question_answer

In the arrangement shown in figure. The strings are light and inextensible. The surface over which blocks are placed is smooth. Find: (a) The acceleration of each block (b) The tension in each string.

Answer:

(a) Let a be the acceleration of each block and \[{{T}_{1}}\]and \[{{T}_{2}}\]be the tensions, in the two strings as shown in figure. Taking the three blocks and the two strings as the system. Using \[\sum {{F}_{x}}=m{{a}_{x}}\]or \[14=(4+2+1)a\,\,or\,\,a=\frac{14}{7}2m/{{s}^{2}}\] (b) Free body diagram (showing the forces in x-direction only) of 4 kg block and 1 kg block are shown in figure. Using \[\sum {{F}_{x}}=m{{a}_{x}}\]For 1 kg block, \[F-{{T}_{1}}=(1)(a)\] or \[14-{{T}_{1}}=(1)(2)=2\] \[\therefore {{T}_{1}}=14-2=12N\] For 4 kg block, \[{{T}_{2}}=(4)(a)\] \[\therefore {{T}_{2}}=(4)(2)=8N\]