question_answer

Two blocks A and B of \[{{m}_{A}}\] mass \[{{m}_{B}}\] and Wg respectively are kept in contact on a frictionless table. The experimenter pushes the block A from behind so that the blocks accelerate. If the block A exerts a force F on the block B. What is the force exerted by the experimenter on A?

Answer:

Let\[{{F}_{1}}\]be the force with which experiments pushes the block A Consider the two mass as a system Let the net force on the system \[\Rightarrow \,\,{{F}_{1}}=({{m}_{A}}+{{m}_{B}})a\] _______ (1) \[\Rightarrow \,\,a={{F}_{1}}/({{m}_{A}}+{{m}_{B}})\] Let FAB be the force exerted by the block A on block B = F given \[\therefore \,\,{{F}_{AB}}=F={{m}_{B}}a\] \[F={{m}_{B}}\frac{{{F}_{1}}}{({{m}_{A}}+{{m}_{B}})}\] \[\therefore {{F}_{1}}=F\left( \frac{{{m}_{A}}+{{m}_{B}}}{{{m}_{B}}} \right)\Rightarrow {{F}_{1}}=F\left( \frac{{{m}_{A}}}{{{m}_{B}}}+1 \right)\]