document.write( "Question 1194515: 1a). A small block of mass 2kg is suspended by two strings of lengths 0.6m and 0.8m
\n" ); document.write( "from two points 1m apart on a horizontal beam. Find the tension in each string.
\n" ); document.write( "1b). A vehicle of mass 6 x 10³ kg moving with a velocity of 43kmh-¹ collides with a
\n" ); document.write( "stationary vehicle of mass 185 x 10³ kg and they stick together and move in the same
\n" ); document.write( "direction. They then came to rest after moving through a distance of 3m. Calculate the
\n" ); document.write( "magnitude of retardation. \n" ); document.write( "

Algebra.Com's Answer #826757 by ikleyn(52780) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "1a). A small block of mass 2kg is suspended by two strings of lengths 0.6m and 0.8m
\n" ); document.write( "from two points 1m apart on a horizontal beam. Find the tension in each string.
\n" ); document.write( "1b). A vehicle of mass 6 x 10³ kg moving with a velocity of 43kmh-¹ collides with a
\n" ); document.write( "stationary vehicle of mass 185 x 10³ kg and they stick together and move in the same
\n" ); document.write( "direction. They then came to rest after moving through a distance of 3m. Calculate the
\n" ); document.write( "magnitude of retardation.
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\n" ); document.write( "\n" ); document.write( " Problem 1a.\r
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document.write( "Let A and B be the points on the horizontal beam where the two strings are attached.\r\n" );
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document.write( "Let C be the point where the mass is attached to the strings.\r\n" );
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document.write( "Notice that the triangle ABC is the right-angled triangle: its sides |AC| = 0.6 m\r\n" );
document.write( "and |BC| = 0.8 m are the legs and its side |AB| = 1 m is the hypotenuse, since\r\n" );
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document.write( "     =  =  = 1 meter.\r\n" );
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document.write( "Let vector P along CA be the tension of CA and let vector Q along CB be the tention of CB.\r\n" );
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document.write( "Let p and q be the magnitudes of these vectors, respectively.\r\n" );
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document.write( "Since the mass is in equilibrium,  the sum of x-components of vectors P and Q is zero:\r\n" );
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document.write( "    Px + Qx = 0,  or  p*cos(A) = q*cos(B).    (1)\r\n" );
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document.write( "Due to the same reason (Since the mass is in equilibrium), the sum of y-components of vectors P and Q \r\n" );
document.write( "is numerically equal to the weight of the mass m*g = 2*10 = 20 newtons (here for simplicity\r\n" );
document.write( "I take g = 10 m/s^2 for the gravity constant).\r\n" );
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document.write( "It gives the second equation\r\n" );
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document.write( "    py + qy = 20 newtons,  or  p*sin(A) + q*cos(A) = 20.    (2)\r\n" );
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document.write( "Now notice that from triangle ABC,  sin(A) = 0.8/1 = 0.8;  sin(B) = 0.6/1 = 0.6;  cos(A) = 0.6/1 = 0.6;  cos(B) = 0.8/1 = 0.8.\r\n" );
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document.write( "Hence, you can write equations (1) and (2) in this equivalent form\r\n" );
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document.write( "    0.6p = 0.8q          (3)\r\n" );
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document.write( "    0.8p + 0.6q = 20     (4)\r\n" );
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document.write( "From equation (3), express p =  =   and substitute it into equation (4)\r\n" );
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document.write( "     +  = 20\r\n" );
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document.write( "     = 20\r\n" );
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document.write( "     = 20\r\n" );
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document.write( "     = 20\r\n" );
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document.write( "    q = (6*20)/10 = 12 newtons.\r\n" );
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document.write( "    p             =  =  = 16 newtons.\r\n" );
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document.write( "ANSWER.  The magnitudes of tensity are  p= 16 N for CA  and  q= 12 N for CB.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Regarding your second problem, it is posed incorrectly, since it uses the term \" retardation \",
\n" ); document.write( "which is not appropriate, not applicable and is IRRELEVANT in this context.\r
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\n" ); document.write( "\n" ); document.write( "The appropriate terms are EITHER the \" deceleration \" OR the \" friction force \".\r
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\n" ); document.write( "\n" ); document.write( "NEVER SUBMIT more than one problem per post.\r
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\n" ); document.write( "\n" ); document.write( "It is the RULE of this forum.\r
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\n" ); document.write( "\n" ); document.write( "About the rules, read on web-page\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/tutors/students/ask.mpl?action=ask_question&topic=Equations&return_url=http://www.algebra.com/algebra/homework/equations/\r
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\n" ); document.write( "\n" ); document.write( "from which you submit your problems.\r
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