document.write( "Question 1182826: A 2 kg block is pulled with uniform speed up a plane which makes 30 degrees with the horizontal by a force of 15 N which is parallel to the plane. Find the coefficient of kinetic friction between the block and the plane.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #812920 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A 2 kg block is pulled with uniform speed up a plane which makes 30 degrees with the horizontal by a force of 15 N
\n" ); document.write( "which is parallel to the plane. Find the coefficient of kinetic friction between the block and the plane.
\n" ); document.write( "~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Since the block is pulled uniformly up the plane, it means that the force of 15 N parallel to the plane\r\n" );
document.write( "is equal to the sum of the rolling force and the friction force.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The rolling force  R  parallel to the inclined plane is  R = m*g*sin(30°) = 2*10*(1/2) = 10 newtons.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The normal reaction force N, which is PERPENDICULAR to the inclined plane, has the value of  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    N = m*g*cos(30°) =  =  = 17.32 newtons.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The friction force    is equal to   = k*N = 17.32*k,  where \"k\" is the kinematic friction coefficient.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we have this equation to find out the kinetic friction coefficient\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    15 = R +  = 10 + 17.32k.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the equation, we find\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    k =  = 0.287   (the dimensionless value).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  Under given condition, the kinetic friction coefficient value is  0.287.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );