-->

Laws Of Motion

Question
CBSEENPH11016623

Three masses 6kg, 2kg and 4kg are kept on a frictionless horizontal surface and pulled by a force 42N. Find the acceleration of system, tension T1 and T2.


Solution
The equations of motion for mass m1, m2 and mas under:
straight F space minus space straight T subscript 1 space equals space straight m subscript 1 straight a space
straight T subscript 1 space minus space straight T subscript 2 space equals space straight m subscript 2 straight a space
straight T subscript 2 space equals space straight m subscript 3 straight a space
Solving the above equations, we get
straight a space equals space fraction numerator straight F over denominator straight m subscript 1 plus straight m subscript 2 plus straight m subscript 3 end fraction and, 
T1fraction numerator left parenthesis straight m subscript 2 plus straight m subscript 3 right parenthesis straight F over denominator straight m subscript 1 plus straight m subscript 2 plus straight m subscript 3 end fraction and
T2fraction numerator straight m subscript 3 straight F over denominator straight m subscript 1 plus straight m subscript 2 plus straight m subscript 3 end fraction
Substituting the value of m1, m2 and m3, we get
Acceleration,  a equals space fraction numerator 42 over denominator 6 plus 2 plus 4 end fraction space space 3.5 space m divided by s squared
Tension, T1fraction numerator left parenthesis 2 plus 6 right parenthesis 42 over denominator 6 plus 2 plus 4 end fraction space equals space 28 space N
Tension, T2fraction numerator 6 left parenthesis 42 right parenthesis over denominator 6 plus 2 plus 4 end fraction space equals space 21 space N