# Outright DEPENDENT MOTION ANALYSIS OF TWO PARTICLES Section 12.9 .

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APPLICATIONS. The link and pulley alter the rate of B in respect to the rate of the engine. It is imperative to relate the different movements to decide the force prerequisites for the engine and the strain in the link.. On the off chance that the rate of the An is known, by what means would we be able to decide the pace of piece B?. . .
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Slide 1

﻿Outright DEPENDENT MOTION ANALYSIS OF TWO PARTICLES (Section 12.9) Objectives : To relate the positions, speeds, and increasing speeds of particles experiencing subordinate movement.

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APPLICATIONS The link and pulley adjust the speed of B with respect to the speed of the engine. It is essential to relate the different movements to decide the power prerequisites for the engine and the pressure in the link. On the off chance that the speed of the An is known, how might we decide the speed of piece B?

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APPLICATIONS (proceeded with) Rope and pulley courses of action are utilized to help with lifting overwhelming articles. The aggregate lifting power required from the truck relies on upon the increasing speed of the bureau A. How might we decide the increasing speed and speed of An if the quickening of B is known?

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DEPENDENT MOTION COMPATABILITY EQUATIONS In numerous kinematics issues, the movement of one protest will rely on upon the movement of another. The pieces are associated by an inextensible string wrapped around a pulley. On the off chance that square A moves descending, obstruct will move. s An and s B characterize movement of squares. Every begins from a settled point , positive toward movement of piece.

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DEPENDENT MOTION (proceeded with) s An and s B are characterized from the focal point of the pulley to hinders An and B. In the event that the rope has a settled length , then: s A + l CD + s B = l T l T is add up to string length and l CD is the length of string ignoring circular segment CD on the pulley.

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DEPENDENT MOTION (proceeded with) Velocities can be found by separating the position condition. Since l CD and l T stay consistent, so dl CD/dt = dl T/dt = 0 ds A/dt + ds B/dt = 0 => v B = - v A The negative sign shows that as A moves down (positive s A ), B climbs (negative s B bearing). Increasing speeds can be found by separating the speed expression. Demonstrate: a B = - an A .

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DEPENDENT MOTION EXAMPLE s An and s B are characterized from settled datum lines, measured along the heading of movement of every square. s B is characterized to the focal point of the pulley above square B, since this piece moves with the pulley. The red shaded sections of the rope and h stay consistent long

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DEPENDENT MOTION EXAMPLE (proceeded with) The position directions are connected by 2s B + h + s A = l Where l is the aggregate string length less the lengths of the red fragments . Speeds and increasing speeds can be connected by two progressive time subsidiaries: 2v B = - v An and 2a B = - an A When square B moves descending (+s B ), obstruct A moves to one side (- s A ).

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DEPENDENT MOTION EXAMPLE (proceeded with) The illustration can likewise be worked by characterizing the s B from the base pulley rather than the top pulley. The position, speed, and increasing speed relations get to be distinctly 2(h – s B ) + h + s A = l and 2v B = v A 2a B = an A Prove that the outcomes are the same, regardless of the possibility that the sign traditions are unique in relation to the past definition.

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EXAMPLE PROBLEM Given: In the figure the string at An is pulled down with a speed of 8 m/s. Find: The speed of piece B.

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DATUM s A s C s B EXAMPLE (Solution) : Define the position arranges one for point A (s A ), one for piece B (s B ), and one relating positions on the two ropes (pulley C). Directions are characterized as +ve down and along the course of movement of every protest.

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DATUM s A s C s B EXAMPLE (proceeded) If l 1 =length of the primary rope, less any fragments of steady length and l 2 for the second: Cord 1: 2s A + 2s C = l 1 Cord 2: s B + (s B – s C ) = l 2 Eliminating s C , 2s A + 4s B = l 1 + 2l 2 Velocities are found by separating: ( l 1 and l 2 constants): 2v A + 4v B = 0 => v B = - 0.5v A = - 0.5(8) = - 4 m/s

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GROUP PROBLEM SOLVING Given: In this framework, obstruct An is moving descending with a speed of 4 m/s while obstruct is moving at 2 m/s. Find: The speed of square B.

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GROUP PROBLEM SOLVING ( Solution ) A datum line is drawn through the upper, settled, pulleys. Characterize s A , s B , and s C Differentiate to relate speeds:

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End of 12.9 Let Learning Continue

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