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Unformatted text preview: al-ameri (aoa434) – Hwk09 – Stokes – (19102)1This print-out should have 16 questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.This is Online Homework No9. It is duebefore 6.00 am on Tuesday 7 April, Abu DhabiTime (Monday 11.00 pm in Texas)001(part 1 of 3) 10.0 pointsTwo small spheres of massm1andm2aresuspended from the ceiling at the same pointby massless strings of equal lengthℓ. Thelighter sphere is pulled aside through an angleofθifrom the vertical and let go.The acceleration of gravity is 9.8 m/s2.gBeforem1ℓθim2gAfterθfAt what speed will the lighter massm1hitthe heavier massm2?1.v1i=g ℓcosθi2.v1i=g ℓ(1-cosθi)3.v1i= 2g ℓ(1-cosθi)4.v1i= 2g ℓcosθi5.v1i=radicalbigg ℓ(1-cosθi)6.v1i=radicalbig2g ℓ(1-cosθi)correct7.v1i=radicalbig2g ℓcosθi8.v1i=radicalbigg ℓcosθiExplanation:The velocity just before the collisionvicanbe determined by energy conservation. Whenparticle 1 is at its initial condition, it is at restand displaced by an angleθifrom the vertical.The total energy is all potential and is givenbyUi=m1g ℓ(1-cosθi)whereℓ(1-cosθi) is the distance above thelowest point. Just before the collision, the en-ergy of sphere 1 is all kinetic energy,12m1v21i.Equating the two energies gives12m1v21i=m1g ℓ(1-cosθi).Solving forv1igivesv1i=radicalbig2g ℓ(1-cosθi).002(part 2 of 3) 10.0 pointsAfter lighter sphere is let go and collides withthe heavier sphere at the bottom of its swing,two spheres immediately bind together.What is conserved in this collision process?LetE= mechanical energy;P= momentum.1.NeitherEnorP2.Pcorrect3.BothEandP4.EExplanation:This is a perfectly inelastic collision. Thespeed of the two spheres after collision is de-termined by momentum conservation.003(part 3 of 3) 10.0 pointsAfter the lighter sphere is let go and collideswith the heavier sphere at the bottom of itsal-ameri (aoa434) – Hwk09 – Stokes – (19102)2swing, the two spheres immediately bind to-gether.What is the speedVfof the combined sys-tem just after the collision?1.Vf=parenleftbiggm1+m2m1parenrightbiggv1i2.Vf=parenleftbigg2m1m1+m2parenrightbiggv1i3.Vf=parenleftbiggm2m1+m2parenrightbiggv1i4.Vf=parenleftbigg2m2m1+m2parenrightbiggv1i5.Vf=parenleftbiggm1m1+m2parenrightbiggv1icorrect6.Vf=parenleftbiggm1+m2m2parenrightbiggv1i7.Vf=parenleftbiggm1+m22m2parenrightbiggv1i8.Vf=parenleftbiggm1+m22m1parenrightbiggv1iExplanation:This is a completely inelastic collision. Thespeed of the two spheres after collision is de-termined by momentum conservationm1v1i= (m1+m2)Vf(1)wherem1is the mass andv1iis the initialvelocity of sphere 1 just before the collision,m2is the mass of sphere 2, andVfis thevelocity of the combined spheres just afterthe collision.Note:v2i= 0....
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