Draw two diagrams for the situation where a moving train (with initial speed Vo)

Question

Draw two diagrams for the situation where a moving train (with initial speed Vo) collides elastically with a target train that is not initially moving, and the trains use their springy bumpers to bounce off each other without damage. One diagram should now the instant just before the collision and the other the instant just after the collision. Assume the trains have different masses (mmoving and mtarget) Make sure you identify your lated system. Show that the final velocity of each train will be: Vtarget = 2Vo/(1 + mtarget/mmoving) Vmoving = (mmoving - mtarget)/(mmoving + mtarget)Vo conservation of momentum and the relation between the relative velocities before llision that arises due to conservation of energy in section 8.3. mass = 3,000 kg) successfully couples with a Train B (mass = 5,000 kg). Train A at 2.5 m/s before the collision, and Train B is initially at rest. What is the final the coupled trains? What is the initial kinetic energy? What is the much kinetic energy is lost?

Explanation / Answer

Initial momentum of moving train= m1v0 Initial momentum of target train = 0 Total momentum = m1v0. --------------------------------------… Final momentum of moving train = m1v1. Final momentum of target train = m2v2 v2 is v target, v1 is v moving. Total momentum = m1v1 + m2v2. --------------------------------------… • Total momentum is conserved. m1v0. = m1v1 + m2v2. • m1 [v0 -v1] = m2v2 • ------------------------------------… Initial kinetic energy before collision = final kinetic energy after collision • ½ m1v0^2. = 1/2m1v1^2 + ½m2v2^2 --------------------------------------… • To obtain expressions for the velocities after the collision, rewrite the above as: • m1 [v0 – v1] [v0 +v1] = = m2v2^2 .--------------------------1 • • using a^2 -b^2 = ( a-b)(a+b) • m1[v0 -v1] = m2v2.--------------------------2 Dividing these relationships gives [v0 +v1] = v2 Using 2 we can find v2 & v1. v2 = 2m1v0 / [m2+m1] v1 = [m1-m2] v2 / [m2+m1]

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