Homework1 - Middle East Technical Universityae262/17/hw/hw1.pdf · Homework1 Preparedby: Harun...
Transcript of Homework1 - Middle East Technical Universityae262/17/hw/hw1.pdf · Homework1 Preparedby: Harun...
2016/2017 SPRING SEMESTER
AE262 DYNAMICS
Homework 1
Prepared by: Harun Levent SAHIN
Given: March 10, 2017Due: March 20, 2017 at 10:35 to Room: 004
Homework Format
There are some rules that you should carefully consider in the homework submission.
• Draw the free body diagrams for each and every particle or body.
• Use the vector notation described in the class.
• Write down every step of your solution procedure neatly.
• Plot necessary graphs with a suitable computer program(s) that you choose (hand sketcheswill not be accepted).
• Include a printout of the plots and the computer routine that you use.
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Problem 1:
Block C starts from rest and moves downward with a constant acceleration. Knowing thatafter 6 [s] the velocity of block A relative to block D is 2.5 [m/s], determine
(a) the acceleration of block C .
(b) the acceleration of portion E of the cable.
Problem 2:
The system shown starts from rest, and each component moves with a constant acceleration.If the relative acceleration of block C with respect to collar B is 140 [mm/s2] upward and therelative acceleration of block D with respect to block A is 240 [mm/s2] downward, determine
(a) the velocity of block C after 7 [s].
(b) the change in position of block D after 12 [s].
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Problem 3:
Slider block B starts from rest and moves to the right with a constant acceleration of 0.5[m/s2]. Determine
(a) the relative acceleration of portion C of the cable with respect to slider block A.
(b) the velocity of portion C of the cable after 3 [s].
Problem 4:
The three-dimensional motion of a particle is defined by the position vectorr = (Rt cosωn t )i+ ct j+ (Rt sinωn t )k. Determine
(a) the magnitudes of the velocity and acceleration of the particle.
(b) the radius of curvature of the path described by the particle when t = 0.
Problem 5:
The rotation of rod O A about O is defined by the relation θ = t 3 +4t , where θ is expressed inradians and t in seconds. Collar B slides along the rod in such a way that its distance fromO is r = t 3 +2t 2, where r is expressed in meters and t in seconds. Derive expressions for thevelocity and acceleration of the collar as functions of t . Consider one revolution of the rodstarting at t = 0 and plot
(a) the path of the particle in the x y plane.
(b) the components of the velocity vr & vθ and the magnitude of the velocity v .
(c) the components of the acceleration ar & aθ and the magnitude of the acceleration a.
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