Transcription of Math 1302, Week 7: Variable mass systems - UCL
{{id}} {{{paragraph}}}
Example: bankruptcy
Math 1302, Week 7: Variable mass systems - UCL
math 1302, week 7: Variable mass systemsExample: Coupling of two moving carriagesConsider two train carriages of massm1,m2moving on the same track with speedsU1andU2,whereU1> U2(see figure 1). When they catch each other up they couple together to make asingle coupled pair of carriages that moves with speedV. : We have conservation of momentum:m1m2m1+m2U1U2 VFigure 1: Two carriages coupling together into a singlemassmomentum before = momentum afterm1U1+m2U2= (m1+m2)VSo thatV=m1U1+m2U2m1+ the coupled carriages move with the speed of the centre of mass of the uncoupled about energy changes? Before colliding the total kinetic energy isTb=12m1U21+12m2U22,and after colliding and joining the kinetic energy isTa=12(m1+m2)(m1U1+m2U2m1+m2)21 Hence the change in kinetic energy T=Ta Tbis given by T=12(m1+m2)(m1U1+m2U2m1+m2)2 12m1U21 12m2U22=12m21U21+m22U22+ 2m1m2U1U2m1+m2 12m1U21 12m2U22=12(m1+m2)[m21U21+m22U22+ 2m1m2U1U2) (m21+m1m2)U21 (m1m2+m22)U22]=12(m1+m2)(2m1m2U1U2) (m1m2)U21 (m1m2)U22)= m1m2(U1 U2)22(m1+m2)< energy is lost in the collision.
Math 1302, Week 7: Variable mass systems Example: Coupling of two moving carriages Consider two train carriages of mass m 1, m 2 moving on the same track with speeds U 1 and U 2,
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document:
Related search queries
Conservation, Handbook, Mass, A FRAMEWORK FOR CONSERVATION OF METALS, Nutrient Mass Balance Study for, WATER CONSERVATION PROGRAM - NOTICE TO, APPENDIX A: NEIGHBORHOOD, Appendix a: neighborhood conservation districts, Equations describing the physical properties, Great Society Upon The Lives, Great Society Upon The Lives of Families and Young Children, Science Georgia Standards of Excellence