question_answer

Four blocks of the same mass m connected by cords are pulled by a force F on a smooth horizontal surface,, as shown in Fig. 3(a).23. Determine the tensions \[{{T}_{1}}\], \[{{T}_{2}}\] and \[{{T}_{3}}\] in the cords.                

Answer:

                Let a be the common acceleration of the whole system. \[\therefore \]  F = (m + m + m + m) a = 4 ma ; a = F/4 m 3. (a)             3. (b) Applying Newton's 2nd law separately for each block, Fig. 3(a).24. \[F-{{T}_{1}}=ma,\,{{T}_{1}}-{{T}_{2}}=ma;\,\,\,{{T}_{2}}-{{T}_{3}}=ma,\,{{T}_{3}}=ma\] On solving these equations, we get\[{{T}_{1}}=\frac{3}{4}F,\,\,\,{{T}_{2}}=\frac{1}{2}F,\,\,\,{{T}_{3}}=\frac{1}{4}F\]