Question

a plank of mass 10 kg rests on a smooth horizontal surface.two blocks A and B of masses 2 kg and 1 kg respectively lie at a distance of 3m .the friction coefficient between the block A nd the plank is 0.3 , nd 0.1 b/w the plank nd block B. a force of 15 N is applied on d plank in d horizontal direction, find the time (in sec)after which the block A collides with block B.

Answer 1

Non inertial frame of reference, so the blocks experience fictitious forces in opposite direction of Force on plank.
Newton's 2nd law:
\[m_Aa_A=m_Aa_p - \mu_Am_Ag \rightarrow a_A= \frac{ F }{m_p } - \mu_Ag\]
\[a_B=\frac{ F }{m_p }-\mu_Bg\]

now equations of motion:

object A
\[s=\frac{ a_At^2 }{ 2 }\]
where s is distance when objects meet each other.
object B
\[s=3+\frac{ a_Bt^2 }{ 2 }\]
so
\[\frac{ a_At^2 }{ 2 }=3+\frac{ a_Bt^2 }{ 2 }\]
\[t=\sqrt{\frac{ 2*3 }{ g(\mu_A-\mu_B) }}=1,75 s\]