document.write( "Question 1201559: hello there. can you please help me w/ this vectors hw question? it's from my \"vectors as forces\" lesson. \r
\n" ); document.write( "\n" ); document.write( "A mass of 20 kg is suspended from a ceiling by two lengths of rope that make
\n" ); document.write( "angles of 30° and 45° with the ceiling. Determine the tension in each of the ropes.\r
\n" ); document.write( "\n" ); document.write( "i tried to do it below...
\n" ); document.write( "30 degrees = F1
\n" ); document.write( "45 degrees = F2
\n" ); document.write( "20 x 9.8m/s^2 = 196 so 20 kg is 196N\r
\n" ); document.write( "\n" ); document.write( "break triangle in half;\r
\n" ); document.write( "\n" ); document.write( "triangle: 120 degrrees in middle, 45 on f2 side, 30 on f1 side
\n" ); document.write( "f1/sin45 = f2/sin30 = 196N/sin120\r
\n" ); document.write( "\n" ); document.write( "i'm not sure what i'm doing from here\r
\n" ); document.write( "\n" ); document.write( "thank you.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #836003 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Let T1 be the tension of the rope 30°;  T2 be the tension of the rope 45°.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "T1 and T2 are the magnitudes of the forces; their dimensions are newtons.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Force F1 has horizontal component T1*cos(30°) = .\r\n" );
document.write( "\r\n" );
document.write( "Force F2 has horizontal component T2*cos(45°) =  in opposite direction.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Equilibrium condition in horizontal direction gives you this equation\r\n" );
document.write( "\r\n" );
document.write( "    } = ,   or\r\n" );
document.write( "\r\n" );
document.write( "     = .        (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Force F1 has vertical component T1*sin(30°) = .\r\n" );
document.write( "\r\n" );
document.write( "Force F2 has vertical component T2*sin(45°) = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Equilibrium condition in vertical direction gives you this equation\r\n" );
document.write( "\r\n" );
document.write( "     + } = 20*g,   or\r\n" );
document.write( "\r\n" );
document.write( "     +  = 40g.     (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus you have a system of two equations (1) and (2),  and now your task is to solve it.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For it, replace in equation (2) the term  }  by , based on equation (1).\r\n" );
document.write( "\r\n" );
document.write( "You will get then\r\n" );
document.write( "\r\n" );
document.write( "    T1 +  = 40g,   or\r\n" );
document.write( "\r\n" );
document.write( "     = 40g,\r\n" );
document.write( "\r\n" );
document.write( "    T1 = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From equation (1), you get then\r\n" );
document.write( "\r\n" );
document.write( "    T2 =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "At this point, the problem is just solved.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If you want to get the numerical values for magnitudes / (tensions)  T1  and  T2,  use your calculator.\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" );