equilibrium of a particle一个粒子的平衡

《equilibrium of a particle一个粒子的平衡》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、EquilibriumofaparticleIfalltheforcesactingonaparticlecanceleachotherout,sothatnothinghappensatall,theforcesaresaidtobeinequilibrium.©Thealgebraicsumofthehorizontalcomponentsiszero.©Thealgebraicsumoftheverticalcomponentsiszero.Example1FindthevalueofPandQi

2、fthefollowingsystemofforcesisinequilibrium.8NQN2NPN30°40°SolutionComponentsdiagram8cos30Qcos408sin302NQsin40PHorizontalcomponent:®:8cos30+Qcos40-P=0[1]Verticalcomponent::8sin30-2-Qsin40=0[2]ÞQsin40=8sin30-2ÞQ=3.1114…SubQinto[1]:8cos30+3.114cos40-P=0ÞP=8c

3、os30+3.114cos40=9.31ForcePis9.31NandforceQis3.11NMathematicsmadesimpleM1Equilibrium-10-Equilibriumofaparticle*Example2FindthevalueofPandQifthefollowingsystemofforcesisinequilibrium.8NQNPN30°40°30°SolutionComponentsdiagram8cos30Qcos408sin30Qsin40Pcos30Psi

4、n30Horizontalcomponent:®:8cos30+Qcos40-Pcos30=0Þ0.866025P=6.928203+0.766044QÞP=8+0.884552Q[1]Verticalcomponent::8sin30+Psin30-Qsin40=0ÞQsin40=8sin30+Psin30Þ0.642788Q=4+0.5P[2]SubPinto[2]:0.642788Q=4+0.5(8+0.884552Q)Þ0.642788Q=4+2+0.442276QÞ0.200512Q=6ÞQ=

5、29.9234SubQinto[1]:P=8+0.884552´29.9234=34.5ForcePis34.5NandforceQis29.9NMathematicsmadesimpleM1Equilibrium-10-EquilibriumofaparticleExampleThefollowingdiagramshowsasystemofforcesactingonaparticleinaplane.Athirdforceisaddedsothattheparticlerestsinequilib

6、rium.Findthemagnitudeofthisforceandtheanglethatmakewiththehorizontal.30°5N6NSolutionComponentsdiagram5cos30Fcosq5sin30Fsinq6Horizontalcomponent:®:5cos30+Fcosq-6=0ÞFcosq=6-5cos30[1]Verticalcomponent::5sin30-Fsinq=0ÞFsinq=5sin30[2]Divide[2]by[1]:Þq=56.2591

7、Subqinto[2]:Fsin56.2591=2.5ÞF=3.00Addedforceis3.00N,actingatanangleof56.3°belowthehorizontal.MathematicsmadesimpleM1Equilibrium-10-EquilibriumofaparticleExercise1.Giventhatthefollowingsystemofforcesisinequilibrium,findtheunknownforcePandQ.4N6NPN20°50°38°

8、Q2.Aparticleisinequilibriumundertheactionofthreecoplanarforcesshowninthediagram.(i)Showthatq=60°(ii)FindthevalueofX.q2XNXN15N3.q20N12NPNThreeforces,ofmagnitude20N,12NandPN,actatapointinthedirectionshowninthediagram.Theforc