document.write( "Question 1057843: A block of mass m1 = 3.00 kg slides along a frictionless table with a speed of 13.0 m/s. Directly in front of it, and moving in the same direction, is a block of mass m2 = 4.00 kg moving at 1.00 m/s. A massless spring with a spring constant k = 1620 N/m is attached to the backside of m2. When the blocks collide, what is the maximum compression (in meters) of the spring? \n" ); document.write( "

Algebra.Com's Answer #672845 by ikleyn(52866) $\"\"$ $\"About$

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\n" ); document.write( "A block of mass m1 = 3.00 kg slides along a frictionless table with a speed of 13.0 m/s. Directly in front of it,
\n" ); document.write( "and moving in the same direction, is a block of mass m2 = 4.00 kg moving at 1.00 m/s. A massless spring with a spring constant
\n" ); document.write( "k = 1620 N/m is attached to the backside of m2. When the blocks collide, what is the maximum compression (in meters) of the spring?
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\n" ); document.write( "\n" ); document.write( "When solving the Physics problems like this one, the key is clearly to understand what happens with the system and what Physics law/laws to apply.\r
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\n" ); document.write( "\n" ); document.write( "What is the time moment when the maximum compression of the spring occurs?
\n" ); document.write( "How do the two bodies move at this time moment?\r
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\n" ); document.write( "\n" ); document.write( "It is very simple.
\n" ); document.write( " At this time moment the two bodies move with equal speeds.\r
\n" ); document.write( "\n" ); document.write( "It is the key.\r
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document.write( "Before this time moment and after it the bodies move with different velocities.\r\n" );
document.write( "But in THIS particular time moment the two bodies have equal velocities. Their relative speed is ZERO at this time moment.\r\n" );
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document.write( "So, in this time moment the collision is similar \"perfectly INELASTIC collision\".\r\n" );
document.write( "Before this time moment and after it, the behavior of the bodies is different, but \r\n" );
document.write( "exactly at this moment it is like \"perfectly INELASTIC collision\":\r\n" );
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document.write( "    In this particular time moment the two mass moves \"together\" as one whole mass.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Very good. Then you can apply the \"momentum conservation law\".\r
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document.write( "It says that the momentum before the collision is equal to momentum after collision.\r\n" );
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document.write( "The momentum before the collision was 3*13 + 4*1  (kg*m/s).\r\n" );
document.write( "The momentum at the \"perfectly INELASTIC collision\" is (3+4)*V,\r\n" );
document.write( "where (3+4) kg is the sum of masses and \"V\" is their unknown common speed.\r\n" );
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document.write( "So, the \"momentum conservation law\" is this equation \r\n" );
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document.write( "3*13 + 4*1 = (3+4)*V,\r\n" );
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document.write( "which allows you to find the common speed of the two bodies\r\n" );
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document.write( "V =  =  m/s\r\n" );
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document.write( "at the particular moment of maximal spring compression.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Now we are on the finish line.\r
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document.write( "The initial kinetic energy of the two bodies (before they contacted via the spring) was \r\n" );
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document.write( " =  + .\r\n" );
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document.write( "The kinetic energy of the \"clued\" mass  at the \"perfectly INELASTIC collision\" is\r\n" );
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document.write( " = .\r\n" );
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document.write( "The difference  -  is the potential energy of the compressed spring               ( !! Yes, the \"Energy conservation law\" !!! ).\r\n" );
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document.write( "where k = 1620 N/m is the spring constant and \"x\" is the maximum compression of the spring.\r\n" );
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document.write( "So, your equation to find \"x\" is \r\n" );
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document.write( " +  -  = .\r\n" );
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document.write( "Substitute the given data and (just found value of) V and find \"x\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved !\r
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\n" ); document.write( "Would you mind to answer couple of my questions.\r
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\n" ); document.write( "\n" ); document.write( "Are you at high school or college?\r
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\n" ); document.write( "\n" ); document.write( "Which textbook do you use?\r
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