Chapter 3 Kinetics of Particles

System & Vision Lab.

Chapter 3Kinetics of Particles

신동원금오공과대학교 기계시스템공학과

System & Vision Lab (SVL)

Introduction

v Kinetics: the study of the relations between unbalanced forces and the resulting changes in motion

v Three general approaches to the solution of kinetics problems:

§ (A) Direct application of Newton’s second law (force-mass-acceleration method)

§ (B) Use of work and energy principles

§ (C) Solution by impulse and momentum methods

System & Vision Lab.svl.kumoh.ac.kr

Newton’s second law

v Considering an ideal experiment§ First conclusion

• The ratios of applied force to corresponding acceleration all equal the same number


• Constant C: inertia of the particle which is its resistance to rate of change of velocity, C=km

• Mass is a quantitative measure of this inertia

§ Second conclusion

• The acceleration is always in the direction of the applied force

Newton’s second law

v The results of the ideal experiment are obtained from measurements made relative to the fixed primary inertial system

v They are equally valid for measurements made with respect to the inertial systems (any nonrotating reference system which translates with a constant velocity with respect to the primary system)


Equation of motion andsolution of problem

v Equation of motion (shortly, EOM)§ When a particle of mass m is subjected to the action of

concurrent forces, F1, F2, F3, … whose vector sum is ΣF, Newton’s second law becomes,

aF m=å

úúúúúúú

û

ù

êêêêêêê

ë

é

+=

-=

=

=

úúúúúúú

û

ù

êêêêêêê

ë

é

==

===

=

=

úúúúúúú

û

ù

êêêêêêê

ë

é

=

=

=

=

åå

åå

åå

qq

q

q

q

qq

&&&&

&&&

&&

&&

&&

&&

rra

rra

maF

maF

βρvva

βv/ρvβρa

maF

maF

ya

xa

maF

maF

r

rr

t

n

tt

nn

y

x

yy

xx

2

coords-r

,

coordst -ncoordsy -x

222



v Two types of dynamics problems (when applying equation of motion)

§ Type 1: Acceleration is specified or determined from kinematic conditions

• aà F = maà obtain force F

§ Type 2: Forces acting on the particles are specified

• Fà F = maà obtain acceleration aà integration à và integration à r



v Constrained and unconstrained motion(Two physically distinct types of motion)§ Unconstrained: the particle is free of mechanical guides and

follows a path determined by its initial motion and by the forces applied to it from external sources

• Airplane or rocket in flight & electron moving in a charged field à 3 DOF

§ Constrained: the path of particle is partially or totally determined by restraining guides

• Partially constrained: ice hockey puck (constrained to horizontal plane of ice) à 2 DOF

• Fully constrained: a train moving along its track à 1 DOF



v Free-body diagram (shortly, FBD)§ It is absolutely necessary to account correctly for all forces acting

on the particles

§ The only reliable way to account for every force is to isolate the particle under consideration from all contacting and influencing bodies and replace the bodies removed by the forces they exert on the particle isolated

§ Free-body diagram is the means by which every force, known and unknown, which acts on the particle is represented and thus accounted for

v Notes for establishing equation of motion§ Make coordinate axes and their positive(+) directions very clear

§ Summation of all forces must be consistent with the choice of these positive direction


자유물체도의 사례


자유물체도


자유물체도의 사례(평면에 놓은 물체)


Rectilinear motion

v Motion of bodies which can be treated as particlesv We are interested only in the motion of the mass center of

the body, in which case, the forces may be treated as concurrent through the mass center

v If we choose the x-direction as the direction of the rectilinear motion,

åå

=

=

0y

xx

F

maF


v If we choose the y-direction as the direction of the rectilinear motion,

åå

=

=

yy

x

maF

F 0

Sample problem 3.1


Problem 3-1


Problem 3-2


v 움직이지 않는다고 가정하고(a=0) 운동방정식을 풀어 마찰력 F를 구해서,

§ F<최대정지마찰력이면,

§ 즉, 접촉면이 a=0이기위한충분한마찰력을제공한다는의미

§ 결국, 움직이지않는다는가정이맞음

v F<최대정지마찰력이 나오면, 위의 가정이 틀린것이므로

§ 박스는움직인다고판단

§ 즉, a는더이상 0이아님.

§ a를미지수로놓고운동방정식을다시풀어야함


Problem 3-4


Problem 3-10


Chapter 3 Kinetics of Particles

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