Find the focal length of a meniscus lens with \(R_{1}=20 \mathrm{~cm} \text { and } R_{2}=15 \mathrm{~cm}\). Assume that the index of refraction of the lens is 1.5.

Text Transcription:

R_1=20 cm and R_2=15 cm

Ch.9:CenterofMassandMomentum A. ChapterGoals • Studyofwhatiscenterofmass • Studyofwhatislinearmomentumandwhenitconserves • StudyofwhatisImpulseandwhatisimpulse-momentum theorem • Studyofwhatiscollisionandwhatareelas▯c,inelas▯c, andperfectinelas▯ccollisions • Studyofwhatthemechanismforrocketpropulsion Ch.9:CenterofMassandMomentum B.CenterofMass(COM) • Thecenterofmassofasystemofpar▯clesisthepointthat movesasthough(1)allofthesystem’smasswere concentratedthereand(2)allexternalforceswereapplied there. • Figureshowsthemo▯on ofabaseballbatandits centerofmass(blackdot). Ch.9:CenterofMassandMomentum • COMforaSystemofPar▯cles Ch.9:CenterofMassandMomentum • COMforaSystemofPar▯cles mx1 1 x2 2..+m xn n 1 n xcom = ∑ mxi i m1+m 2...+m n M i=1 n n 1 1 ycom ∑ mi iz com= ∑ mi i M i=1 M i=1 whereM=m +m +...+m isthetotalm ass 1 2 n n Itsvectorformis: r = 1 mr com M ∑ i i i=1 Ch.9:CenterofMassandMomentum • Example:Findthecenterofmassofasystemwiththree par▯cles mx1 1 x 2 2x 3 3 xcom= m1+m +2 3 y m1= 2 kg 2⋅0+3⋅3+4⋅0 m =3