Algebra.Com's Answer #812884 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "The coefficient of static friction between a 20-kg block and a horizontal surface is 0.25
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document.write( "and the coefficient of kinetic friction is 0.15. A cord is attached to the block,
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document.write( "the cord making an angle of 10 degrees with the horizontal.
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document.write( "(a) What tension in the cord will just start the block?
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document.write( "(b) What is the tension in the cord when the block moves with uniform velocity?
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document.write( "The plot to the problem is shown in the Figure below.\r\n" );
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document.write( " Figure. The body on the horizontal floor\r\n" );
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document.write( "Decompose the given force F into horizontal Fx and vertical Fy components. \r\n" );
document.write( "Horizontal component Fx is equal to F*cos(10°); vertical component Fy is F*sin(10°).\r\n" );
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document.write( "The reaction force N acts from the floor vertically up to the box. Together with \r\n" );
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document.write( "vertical component Fy it balances the weight: W = Fy + N. So, N = W - Fy = mg - Fy. \r\n" );
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document.write( "The condition of start moving is that the horizontal force component Fx is equal \r\n" );
document.write( "to the reaction force multiplied by the static friction coefficient\r\n" );
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document.write( " Fx =  , or F*cos(10°) = 0.25*(mg - F*sin(10°)).\r\n" );
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document.write( "From the last equation, F*cos(10°) + 0.25*F*sin(10°) = 0.25*mg, which gives for the magnitude of F\r\n" );
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document.write( " F =  =  = 48.614 N. \r\n" );
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document.write( "So, the tension of the cord, the force F, to start moving is 48.614 newtons.\r\n" );
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document.write( "It is the answer to question (a).\r\n" );
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document.write( "The condition of moving with the constant velocity is that the horizontal force component Fx is equal \r\n" );
document.write( "to the reaction force multiplied by the kinetic friction coefficient\r\n" );
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document.write( " Fx =  , or F*cos(10°) = 0.15*(mg - F*sin(10°)).\r\n" );
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document.write( "From the last equation, F*cos(10°) + 0.15*F*sin(10°) = 0.15*mg, which gives for the magnitude of F\r\n" );
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document.write( " F =  =  = 29.67 N. \r\n" );
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document.write( "So, the tension of the cord, the force F, to move the block uniformly is 29.67 newtons.\r\n" );
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document.write( "It is the answer to question (b).\r\n" );
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document.write( "Solved.\r
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document.write( "In this solution, I used the approximate value of 10 m/s^2 for the gravity acceleration
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document.write( "instead of the more precise value of 9.81 m/s^2.\r
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