Aug 26, 2014 ******************************** QUIZ SOLUTION ******************************** ********* MY SOLUTIONS ARE MORE THAN JUST SOLUTIONS ********** THEY ARE MINI LECTURES, IF YOU READ THEM YOU WILL LEARN SOME PHYSICS Both cases are completely inelastic collisions. The bullet gets stuck inside the block. That means that heat is produced due to friction of the bullet inside the block. IMPORTANT: There is no law in physics that states that the amount of heat produced is the same in case 1 and case 2. Thus to assume that the sum of potential energy and rotational kinetic energy, when the block reaches its highest point, is the same in both cases is wrong. This wrong reasoning (wrong physics) leads to the WRONG ANSWER H>L. About XX responses went this route and thus got the wrong answer. The ONLY laws that hold are: comparing the situation just before the collision with just after the collision * momentum is conserved * angular momentum is conserved. CASE 1 In Case 1 there is no angular momentum before and thus none after the coll. Thus ONLY momentum is conserved. Speed bullet just before it hits the block = v, its mass is m mass block is M. Speed of the block with the bullet inside after the coll is v Thus mv = (M+m)v and H=[(v)^2]/2g CASE 2 Momentum is conserved, thus mv = (M+m)v. Thus the speed v of the center of mass just after the collision is the same in both cases, thus ************************************** L=H ***************************************** The block (bullet inside) will in both cases reach the exact same height INDEPENDENT of where the bullet hits the block (as long as you shoot the bullet vertically upwards). If the bullet hits the block a distance r from the center of mass (in horizontal direction) then the angular momentum just before the bullet hits is mvr. If the angular velocity of the rotating block (with bullet inside) is w after the coll and its moment of inertia is I, then mvr=Iw. Thus w can be calculated if you could calculate I. Notice if r=0, then w is 0. I is determined by both M,m and r. But since m
Posted on: Tue, 26 Aug 2014 08:29:45 +0000
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