# ws 25 - MEEN 221 Summer 2009 Worksheet 14 Dr A Palazzolo(1...

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Unformatted text preview: MEEN 221 Summer 2009 - Worksheet 14 Dr. A. Palazzolo (1) HWSl4 . Ch 13 (1, 23, 27, 39, 69, 71) d— 3 me 'Tmec. 2% Disk, (2) Attendance Mandatory fbr 10:00 am — 12:39pm, unless excused by instructor. Multiple Quizzes may be given anytime during this period. (3) Today’s Material: Kinematics Straight Line Motion Sections 13.1 — 13.4 EXAM II WILL BE HELD %Mmsrw Weou- 31* am), 6:00 - 8:00 PM MATERIAL: Worksheets'l— mend related HW’s, Quizzes and book material. Bring your calculator. PART 2 EN GR 221 KINEMATICS AND DYNAMICS THE SECOND HALF OF THIS COURSE FOCUSES ON UTILIZING NEWTON’S LAW OF MOTION : FORCE = MASS * ACCELERATION THIS WILL PROVIDE YOU WITH CAPABILITIES TO PREDICT ( SIMULATE) : (1) MOTIONS OF A RIGID BODY DUE TO APPLIED FORCES OR TORQUES ( e.g. the rpm vs. time response of a fan that’s driven by a motor with a known torque and is also subjected to known drag torques due to its bearings and windage) (2) THE FORCES ( OR TORQUES ) REQUIRED TO PRODUCE A DESIRED MOTION ( e. g. the engine thrust forces that are required to produce a desired liﬁoff speed for a jet) . (3) THE TIME REQUIRED FOR THE POSITION OR VELOCITY OF AN OBJECT TO CHANGE BY A SPECIFIED AMOUNT ( e. g. the time required for a train to brake from full speed to zero speed ) (4) THE CHANGE IN POSITION AND VELOCITY OF AN OBJECT THAT IS CHANGING MASS (e. g. liﬁoff of a rocket) WE WILL BEGIN OUR STUDY OF THE LAW OF MOTION BY CONSIDERING MOTIONS IN THE ABSTRACT , I.E. INDEPENDENTLY OF HOW THEY ARE CAUSED . THIS IS COMMONLY REFERRED TO AS KINEMATICS. THIS IS THE STUDY OF THE RELATIONSHIPS BETWEEN POSITION , VELOCITY , AND ACCELERATION . (I) Straight Line Absolute Motion (a The simplest relationships between a particle undergoing straight line ‘ motion are:- —-~~ ' ' I velocity = v = dx/dt I acceleration = a = dv/dt = dzx/dt2 (1) The corresponding integral relationships are x = Ivdt v = Iadt (2) (b) Note that if a is given as a function of x then dv dv dx dv 0-3—3274; (3) :> vdv = a(x)dx (d) If a ‘is given as a function of v V2 v; _, ‘ =ﬂ=ﬂéi= Li: 7 ‘7 — Io “00‘1" dt dx dt vdx 0) where: v0 = v(x = 0) :> vdv (c) If v is given as a function of x then ' ‘ dv 22> x :: G We; 2, =% ) am ) t v x (6 dx :> t= —— v(x) A W 13-2* The position of a particle moving along the x—axis is given as a function of time by x(t) = 15 - 4t m. a. b. Determine the velocity of the particle as a function of time. Determine the acceleration of the particle as a function of time. Evaluate the position, velocity, and acceleration of the particle.at' t = 5 5. Determine the total distance traveled by the particle between t = O and t = 5 5. Sketch x(t), v(t), and a(t); 0 < t < 8 5. Problem 13-2 The velocity of a particle moving along the x-axis is given as a‘ 13-8* function of time by IV(t) = —4t2 + 40t - 70 m/s and x(0) = 20 m. a. Determine the position of the particle as a function of time. b. betermine the acceleration of the particle as a function of time. c. Evaluate the position, velocity, and acceleratiOn of the particle at t = 8 s. d. Determine the total distance traveled by the particle between t = 5 and t = 8 s. e. Sketch x(t), v(t); and a(t), O < t < 10 s. x,v,a 0123 456 Time.t(s) 7 (J) 13125 The jet shown is' catapulted from the deck of an aircraft carrier by a hydraulic ram. Determine the_acceleration of the jet if it accelerates- uniformly frcm rest to 160 mi/h in 300 ft. Train A is traveling eastward at 80 mi/h while train 8 traveling westward at 60 mi/h. Determine a. The velocity of train A relative to train 8. b. The velocity of train 8 relative to train A. is 4) 13—72* In Fig. P13-72 block 3 has a constant downward acceleration of 0.8 m/sz. Determine the speed and acceleration of block A 5 s after the system starts from rest. 13-73* In Fig. P13-73 the elevator E is moving upward at a speed of 6 ft/s and its speed is decreasing at the rate of 0.5 ft/sz. Determine the velocity and acceleration of the counterWeight C. .13-77* A railroad car is loose on a siding and rolling at a constant speed of 8 mi/h. A switch engine dispatched to catch the runaway car has 2 2 a maximum acceleration of 3 ft/s , a maximum deceleration of 5 ft/s I-and a maximum speed of 45 mi/h. Determine the minimum distance required to catch the runaway car. (Assume that the switch engine starts from rest when the runaway car is 500 ft down the track and that the relative velocity when the engine catches the car must be less than 3 mi/h.) SOOft IIII“‘HIHJ‘IHIfHIHH“IIHIHIIIHH 8mi/h ...
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