document.write( "Question 1130038: A block of mass 98.0 g is sitting on a frictionless horizontal surface, and attached to a spring with spring constant 11.6 N/m. The block is then pulled a certain distance from its equilibrium position and released such that it undergoes simple harmonic motion and attains a maximum acceleration of 1.8 m/s2. What is the maximum speed of the block as it oscillates in this way? Express your answer in m/s. \n" ); document.write( "

Algebra.Com's Answer #746694 by ikleyn(52775) $\"\"$ $\"About$

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document.write( "Since the maximum acceleration is 1.8 m/s^2 (given), then the maximal force is\r\n" );
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document.write( "    F = ma (the Newton second law) = 0.098*1.8 = 0.1764 Newtons (N).\r\n" );
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document.write( "It is when the block is in his farthest displacement from the equilibrium position.\r\n" );
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document.write( "Since  F = k*L  (the spring law),  we can determine this maximum displacement\r\n" );
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document.write( "    L =  =  = 0.0152 meters (= 1.52 centimeters)\r\n" );
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document.write( "The potential energy of the block in this position is\r\n" );
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document.write( "    P = .\r\n" );
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document.write( "Now apply the Mechanical Energy conservation law.\r\n" );
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document.write( "The kinetic energy (when the body has its maximum speed - at the equilibrium position) is\r\n" );
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document.write( "    E = .\r\n" );
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document.write( "The conservation of energy law gives you  \r\n" );
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document.write( "    E = P,  which implies   = ,   or\r\n" );
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document.write( "    V = .\r\n" );
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document.write( "Substitute the known data to determine V:\r\n" );
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document.write( "    V =  = 0.165 m/s    ANSWER\r\n" );
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