An atwood machinre consisting of two objects of mass 300g and600g,connected by an inextensible massless string .The tension in the string is?

Asked by goyal.rishabh77 | 21st Jun, 2015, 03:43: PM

Expert Answer:

Let a be the accelaration in the masses and T be the tension in the string. The tension is same through out the srting.
Let m1 = 600 g and m2 = 300 g be the masses. Since m1 is heavier, it will ove downwards (with acceleration a) and m2 will move upwards (with acceleration a).
According to the Newton's second law of motion, net forces on the masses will be equal to the product of thier mass and acceleartion.
begin mathsize 12px style straight m subscript 1 straight g space minus space straight T space equals space straight m subscript 1 straight a space minus negative negative negative negative left parenthesis Eqn. space 1 right parenthesis straight T minus straight m subscript 2 straight g space equals space straight m subscript 2 straight a space space minus negative negative negative negative left parenthesis Eqn. space 2 right parenthesis end style
Adding 1 and 2, we get:
begin mathsize 12px style straight a equals fraction numerator left parenthesis straight m subscript 1 minus straight m subscript 2 right parenthesis straight g over denominator straight m subscript 1 plus straight m subscript 2 end fraction straight a equals fraction numerator left parenthesis 0.6 minus 0.3 right parenthesis 9.8 over denominator 0.6 plus 0.3 end fraction straight a equals 3.26 space straight m divided by straight s squared Substituting space the space value space of space straight a space in space equation space 1 comma space we space get colon 0.6 cross times 9.8 space minus space straight T space equals space 0.6 cross times 3.26 straight T equals 5.88 space minus space 1.956 straight T equals 3.92 space straight N end style


Answered by Yashvanti Jain | 15th Dec, 2017, 02:58: PM