Algebra.Com's Answer #812890 by ikleyn(52781)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
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document.write( "A string is attached to a body of mass 4 kg which rests on a frictionless plane that is inclined 30° with the horizontal.
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document.write( "The string passes over a pulley at the upper end of the plane, and another body of mass 3 kg is attached to the other
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document.write( "end of the string, this body hanging vertically.
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document.write( "(a) Find the direction and magnitude of the acceleration of the two bodies
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document.write( "(b) Find the tension in the string.
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document.write( " Part (a)\r
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document.write( "Physically, the idea of the solution is VERY SIMPLE.\r\n" );
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document.write( "To answer question (a), we should compare two forces, acting at the ends of the string.\r\n" );
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document.write( "One force is the weight of the 3 kg mass hanging vertically. This force is the product \r\n" );
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document.write( "  = 3*10 = 30 newtons.\r\n" );
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document.write( "The other force is the rolling force acting on the body on the inclined plane.\r\n" );
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document.write( "This force is  =  = 2*10 = 20 newtons.\r\n" );
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document.write( "From the comparison, the weight of the 3-kg mass is greater --- HENCE what ? - - - \r\n" );
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document.write( " | But of course, this 3-kg mass will move down, |\r\n" );
document.write( " | and will pull the 4-kg mass up along the incline plane. |\r\n" );
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document.write( "It is the ANSWER to question (a), and this part is just COMPLETED.\r\n" );
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document.write( " Part (b)\r
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document.write( "There are two ways to solve and to answer this part.\r\n" );
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document.write( "One way is EASY. It is how the beginners start solve such problems, and I will show it to you first.\r\n" );
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document.write( " The acting force (its other name is \"the net force\") in the system of the two connected masses \r\n" );
document.write( " is the difference of the two forces applied at the ends \r\n" );
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document.write( " F = - = 30 N - 20 N = 10 N.\r\n" );
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document.write( " The total mass of the system is  +  = 4 kg + 3 kg = 7 kg.\r\n" );
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document.write( " According to the Newton's second law, the acceleration of masses is a =  =  = 1.429 m/s^2.\r\n" );
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document.write( " Then the tension T is T =  =  =  =  = 25.714 newtons.\r\n" );
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document.write( "Another way is longer. It is to write the system of two equations in two unknown: the tension T and the acceleration \"a\".\r\n" );
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document.write( " First equation is for the 3-kg mass. \r\n" );
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document.write( " Two forces act on it: the weight of 30 N directed vertically down and the tension T directed vertically up.\r\n" );
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document.write( " So, the Newton second law for this mass is\r\n" );
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document.write( "  = 30 - T, or 3a = 30 - T. (1)\r\n" );
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document.write( " Second equation is for the 4-kg mass on inclined plane. It is\r\n" );
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document.write( "  = T - , or 4a = T - 20. (2)\r\n" );
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document.write( " So, again, the system of two equations is\r\n" );
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document.write( " 3a = 30 - T (1)\r\n" );
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document.write( " 4a = T - 20 (2)\r\n" );
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document.write( " You can add equations (1) and (2), eliminating T. Doing this way, you find \r\n" );
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document.write( " 7a = 10, a =  = 1.429 m/s^2 for the acceleration.\r\n" );
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document.write( " By subtracting equations (1) and (2) with appropriate coefficients, you can eliminate \"a\" and find T\r\n" );
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document.write( " 4*(30- T) = 3*(T-20),\r\n" );
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document.write( " 120 - 4T = 3T - 60\r\n" );
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document.write( " 120 + 60 = 3T + 7T\r\n" );
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document.write( " 180 = 7T\r\n" );
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document.write( " T = = 25.714 newtons.\r\n" );
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document.write( " As you see, this second way leads you to the same answer as the first way.\r\n" );
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document.write( "The problem is just solved. The ANSWER is a = = 1.429 m/s^2 for the acceleration and = 25.714 newtons for the tension.\r\n" );
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document.write( "The solution is completed.\r
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document.write( "When I entered the University many years ago, the ability to solve such problems \r
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document.write( "(and not only solve, but TACKLE them) was a necessary condition of passing entrance exams.\r
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document.write( "I do not think that you will find many Physics sites in the Internet, where they will explain the solution to you\r
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document.write( "in such details and so perfectly, as I did it here.\r
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document.write( "Moreover, I am almost convinced, that you will find NO ONE such site in the English segment of the Internet.\r
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