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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