations of Constant Acceleration Vertical component: a = m/s 2 v 2 = at D = ½ at 2 V 2 2 = 2ad Vertical component at apex: v = 0 0 = v ad 0 = v 1 + at

30 Goals for Projectiles Maximize range (shot put, long jump) Maximize total distance (golf) Optimize range and flight time (punt) Maximize height (vertical jump) Optimize height and range (high jump) Minimize flight time (baseball throw) Accuracy (basketball shot)

31 Goals for Projectiles Maximize range (shot put, long jump) Shot put optimum angle is approximately 42 Long jump theoretical optimum is approximately 43 ; however, due to human limits, the actual angle for elite jumpers is approximately 20-22

32 Goals for Projectiles Maximize total distance (golf) Because the total distance (flight plus roll) is most important, trajectory angles are lower than 45 Distance is controlled by the pitch of the club Driver ~ 10

33 Goals for Projectiles Optimize range and flight time (punt) Maximum range occurs with 45 trajectory Higher trajectory increases hang time with minimal sacrifice in distance Lower trajectory usually results in longer punt returns Less time for kicking team to get downfield to cover the punt returner

34 Goals for Projectiles Maximize height (vertical jump) Maximize height of COM at takeoff Maximize vertical velocity by exerting maximum vertical force against ground.

35 Goals for Projectiles Optimize height and range (high jump) Basic goal is to clear maximum height Horizontal velocity is necessary to carry jumper over bar into pit Typical takeoff velocity for elite high jumpers is approximately 45

36 Goals for Projectiles Minimize flight time (baseball throw) Baseball players use low trajectories (close to horizontal) Outfielders often throw the ball on one bounce with minimal loss of velocity

37 Goals for Projectiles Accuracy (basketball shot)

38 Projecting for Accuracy

39 Minimum Speed Trajectory

40 Angle of Entry

41 Margin for Error

42 Free Throw Optimum Angle

43 Summary Linear kinematics is the study of the form or sequencing of linear motion with respect to time. Linear kinematic quantities include the scalar quantities of distance and speed, and the vector quantities of displacement, velocity, and acceleration. Vector quantities or scalar equivalent may be either an instantaneous or an average quantity

44 Summary A projectile is a body in free fall that is affected only by gravity and air resistance. Projectile motion is analyzed in terms of its horizontal and vertical components. Vertical is affected by gravity Factors that determine the height & distance of a projectile are: projection angle, projection speed, and relative projection height The equation for constant acceleration can be used to quantitatively analyze projectile motion.

45 The End

Chapter 07 Test A. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Chapter 07 Test A. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Class: Date: Chapter 07 Test A Multiple Choice Identify the choice that best completes the statement or answers the question. 1. An example of a vector quantity is: a. temperature. b. length. c. velocity.

More information

Projectile motion simulator. http://www.walter-fendt.de/ph11e/projectile.htm

Projectile motion simulator. http://www.walter-fendt.de/ph11e/projectile.htm More Chapter 3 Projectile motion simulator http://www.walter-fendt.de/ph11e/projectile.htm The equations of motion for constant acceleration from chapter 2 are valid separately for both motion in the x

More information

Speed A B C. Time. Chapter 3: Falling Objects and Projectile Motion

Speed A B C. Time. Chapter 3: Falling Objects and Projectile Motion Chapter 3: Falling Objects and Projectile Motion 1. Neglecting friction, if a Cadillac and Volkswagen start rolling down a hill together, the heavier Cadillac will get to the bottom A. before the Volkswagen.

More information

1 of 7 9/5/2009 6:12 PM

1 of 7 9/5/2009 6:12 PM 1 of 7 9/5/2009 6:12 PM Chapter 2 Homework Due: 9:00am on Tuesday, September 8, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View]

More information

Projectile Motion 1:Horizontally Launched Projectiles

Projectile Motion 1:Horizontally Launched Projectiles A cannon shoots a clown directly upward with a speed of 20 m/s. What height will the clown reach? How much time will the clown spend in the air? Projectile Motion 1:Horizontally Launched Projectiles Two

More information

B) 286 m C) 325 m D) 367 m Answer: B

B) 286 m C) 325 m D) 367 m Answer: B Practice Midterm 1 1) When a parachutist jumps from an airplane, he eventually reaches a constant speed, called the terminal velocity. This means that A) the acceleration is equal to g. B) the force of

More information

Scalar versus Vector Quantities. Speed. Speed: Example Two. Scalar Quantities. Average Speed = distance (in meters) time (in seconds) v =

Scalar versus Vector Quantities. Speed. Speed: Example Two. Scalar Quantities. Average Speed = distance (in meters) time (in seconds) v = Scalar versus Vector Quantities Scalar Quantities Magnitude (size) 55 mph Speed Average Speed = distance (in meters) time (in seconds) Vector Quantities Magnitude (size) Direction 55 mph, North v = Dx

More information

Exam 1 Review Questions PHY 2425 - Exam 1

Exam 1 Review Questions PHY 2425 - Exam 1 Exam 1 Review Questions PHY 2425 - Exam 1 Exam 1H Rev Ques.doc - 1 - Section: 1 7 Topic: General Properties of Vectors Type: Conceptual 1 Given vector A, the vector 3 A A) has a magnitude 3 times that

More information

WWW.MIAMI-BEST-MATH-TUTOR.COM E-MAIL: MIAMIMATHTUTOR@GMAIL.COM CONTACT NUMBER: (786)556-4839 PHYSICS I

WWW.MIAMI-BEST-MATH-TUTOR.COM E-MAIL: MIAMIMATHTUTOR@GMAIL.COM CONTACT NUMBER: (786)556-4839 PHYSICS I WWW.MIAMI-BEST-MATH-TUTOR.COM PAGE 1 OF 10 WWW.MIAMI-BEST-MATH-TUTOR.COM E-MAIL: MIAMIMATHTUTOR@GMAIL.COM CONTACT NUMBER: (786)556-4839 PHYSICS I PROJECTILE MOTION 4.1 1. A physics book slides off a horizontal

More information

2008 FXA DERIVING THE EQUATIONS OF MOTION 1. Candidates should be able to :

2008 FXA DERIVING THE EQUATIONS OF MOTION 1. Candidates should be able to : Candidates should be able to : Derive the equations of motion for constant acceleration in a straight line from a velocity-time graph. Select and use the equations of motion for constant acceleration in

More information

Physics 160 Biomechanics. Angular Kinematics

Physics 160 Biomechanics. Angular Kinematics Physics 160 Biomechanics Angular Kinematics Questions to think about Why do batters slide their hands up the handle of the bat to lay down a bunt but not to drive the ball? Why might an athletic trainer

More information

Physics Kinematics Model

Physics Kinematics Model Physics Kinematics Model I. Overview Active Physics introduces the concept of average velocity and average acceleration. This unit supplements Active Physics by addressing the concept of instantaneous

More information

Maximum Range Explained range Figure 1 Figure 1: Trajectory Plot for Angled-Launched Projectiles Table 1

Maximum Range Explained range Figure 1 Figure 1: Trajectory Plot for Angled-Launched Projectiles Table 1 Maximum Range Explained A projectile is an airborne object that is under the sole influence of gravity. As it rises and falls, air resistance has a negligible effect. The distance traveled horizontally

More information

Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE

Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE 1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object

More information

2-1 Position, Displacement, and Distance

2-1 Position, Displacement, and Distance 2-1 Position, Displacement, and Distance In describing an object s motion, we should first talk about position where is the object? A position is a vector because it has both a magnitude and a direction:

More information

TIME OF COMPLETION DEPARTMENT OF NATURAL SCIENCES. PHYS 1111, Exam 2 Section 1 Version 1 October 30, 2002 Total Weight: 100 points

TIME OF COMPLETION DEPARTMENT OF NATURAL SCIENCES. PHYS 1111, Exam 2 Section 1 Version 1 October 30, 2002 Total Weight: 100 points TIME OF COMPLETION NAME DEPARTMENT OF NATURAL SCIENCES PHYS 1111, Exam 2 Section 1 Version 1 October 30, 2002 Total Weight: 100 points 1. Check your examination for completeness prior to starting. There

More information

Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide)

Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide) Free Fall: Observing and Analyzing the Free Fall Motion of a Bouncing Ping-Pong Ball and Calculating the Free Fall Acceleration (Teacher s Guide) 2012 WARD S Science v.11/12 OVERVIEW Students will measure

More information

Name DATE Per TEST REVIEW. 2. A picture that shows how two variables are related is called a.

Name DATE Per TEST REVIEW. 2. A picture that shows how two variables are related is called a. Name DATE Per Completion Complete each statement. TEST REVIEW 1. The two most common systems of standardized units for expressing measurements are the system and the system. 2. A picture that shows how

More information

Review Assessment: Lec 02 Quiz

Review Assessment: Lec 02 Quiz COURSES > PHYSICS GUEST SITE > CONTROL PANEL > 1ST SEM. QUIZZES > REVIEW ASSESSMENT: LEC 02 QUIZ Review Assessment: Lec 02 Quiz Name: Status : Score: Instructions: Lec 02 Quiz Completed 20 out of 100 points

More information

The Bullet-Block Mystery

The Bullet-Block Mystery LivePhoto IVV Physics Activity 1 Name: Date: 1. Introduction The Bullet-Block Mystery Suppose a vertically mounted 22 Gauge rifle fires a bullet upwards into a block of wood (shown in Fig. 1a). If the

More information

8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight

8. As a cart travels around a horizontal circular track, the cart must undergo a change in (1) velocity (3) speed (2) inertia (4) weight 1. What is the average speed of an object that travels 6.00 meters north in 2.00 seconds and then travels 3.00 meters east in 1.00 second? 9.00 m/s 3.00 m/s 0.333 m/s 4.24 m/s 2. What is the distance traveled

More information

Chapter 7: Momentum and Impulse

Chapter 7: Momentum and Impulse Chapter 7: Momentum and Impulse 1. When a baseball bat hits the ball, the impulse delivered to the ball is increased by A. follow through on the swing. B. rapidly stopping the bat after impact. C. letting

More information

5. Unable to determine. 6. 4 m correct. 7. None of these. 8. 1 m. 9. 1 m. 10. 2 m. 1. 1 m/s. 2. None of these. 3. Unable to determine. 4.

5. Unable to determine. 6. 4 m correct. 7. None of these. 8. 1 m. 9. 1 m. 10. 2 m. 1. 1 m/s. 2. None of these. 3. Unable to determine. 4. Version PREVIEW B One D Kine REVIEW burke (1111) 1 This print-out should have 34 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Jogging

More information

PHY121 #8 Midterm I 3.06.2013

PHY121 #8 Midterm I 3.06.2013 PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension

More information

Physics 53. Kinematics 2. Our nature consists in movement; absolute rest is death. Pascal

Physics 53. Kinematics 2. Our nature consists in movement; absolute rest is death. Pascal Phsics 53 Kinematics 2 Our nature consists in movement; absolute rest is death. Pascal Velocit and Acceleration in 3-D We have defined the velocit and acceleration of a particle as the first and second

More information

Gravitational Potential Energy

Gravitational Potential Energy Gravitational Potential Energy Consider a ball falling from a height of y 0 =h to the floor at height y=0. A net force of gravity has been acting on the ball as it drops. So the total work done on the

More information

AP Physics B Practice Workbook Book 1 Mechanics, Fluid Mechanics and Thermodynamics

AP Physics B Practice Workbook Book 1 Mechanics, Fluid Mechanics and Thermodynamics AP Physics B Practice Workbook Book 1 Mechanics, Fluid Mechanics and Thermodynamics. The following( is applicable to this entire document copies for student distribution for exam preparation explicitly

More information

Long Jump Mechanics THE 13 PACE RUN-UP THE LAST 3 STRIDES THE TAKEOFF

Long Jump Mechanics THE 13 PACE RUN-UP THE LAST 3 STRIDES THE TAKEOFF Long Jump Mechanics Two major techniques are used in long jumping: the hang technique and the hitch-kick technique. In the hang technique, the jumper appears to temporarily hang in the air during flight.

More information

AP1 Dynamics. Answer: (D) foot applies 200 newton force to nose; nose applies an equal force to the foot. Basic application of Newton s 3rd Law.

AP1 Dynamics. Answer: (D) foot applies 200 newton force to nose; nose applies an equal force to the foot. Basic application of Newton s 3rd Law. 1. A mixed martial artist kicks his opponent in the nose with a force of 200 newtons. Identify the action-reaction force pairs in this interchange. (A) foot applies 200 newton force to nose; nose applies

More information

Page Topic Further Support Materials

Page Topic Further Support Materials This booklet will discuss some of the principles involved in the design of a roller coaster. It is intended for the middle or high school teacher. Physics students may find the information helpful as well.

More information

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N

C B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a

More information

Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same.

Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same. 1. A cart full of water travels horizontally on a frictionless track with initial velocity v. As shown in the diagram, in the back wall of the cart there is a small opening near the bottom of the wall

More information

PROBLEM SET. Practice Problems for Exam #1. Math 2350, Fall 2004. Sept. 30, 2004 ANSWERS

PROBLEM SET. Practice Problems for Exam #1. Math 2350, Fall 2004. Sept. 30, 2004 ANSWERS PROBLEM SET Practice Problems for Exam #1 Math 350, Fall 004 Sept. 30, 004 ANSWERS i Problem 1. The position vector of a particle is given by Rt) = t, t, t 3 ). Find the velocity and acceleration vectors

More information

Solutions to old Exam 1 problems

Solutions to old Exam 1 problems Solutions to old Exam 1 problems Hi students! I am putting this old version of my review for the first midterm review, place and time to be announced. Check for updates on the web site as to which sections

More information

1.3.1 Position, Distance and Displacement

1.3.1 Position, Distance and Displacement In the previous section, you have come across many examples of motion. You have learnt that to describe the motion of an object we must know its position at different points of time. The position of an

More information

SQA Higher Physics Unit 1 Mechanics and Properties of Matter

SQA Higher Physics Unit 1 Mechanics and Properties of Matter SCHOLAR Study Guide SQA Higher Physics Unit 1 Mechanics and Properties of Matter John McCabe St Aidan s High School Andrew Tookey Heriot-Watt University Campbell White Tynecastle High School Heriot-Watt

More information

SQA CfE Higher Physics Unit 1: Our Dynamic Universe

SQA CfE Higher Physics Unit 1: Our Dynamic Universe SCHOLAR Study Guide SQA CfE Higher Physics Unit 1: Our Dynamic Universe Authored by: Ian Holton Previously authored by: Douglas Gavin John McCabe Andrew Tookey Campbell White Reviewed by: Grant McAllister

More information

Module 8 Lesson 4: Applications of Vectors

Module 8 Lesson 4: Applications of Vectors Module 8 Lesson 4: Applications of Vectors So now that you have learned the basic skills necessary to understand and operate with vectors, in this lesson, we will look at how to solve real world problems

More information

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information

Solving Simultaneous Equations and Matrices

Solving Simultaneous Equations and Matrices Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering

More information

5 PROJECTILES. 5.0 Introduction. Objectives

5 PROJECTILES. 5.0 Introduction. Objectives 5 PROJECTILES Chapter 5 Projectiles Objectives After studying this chapter you should recognise that projectile motion is common; understand how to obtain a simple mathematical model of projectile motion;

More information

Exam Three Momentum Concept Questions

Exam Three Momentum Concept Questions Exam Three Momentum Concept Questions Isolated Systems 4. A car accelerates from rest. In doing so the absolute value of the car's momentum changes by a certain amount and that of the Earth changes by:

More information

KINEMATICS OF PARTICLES RELATIVE MOTION WITH RESPECT TO TRANSLATING AXES

KINEMATICS OF PARTICLES RELATIVE MOTION WITH RESPECT TO TRANSLATING AXES KINEMTICS OF PRTICLES RELTIVE MOTION WITH RESPECT TO TRNSLTING XES In the previous articles, we have described particle motion using coordinates with respect to fixed reference axes. The displacements,

More information

Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion

Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckle-up? A) the first law

More information

Example SECTION 13-1. X-AXIS - the horizontal number line. Y-AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross

Example SECTION 13-1. X-AXIS - the horizontal number line. Y-AXIS - the vertical number line ORIGIN - the point where the x-axis and y-axis cross CHAPTER 13 SECTION 13-1 Geometry and Algebra The Distance Formula COORDINATE PLANE consists of two perpendicular number lines, dividing the plane into four regions called quadrants X-AXIS - the horizontal

More information

Chapter 6 Quadratic Functions

Chapter 6 Quadratic Functions Chapter 6 Quadratic Functions Determine the characteristics of quadratic functions Sketch Quadratics Solve problems modelled b Quadratics 6.1Quadratic Functions A quadratic function is of the form where

More information

Problem Set #8 Solutions

Problem Set #8 Solutions MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01L: Physics I November 7, 2015 Prof. Alan Guth Problem Set #8 Solutions Due by 11:00 am on Friday, November 6 in the bins at the intersection

More information

Supplemental Questions

Supplemental Questions Supplemental Questions The fastest of all fishes is the sailfish. If a sailfish accelerates at a rate of 14 (km/hr)/sec [fwd] for 4.7 s from its initial velocity of 42 km/h [fwd], what is its final velocity?

More information

CS100B Fall 1999. Professor David I. Schwartz. Programming Assignment 5. Due: Thursday, November 18 1999

CS100B Fall 1999. Professor David I. Schwartz. Programming Assignment 5. Due: Thursday, November 18 1999 CS100B Fall 1999 Professor David I. Schwartz Programming Assignment 5 Due: Thursday, November 18 1999 1. Goals This assignment will help you develop skills in software development. You will: develop software

More information

Study Guide for Mechanics Lab Final

Study Guide for Mechanics Lab Final Study Guide for Mechanics Lab Final This study guide is provided to help you prepare for the lab final. The lab final consists of multiple-choice questions, usually 2 for each unit, and 4 work-out problems

More information

Angular acceleration α

Angular acceleration α Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 7-0 Linear and Circular Motion Compared Slide 7- Linear and Circular Kinematics Compared Slide 7-

More information

Natural Convection. Buoyancy force

Natural Convection. Buoyancy force Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient

More information

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014

Lecture 07: Work and Kinetic Energy. Physics 2210 Fall Semester 2014 Lecture 07: Work and Kinetic Energy Physics 2210 Fall Semester 2014 Announcements Schedule next few weeks: 9/08 Unit 3 9/10 Unit 4 9/15 Unit 5 (guest lecturer) 9/17 Unit 6 (guest lecturer) 9/22 Unit 7,

More information

2After completing this chapter you should be able to

2After completing this chapter you should be able to After completing this chapter you should be able to solve problems involving motion in a straight line with constant acceleration model an object moving vertically under gravity understand distance time

More information

10.1 Quantitative. Answer: A Var: 50+

10.1 Quantitative. Answer: A Var: 50+ Chapter 10 Energy and Work 10.1 Quantitative 1) A child does 350 J of work while pulling a box from the ground up to his tree house with a rope. The tree house is 4.8 m above the ground. What is the mass

More information

At the skate park on the ramp

At the skate park on the ramp At the skate park on the ramp 1 On the ramp When a cart rolls down a ramp, it begins at rest, but starts moving downward upon release covers more distance each second When a cart rolls up a ramp, it rises

More information

Interactive Animation: A new approach to simulate parametric studies

Interactive Animation: A new approach to simulate parametric studies Interactive Animation: A new approach to simulate parametric studies Darwin Sebayang and Ignatius Agung Wibowo Kolej Universiti Teknologi Tun Hussein Onn (KUiTTHO) Abstract Animation is the one of novel

More information

To provide insight into the physics of arrow flight and show how archers adapt their equipment to maximize effectiveness.

To provide insight into the physics of arrow flight and show how archers adapt their equipment to maximize effectiveness. The Science of Archery Godai Katsunaga Purpose To provide insight into the physics of arrow flight and show how archers adapt their equipment to maximize effectiveness. Archery Archery is one of the events

More information

CONDITIONING PROGRAM

CONDITIONING PROGRAM CONDITIONING PROGRAM Speed and Agility are two major components of sport that need to be trained just like strength, size, and power are developed in the weight room. It is true that no matter what your

More information

To define concepts such as distance, displacement, speed, velocity, and acceleration.

To define concepts such as distance, displacement, speed, velocity, and acceleration. Chapter 7 Kinematics of a particle Overview In kinematics we are concerned with describing a particle s motion without analysing what causes or changes that motion (forces). In this chapter we look at

More information

EDUH 1017 - SPORTS MECHANICS

EDUH 1017 - SPORTS MECHANICS 4277(a) Semester 2, 2011 Page 1 of 9 THE UNIVERSITY OF SYDNEY EDUH 1017 - SPORTS MECHANICS NOVEMBER 2011 Time allowed: TWO Hours Total marks: 90 MARKS INSTRUCTIONS All questions are to be answered. Use

More information

Lecture Presentation Chapter 7 Rotational Motion

Lecture Presentation Chapter 7 Rotational Motion Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class

More information

Fundamental Mechanics: Supplementary Exercises

Fundamental Mechanics: Supplementary Exercises Phys 131 Fall 2015 Fundamental Mechanics: Supplementary Exercises 1 Motion diagrams: horizontal motion A car moves to the right. For an initial period it slows down and after that it speeds up. Which of

More information

G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M

G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M G U I D E T O A P P L I E D O R B I T A L M E C H A N I C S F O R K E R B A L S P A C E P R O G R A M CONTENTS Foreword... 2 Forces... 3 Circular Orbits... 8 Energy... 10 Angular Momentum... 13 FOREWORD

More information

Episode 207: Projectile motion

Episode 207: Projectile motion Episode 207: Projectile motion This episode looks at the independence of vertical and horizontal motion. It concerns objects accelerating vertically when projected horizontally or vertically. The crucial

More information

Jump Shot Mathematics Howard Penn

Jump Shot Mathematics Howard Penn Jump Shot Mathematics Howard Penn Abstract In this paper we exae variations of standard calculus problems in the context of shooting a basketball jump shot. We believe that many students will find this

More information

COMPONENTS OF VECTORS

COMPONENTS OF VECTORS COMPONENTS OF VECTORS To describe motion in two dimensions we need a coordinate sstem with two perpendicular aes, and. In such a coordinate sstem, an vector A can be uniquel decomposed into a sum of two

More information

Biomechanics Sample Problems

Biomechanics Sample Problems Biomechanics Sample Problems Forces 1) A 90 kg ice hockey player collides head on with an 80 kg ice hockey player. If the first person exerts a force of 450 N on the second player, how much force does

More information

Penalty Stroke in Field Hockey: A Biomechanical Study

Penalty Stroke in Field Hockey: A Biomechanical Study ISSN 1750-9823 (print) International Journal of Sports Science and Engineering Vol. 05 (2011) No. 01, pp. 053-057 Penalty Stroke in Field Hockey: A Biomechanical Study Ikram Hussain 1, Arif Mohammad 2,

More information

Motion Graphs. It is said that a picture is worth a thousand words. The same can be said for a graph.

Motion Graphs. It is said that a picture is worth a thousand words. The same can be said for a graph. Motion Graphs It is said that a picture is worth a thousand words. The same can be said for a graph. Once you learn to read the graphs of the motion of objects, you can tell at a glance if the object in

More information

Vector Spaces; the Space R n

Vector Spaces; the Space R n Vector Spaces; the Space R n Vector Spaces A vector space (over the real numbers) is a set V of mathematical entities, called vectors, U, V, W, etc, in which an addition operation + is defined and in which

More information

Digital Energy ITI. Instrument Transformer Basic Technical Information and Application

Digital Energy ITI. Instrument Transformer Basic Technical Information and Application g Digital Energy ITI Instrument Transformer Basic Technical Information and Application Table of Contents DEFINITIONS AND FUNCTIONS CONSTRUCTION FEATURES MAGNETIC CIRCUITS RATING AND RATIO CURRENT TRANSFORMER

More information

1. Watch or research. Choose option a, b, or c and complete all the requirements: a. Watch 3 episodes/hours of NOVA, NASA, or other media productions

1. Watch or research. Choose option a, b, or c and complete all the requirements: a. Watch 3 episodes/hours of NOVA, NASA, or other media productions 1. Watch or research. Choose option a, b, or c and complete all the requirements: a. Watch 3 episodes/hours of NOVA, NASA, or other media productions (examples include Discovery Channel, Science Channel,

More information

Mechanics lecture 7 Moment of a force, torque, equilibrium of a body

Mechanics lecture 7 Moment of a force, torque, equilibrium of a body G.1 EE1.el3 (EEE1023): Electronics III Mechanics lecture 7 Moment of a force, torque, equilibrium of a body Dr Philip Jackson http://www.ee.surrey.ac.uk/teaching/courses/ee1.el3/ G.2 Moments, torque and

More information

= f x 1 + h. 3. Geometrically, the average rate of change is the slope of the secant line connecting the pts (x 1 )).

= f x 1 + h. 3. Geometrically, the average rate of change is the slope of the secant line connecting the pts (x 1 )). Math 1205 Calculus/Sec. 3.3 The Derivative as a Rates of Change I. Review A. Average Rate of Change 1. The average rate of change of y=f(x) wrt x over the interval [x 1, x 2 ]is!y!x ( ) - f( x 1 ) = y

More information

How to Write a Formal Lab Report

How to Write a Formal Lab Report Union College Physics and Astronomy How to Write a Formal Lab Report A formal lab report is essentially a scaled-down version of a scientific paper, reporting on the results of an experiment that you and

More information

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m

Midterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of

More information

REHAB 442: Advanced Kinesiology and Biomechanics INTRODUCTION - TERMS & CONCEPTS

REHAB 442: Advanced Kinesiology and Biomechanics INTRODUCTION - TERMS & CONCEPTS Rehab 442: Introduction - Page 1 REHAB 442: Advanced Kinesiology and Biomechanics INTRODUCTION - TERMS & CONCEPTS Readings: Norkin & Levangie, Chapters 1 & 2 or Oatis, Ch. 1 & 2 (don't get too bogged down

More information

Derivatives as Rates of Change

Derivatives as Rates of Change Derivatives as Rates of Change One-Dimensional Motion An object moving in a straight line For an object moving in more complicated ways, consider the motion of the object in just one of the three dimensions

More information

Chapter 11 Equilibrium

Chapter 11 Equilibrium 11.1 The First Condition of Equilibrium The first condition of equilibrium deals with the forces that cause possible translations of a body. The simplest way to define the translational equilibrium of

More information

General Physical Science

General Physical Science General Physical Science Chapter 4 Work and Energy Work The work done by a constant force F acting upon an object is the product of the magnitude of the force (or component of the force) and the parallel

More information

2 ONE- DIMENSIONAL MOTION

2 ONE- DIMENSIONAL MOTION 2 ONE- DIMENSIONAL MOTION Chapter 2 One-Dimensional Motion Objectives After studying this chapter you should be able to derive and use formulae involving constant acceleration; be able to understand the

More information

Kinematic Physics for Simulation and Game Programming

Kinematic Physics for Simulation and Game Programming Kinematic Phsics for Simulation and Game Programming Mike Baile mjb@cs.oregonstate.edu phsics-kinematic.ppt mjb October, 05 SI Phsics Units (International Sstem of Units) Quantit Units Linear position

More information

Chapter 9. particle is increased.

Chapter 9. particle is increased. Chapter 9 9. Figure 9-36 shows a three particle system. What are (a) the x coordinate and (b) the y coordinate of the center of mass of the three particle system. (c) What happens to the center of mass

More information

Exam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis

Exam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis * By request, but I m not vouching for these since I didn t write them Exam 2 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis There are extra office hours today & tomorrow Lots of practice exams

More information

AP Physics 1 and 2 Lab Investigations

AP Physics 1 and 2 Lab Investigations AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks

More information

Midterm Exam 1 October 2, 2012

Midterm Exam 1 October 2, 2012 Midterm Exam 1 October 2, 2012 Name: Instructions 1. This examination is closed book and closed notes. All your belongings except a pen or pencil and a calculator should be put away and your bookbag should

More information

1.3. DOT PRODUCT 19. 6. If θ is the angle (between 0 and π) between two non-zero vectors u and v,

1.3. DOT PRODUCT 19. 6. If θ is the angle (between 0 and π) between two non-zero vectors u and v, 1.3. DOT PRODUCT 19 1.3 Dot Product 1.3.1 Definitions and Properties The dot product is the first way to multiply two vectors. The definition we will give below may appear arbitrary. But it is not. It

More information

SYLLABUS FORM WESTCHESTER COMMUNITY COLLEGE Valhalla, NY lo595. l. Course #: PHYSC 111 2. NAME OF ORIGINATOR /REVISOR: Dr.

SYLLABUS FORM WESTCHESTER COMMUNITY COLLEGE Valhalla, NY lo595. l. Course #: PHYSC 111 2. NAME OF ORIGINATOR /REVISOR: Dr. SYLLABUS FORM WESTCHESTER COMMUNITY COLLEGE Valhalla, NY lo595 l. Course #: PHYSC 111 2. NAME OF ORIGINATOR /REVISOR: Dr. Neil Basescu NAME OF COURSE: College Physics 1 with Lab 3. CURRENT DATE: 4/24/13

More information

A vector is a directed line segment used to represent a vector quantity.

A vector is a directed line segment used to represent a vector quantity. Chapters and 6 Introduction to Vectors A vector quantity has direction and magnitude. There are many examples of vector quantities in the natural world, such as force, velocity, and acceleration. A vector

More information

BIOMECHANICAL ANALYSIS OF THE STANDING LONG JUMP

BIOMECHANICAL ANALYSIS OF THE STANDING LONG JUMP APPLICATIONS, BASIS & COMMUNICATIONS 186 BIOMECHANICAL ANALYSIS OF THE STANDING LONG JUMP WEN-LAN WU 1, JIA-HROUNG WIT, HWAI-TING LIN\ GWO-JAW WANG 4 1 School of Sports Medicine, Kaohsiung Medical University,

More information

Slope and Rate of Change

Slope and Rate of Change Chapter 1 Slope and Rate of Change Chapter Summary and Goal This chapter will start with a discussion of slopes and the tangent line. This will rapidly lead to heuristic developments of limits and the

More information

review/assessment questions

review/assessment questions Student Activity Sheet 6 Page 1 Name physics, technology and engineering in automobile racing review/assessment questions 1. Draw a free-body diagram for a block being pushed across the floor. 2. Use all

More information

An Introduction to Applied Mathematics: An Iterative Process

An Introduction to Applied Mathematics: An Iterative Process An Introduction to Applied Mathematics: An Iterative Process Applied mathematics seeks to make predictions about some topic such as weather prediction, future value of an investment, the speed of a falling

More information

3600 s 1 h. 24 h 1 day. 1 day

3600 s 1 h. 24 h 1 day. 1 day Week 7 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution

More information

Welcome back to Physics 211. Physics 211 Spring 2014 Lecture 04-1 1. ask a physicist

Welcome back to Physics 211. Physics 211 Spring 2014 Lecture 04-1 1. ask a physicist Welcome back to Physics 211 Today s agenda: Rotations What s on the exam? Relative motion Physics 211 Spring 2014 Lecture 04-1 1 ask a physicist Why are neutrinos faster than light (photons)? I thought

More information

Adequate Theory of Oscillator: A Prelude to Verification of Classical Mechanics Part 2

Adequate Theory of Oscillator: A Prelude to Verification of Classical Mechanics Part 2 International Letters of Chemistry, Physics and Astronomy Online: 213-9-19 ISSN: 2299-3843, Vol. 3, pp 1-1 doi:1.1852/www.scipress.com/ilcpa.3.1 212 SciPress Ltd., Switzerland Adequate Theory of Oscillator:

More information

Despite its enormous mass (425 to 900 kg), the Cape buffalo is capable of running at a top speed of about 55 km/h (34 mi/h).

Despite its enormous mass (425 to 900 kg), the Cape buffalo is capable of running at a top speed of about 55 km/h (34 mi/h). Revised Pages PART ONE Mechanics CHAPTER Motion Along a Line 2 Despite its enormous mass (425 to 9 kg), the Cape buffalo is capable of running at a top speed of about 55 km/h (34 mi/h). Since the top speed

More information

Orbital Mechanics. Angular Momentum

Orbital Mechanics. Angular Momentum Orbital Mechanics The objects that orbit earth have only a few forces acting on them, the largest being the gravitational pull from the earth. The trajectories that satellites or rockets follow are largely

More information