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# MEM 238 Dynamics, Week 1 Notes MEM 238

Drexel

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This 37 page Class Notes was uploaded by Haikal Fouzi on Monday January 11, 2016. The Class Notes belongs to MEM 238 at Drexel University taught by Dr. Sorin Siegler in Winter 2016. Since its upload, it has received 109 views. For similar materials see Dynamics in Engineering and Tech at Drexel University.

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Date Created: 01/11/16

About the Course – Instructors and Office Hours DREXEL UNIVERSITY Mechanical Engineering and Mechanics MEM 238 Dynamics Winter 2015-2016 Instructor: Dr. Sorin Siegler Office: Alumni Building Rm. 171A Phone: 215-895-2316 Email: ssiegler@coe.drexel.edu TA: Richard Vallett TA: Sergio Machaca Office: Bosson, Rm 405 Office: Alumni Building, Room 179B Phone: 856-745-0591 Phone:267-261-8456 Email: rjvallett@gmail.edu Email: sam526@drexel.edu Office Hour: Sorin Siegler: Thursdays 11AM-12PM or by appointment Alumni Building Rm. 4 – 171A) Richard Vallett Wednesday 10AM-12PM or by appointment Bosson Rm. 405 Sergio Machaca Wednesday TBD About the Course – Textbook and Class Schedule Textbook (Required): Engineering Mechanics: Dynamics (8th edition), J. L. Meriam, L.G. Craig and J.N. Bolton Publisher: Wiley ISBN: 97891119034711 On-Line Course Access Code: WileyPlus.com Code: 484576 Class Schedule: Lecture: TR 3:30-4:50 (Stratton Hall 113) Recitations: W 12:00-12:50 (Randell Hall 329), W 1:00-1:50 (Randell Hall 329), W 2:00-2:50 (Randell Hall 329), W 3:00-3:50 (Randell Hall 329), W 4:00-4:50 (Randell Hall 329) About the Course – Grading Policy Grading Policy: Homework: 10% - Weekly homework assignments will be posted on-line on WileyPlus every Thursdayand will be due by Wednesday Midnight.) Weekly Quizes: 20% (In-class during Recitation, short one problem quizzes) Midterm Exam 30%, (Dynamics, Chapters 1-4) Final Exam 40% (Rigid Body Dynamics, Chapters 5-7) Attendance Policy: Attendance at each class is highly recommended; students will be responsible for all material covered during lectures. Textbooks and notebooks should be brought to each class. About the Course – Course Outline Course Outline: Week 1 Chapter 1 Review of Fundamental Concepts, Chapter 2 Kinematics of Particles Week 2 Chapter 3 Kinetics of Particles: Force and Acceleration Week 3 Chapter 3 Kinetics of Particles: Force and Acceleration Week 4 Chapter 3 Kinetics of Particles: Work and Energy Week 5 Chapter 3 Kinetics of Particles: Impulse and Momentum Week 6 Midterm Exam (July 28, Chapters 1-4) Chapter 5 Planar Kinematics of Rigid Bodies Week 7 Chapter 5 Plane Kinematics of Rigid Bodies Week 8 Chapter 6 Plane Kinetics of Rigid Bodies: Force and Acceleration Week 9 Chapter 6 Planar Kinetics of Rigid Bodies: Work and Energy Week 10 Chapter 6 Planar Kinetics of Rigid Bodies: Impulse and Momentum Week 11 Chapter 7 Introduction to 3-Dimensional Dynamics of Rigid Bodies Final during Exam (Date TBD, Chapters 5-7) Introduction – Basic Concepts DYNAMICS – Study of Motion of objects under the action of forces Kinematics – Study of Motion with no references to the forces Kinetics – Relation between forces and the produced motion BASIC CONCEPTS: Scalar, Vector, Particle, Rigid Body, Flexible Body, Reference Frame. BASICUNITS: Time (SEC), Length (meters, feet), Mass (Kg.) Introduction – Basic Math Skills Law of Sines Law of Cosines Introduction – Basic Math Skills Dot Product of Two Vectors Cross Product of Two Vectors Introduction – Basic Statics Introduction – Basic Statics Equilibrium: ������������� = 0 ������������� = 0 Example 1 – Moment of a Force (2D) Calculate the Moment about the base point O of the 600N force Example 2 – Moment of a Force (3D) 2. Calculate the moment of the force P about line lA. Example 1 A stone is thrown upwards from a point on a bridge located 125 feet above the water. Knowing that it strikes the water 4 seconds after release, determine a) The speed with which the stone was thrown upwards b) The speed with which the stone strikes the water. Example 2 The spring-mounted slider moves in the horizontal guide with negligible friction and has a velocity v0 in the s-direction as it crosses the mid-position where s=0 and t=0. The two springs together exert a retarding force to the motion of the slider, which gives it an acceleration proportional to the displacement but oppositely directed and equal to a=−k2s, where k is constant. (The constant is arbitrarily squared for later convenience in the form of the expressions.) Determine the expressions for the velocity v as a function of the position s of the slider. Example 1 A stone is thrown upwards from a point on a bridge located 125 feet above the water. Knowing that it strikes the water 4 seconds after release, determine a) The speed with which the stone was thrown upwards b) The speed with which the stone strikes the water. Example 2 The spring-mounted slider moves in the horizontal guide with negligible friction and has a velocity v0 in the s-direction as it crosses the mid-position where s=0 and t=0. The two springs together exert a retarding force to the motion of the slider, which gives it an acceleration proportional to the displacement but oppositely directed and equal to a=−k2s, where k is constant. (The constant is arbitrarily squared for later convenience in the form of the expressions.) Determine the expressions for the velocity v as a function of the position s of the slider. Example 1 A team of engineering students designs a medium-size catapult which launches 8-lb steel spheres. The launch speed is v0=80 ft/sec, the launch angle is θ=35° above the horizontal, and the launch position is 6 ft above ground level. The students use an athletic field with an adjoining slope topped by an 8 ft fence as shown. Determine: (a)the time duration tf of the flight (b)the x-y coordinates of the point of first impact (c)the maximum height h above the horizontal field attained by the ball (d)the velocity (expressed as a vector) with which the projectile strikes the ground (or the fence) Example 2 With what minimum horizontal velocityu can a boy throw a rock at A and have it just clear the obstruction atB? Example 1 A projectile is fired with a speed of v0 = 180 m/sec and at an angle of 30 degrees with the horizontal. Determine the minimum radius of curvature of the trajectory described by the projectile. Example 2 A motorist starts from rest on a curve of 400 feet radius and accelerates at a constant rate of 3 ft/sec2. Determine the distance travelled before the magnitude of the total acceleration is 6 ft/sec2. Example 3 An overhead view of part of a pinball game is shown. If the plunger imparts a speed of 3 m/s to the ball which travels in the smooth horizontal slot, determine the acceleration a of the ball (a) just before it exits the curve at C and (b) when it is halfway between points D and E. Use the values r=150 mm and θ=60°. Example 1 Space Curvilinear Motion Rectangular Cylindrical Relative Motion Example 1 Example 2 Example 2 - Solution Constrained Motion of Connected Particles Example 1 Example 2

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