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19 An 800-g bullet is fired horizontally into a 900-kg block of wood on an air table and is embedded in it After the collision, the block and bullet slide along the frictionless surface together with a speed of 100 cm/s What was the initial speed of the bullet 20 A 073-kg magnetic target is suspended on a string A 0025-kg magnetic dart, shot horizontally, strikes the target head-on The dart and the target together, acting like a pendulum, swing 120 cm above the initial level before instantaneously coming to rest a Sketch the situation and choose a system b Decide what is conserved in each part and explain your decision c What was the initial velocity of the dart 21 A 910-kg hockey player is skating on ice at 550 m/s Another hockey player of equal mass, moving at 81 m/s in the same direction, hits him from behind They slide off together a What are the total energy and momentum in the system before the collision b What is the velocity of the two hockey players after the collision c How much energy was lost in the collision



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In collisions, you can see how momentum and energy are really very different Momentum is almost always conserved in a collision Energy is conserved only in elastic collisions Momentum is what makes objects stop A 100-kg object moving at 500 m/s will stop a 200-kg object moving at 250 m/s if they have a head-on collision However, in this case, the smaller object has much more kinetic energy The kinetic energy of the smaller object is KE 1 (100 kg)(50 m/s)2 125 J The kinetic energy of 2 1 the larger object is KE (200 kg)(250 m/s)2 625 J Based on the 2 work-energy theorem, you can conclude that it takes more work to make the 100-kg object move at 500 m/s than it does to move the 200-kg object at 250 m/s It sometimes is said that in automobile collisions, the momentum stops the cars but it is the energy in the collision that causes the damage It also is possible to have a collision in which nothing collides If two lab carts sit motionless on a table, connected by a compressed spring, their total momentum is zero If the spring is released, the carts will be forced to move away from each other The potential energy of the spring will be transformed into the kinetic energy of the carts The carts will still move away from each other so that their total momentum is zero





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A bullet of mass m, moving at speed v1, goes through a motionless wooden block and exits with speed v2 After the collision, the block, which v 1 has mass mB, is moving 1 What is the final speed, vB, of the block 2 How much energy was lost to the bullet 3 How much energy was lost to friction inside the block

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It is useful to remember two simple examples of collisions One is the elastic collision between two objects of equal mass, such as when a cue ball with velocity, v, hits a motionless billiard ball head-on In this case, after the collision, the cue ball is motionless and the other ball rolls off at velocity, v It is easy to prove that both momentum and energy are conserved in this collision The other simple example is to consider a skater of mass m, with velocity v, running into another skater of equal mass who happens to be standing motionless on the ice If they hold on to each other after the collision, they will slide off at a velocity of 1 v because of the conservation 2 of momentum The final kinetic energy of the pair would be equal to KE 1 1 1 (2m)( 2 v)2 4 mv2, which is half the initial kinetic energy This is 2 because the collision was inelastic You have investigated examples in which the conservation of energy, and sometimes the conservation of momentum, can be used to calculate the motions of a system of objects These systems would be too complicated to comprehend using only Newton s second law of motion The understanding of the forms of energy and how energy flows from one form to another is one of the most useful concepts in science The term energy conservation appears in everything from scientific papers to electric appliance commercials Scientists use the concept of energy to explore topics much more complicated than colliding billiard balls

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