The collision is 1 dimensional a If the collision is perfectly elastic what is

# The collision is 1 dimensional a if the collision is

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sitting at rest. The collision is 1-dimensional. (a) If the collision is perfectly elastic, what is the final speed of the puck that was initially at rest? (b) If the collision is perfectly inelastic, what is the final speed of the two pucks after the collision? (c) If the collision is perfectly inelastic, what fraction of the total energy was lost during the collision? (d) If one-fourth of the initial kinetic energy was lost during the collision, what is the final speed of the puck that was initially at rest? 8-m7 A bullet of mass m strikes a block of mass M which is hanging by a string of length L from the ceiling. It is observed that, after the sticky collision, the maximum angle that the string makes with the vertical is θ . This setup is called a ballistic pendulum, and it can be used to measure the speed of the bullet. (a) What vertical height does the block reach? (b) What was the speed of the block just after the collision? (c) What was the speed of the bullet just before it struck the block? 8-m8 A car of mass M and a truck of mass 2 M collide head-on with equal speeds v , and the collision is perfectly inelastic. (a) What is the magnitude of the change in mo- mentum of the car? (b) What is the magnitude of the change in mo- mentum of the truck? (c) What is the final speed of the two vehicles? (d) What fraction of the initial kinetic energy was lost as a result of the collision? 8-m9 A 5 . 00 kg firework is launched straight up into the air. When it reaches its maximum height of H = 140 m, it explodes into two frag- ments that fly off in horizontal directions. The explosion is very quick, and only lasts 15 ms. One of the two fragments (fragment A, with mass M A = 2 . 00 kg) lands 290 meters away from the initial launch position. (a) Find the speed of fragment A just after the explosion. (b) By using conservation of momentum and your answer from part a, find the speed of the other fragment (call this fragment B) just after the explosion. (c) Calculate the magnitude of the momentum transferred to fragment A due to the explosion. (d) Calculate the magnitude of the momentum transferred to fragment A due to the force of
PROBLEMS 101 gravity. (e) How far away from the initial launch position does fragment B land? Hint: the center of mass of the two fragments lands at the location where the firework was initially launched. 8-m10 An object of mass m , moving at veloc- ity u , undergoes a one-dimensional elastic colli- sion with a mass km that is initially at rest. Let the positive direction be in the direction of the initial motion, so that u > 0. (a) What is the final velocity of mass m ? (b) What is the final velocity of the mass km ? ? 8-m11 Two blocks, each of mass M , are con- nected by a thread and moving with speed v 0 .

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