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hwk10 - Solution for Long-answer Homework 10 Reference...

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Solution for Long-answer Homework 10 Reference Frames problems Solution to Long-answer Homework Problem 10.1(Indy-Comprehensive Inelastic Colli- sion) Problem: Indiana Jones is in a 1000kg train car coasting at 15 m s . The bad guys chasing him are in a 1500kg caboose coasting at 25 m s so it rear-ends Indy’s train car. The caboose becomes attached to the train car and the two roll down the track together. (a)What is the final velocity of the system? (b)What is the minimum amount of kinetic energy required to conserve the momentum of the system? (c)What is the velocity of the zero momentum frame, v cm , for this system? (d)Using K cm = 1 2 M tot v 2 cm , find the center of mass kinetic energy of the system. (e)How much kinetic energy is lost to other forms of energy in this collision? (f)Where does this lost kinetic energy go? (g)Find the kinetic energy for the system in the zero momentum frame before the collision. (h)What are the upper and lower limits on how much kinetic energy can be converted to other forms for this system for inelastic collisions? (i)Please make sure you included your name and lab section .... Solution to Part (a) Conserve momentum, where the mass of Indiana and the train car is m indy and the mass of the bad guys in the caboose is m cab : m indy v indy,i + m cab v cab,i = m indy v indy,f + m cab v cab,f Since they stick together, v indy,f = v cab,f = m indy v indy,i + m cab v cab,i m indy + m cab v indy,f = (1000kg) ( 15 m s ) + (1500kg) ( 25 m s ) (1000kg) + (1500kg) = 21 m s Grading Key: Part (a) 7 Points 2 point(s) : conserve momentum 1 point(s) : all same sign 1 point(s) : v f same for both 2 point(s) : correct substitutions for each of the initial momenta. 1 point(s) : correct answer with units Solution to Part (b) This would be the least energy required for a totally inelastic collision, which would be K = 1 2 M tot v 2 f K = 1 2 (2500kg) parenleftBig 21 m s parenrightBig 2 = 5 . 51 × 10 5 J 1
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Grading Key: Part (b) 5 Points 3 point(s) : correctly identifies as energy associated with center of mass, or totally inelastic collision, or that part of the K equation. 1 point(s) : v from (a) if do it based on reasoning about com motion 1 point(s) : correct answer with units (consistent with (a)). Solution to Part (c) As always with an inelastic collision, the velocity of the center of mass is the velocity of the combination after the collision, so the zero momentum frame has that velocity, v cm = 21 m s Grading Key: Part (c) 2 Points 2 point(s) : same as (a). They could calculate it as well. If the calculate it and get it wrong, full credit if they say they know they made a mistake, since it should have been the same as (a). Solution to Part (d) Since the zero momentum frame has the same velocity as the Indy/Bad Guy combination after the collision ( v cm = v f ), the center of mass kinetic energy is the same as in part (b), K = 5 . 51 × 10 5 J Grading Key: Part (d) 4 Points 1 point(s) : it is the same as (b) or they say it should have been the same as (b).
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