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Слайд 1

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Chapter 12: Kinematics of a Particle Section 12.1: Introduction

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Learning objective Be able to find the kinematic quantities (position, displacement, velocity, and acceleration) of a particle traveling along a straight path.

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Applications

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Applications

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An Overview of Mechanics

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Chapter 12: Kinematics of a Particle Section 12.2: Rectilinear Kinematics: Continuous Motion

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Continuous Motion

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Velocity

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Acceleration

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Summary of Kinematic Relations

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Constant Acceleration

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Example

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Solution

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Channel Setting Instructions for ResponseCard RF 1. Press and release the "GO" or "CH" button. 2. While the light is flashing red and green, enter the 2 digit channel code (i.e. channel 1 = 01, channel 21 = 21). Channel is 11 3. After the second digit is entered, Press and release the "GO" or "CH" button. The light should flash green to confirm. 4. Press and release the "1/A" button. The light should flash amber to confirm.

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Quiz

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A particle moves along a horizontal path with its velocity varying with time as shown. The average acceleration of the particle is? 0.4 m/s2 0.4 m/s2 1.6 m/s2 1.6 m/s2

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A particle has an initial velocity of 30 m/s to the left. If it then passes through the same location 5 seconds later with a velocity of 50 m/s to the right, the average velocity of the particle during the 5 s time interval is? 10 m/s 40 m/s 16 m/s 0 m/s

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Example

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Solution

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Solution

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Quiz

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A particle has an initial velocity of 3 m/s to the left at s0 = 0 m. Determine its position when t = 3 s if the acceleration is 2 m/s2 to the right. 0.0 m 6.0 m 18.0 m 9.0 m

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A particle is moving with an initial velocity of v = 12 m/s and constant acceleration of 3.78 m/s2 in the same direction as the velocity. Determine the distance the particle has traveled when the velocity reaches 30 m/s. 50 m 100 m 150 m 200 m

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Ugly aircraft competition

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Scale of Ugliness

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Focke Wulf 19a Ente (1927) 1 2 3 4 5 6 7 8 9 10

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Chapter 12: Kinematics of a Particle Section 12.3: Rectilinear Kinematics: Erratic Motion

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Learning Objective Be able to calculate position, velocity, and acceleration of a particle using graphs.

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Erratic Motion

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s-t-graph

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v-t-graph

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a-t-graph

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a-s-graph

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v-s-graph

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Example

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Solution

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Solution

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Quiz

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If a particle starts from rest and accelerates according to the graph shown, the particle’s velocity at t = 20 s is 200 m/s 100 m/s 0 20 m/s

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The particle in the previous stops moving at t = ……. 10 s 20 s 30 s 40 s

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Example

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Example

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Solution

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Solution

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Example

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Solution

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Solution

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Example

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Solution

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Quiz

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If a car has the velocity curve shown, determine the time t necessary for the car to travel 100 meters. 8 s 4 s 10 s 6 s

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Select the correct a-t graph for the velocity curve shown. A) B) C) D)

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Ugly aircraft competition

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Miles M.35 Libellula (1942) 1 2 3 4 5 6 7 8 9 10

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Chapter 12: Kinematics of a Particle Section 12.4: General Curvilinear Motion

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Learning Objective

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Applications

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Applications

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General Curvilinear Motion

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Velocity

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Acceleration

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Chapter 12: Kinematics of a Particle Section 12.5: Curvilinear Motion Rectangular Components

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Learning Objective

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Rectangular Components

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Rectangular Components: Velocity

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Rectangular Components: Acceleration

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Example

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Solution

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Solution

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Quiz

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If the position of a particle is defined by r = [(1.5t2 + 1) i + (4t – 1) j ] (m), its speed at t = 1 s is 2 m/s 3 m/s 5 m/s 7 m/s

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The position of a particle is given as r = (4t2 i - 2x j) m. Determine the particle’s acceleration. (4 i +8 j ) m/s2 (8 i -16 j ) m/s2 (8 i) m/s2 (8 j ) m/s2

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Ugly aircraft competition

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Kyushu J7W-1 Shinden (1945) 1 2 3 4 5 6 7 8 9 10

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Chapter 12: Kinematics of a Particle Section 12.6: Motion of a Projectile

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Learning Objective

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Applications

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Motion of a Projectile

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Motion of a Projectile

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Kinematic Equations: Horizontal Motion

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Kinematic Equations: Vertical Motion

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Example

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Solution

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Example

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Solution

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Quiz

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The time of flight of a projectile, fired over level ground, with initial velocity Vo at angle θ, is equal to? (vo sin θ)/g (2vo sin θ)/g (vo cos θ)/g (2vo cos θ)/g

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Ugly aircraft competition

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VariViggen (1967) 1 2 3 4 5 6 7 8 9 10

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Chapter 12: Kinematics of a Particle Section 12.7: Curvilinear Motion Normal and Tangential Components

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Learning Objective

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Application

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Normal and Tangential Components

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Normal and Tangential Components

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Velocity in the n-t-Coordinate System

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Velocity in the n-t-Coordinate System

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Velocity in the n-t-Coordinate System

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Special Cases of Motion

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Special Cases of Motion

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Three-dimensional Motion

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Example

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Solution

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Example

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Solution

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Quiz

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An aircraft traveling in a circular path of radius 300 m has an instantaneous velocity of 30 m/s and its velocity is increasing at a constant rate of 4 m/s2. What is the magnitude of its total acceleration at this instant? 3 m/s2 4 m/s2 5 m/s2 -5 m/s2

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Example

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Solution

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Chapter 12: Kinematics of a Particle Section 12.8: Curvilinear Motion Cylindrical Components

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Learning Objective

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Applications

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Cylindrical Components

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Velocity in Polar Coordinates

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Acceleration in Polar Coordinates

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Cylindrical Coordinates

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Example

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Solution

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Solution

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Example

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Solution

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Solution

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Ugly aircraft competition

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Curtis Aerodrome (1914) 1 2 3 4 5 6 7 8 9 10

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Chapter 12: Kinematics of a Particle Section 12.9: Absolute Dependent Motion of Two Particles

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Learning Objective

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Applications

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Applicatons

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Dependent Motion

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Dependent Motion

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Dependent Motion

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Example

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Solution

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Solution

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Dependent Motion: Procedure

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Example

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Solution

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Solution

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Quiz

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Determine the speed of block B. 1 m/s 2 m/s 4 m/s None of the above.

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Example

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Solution

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Quiz

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Determine the speed of block B when block A is moving down at 6 m/s while block C is moving down at 18 m/s. 24 m/s 3 m/s 12 m/s 9 m/s

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Ugly aircraft competition

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Koechlin biplane (1908) 1 2 3 4 5 6 7 8 9 10

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Chapter 12: Kinematics of a Particle Section 12.10: Relative Motion of Two Particles Using Translating Axes

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Learning Objective

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Applications

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Relative Motion: Position

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Relative Motion: Velocity and Acceleration

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Relative Motion: Procedure

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Example

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Example

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Quiz

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Two planes A and B are flying at constant speed. Determine the magnitude of the velocity of plane B relative to plane A 693 km/h 650 km/h 400 km/h 1258 km/h