The friction coefficient between the two blocks shown in figure is `mu` but the floor is smooth. A. What maximum horizontal force F can be applied without disturbing the equilibrium of the systme? b.suppose the horizontal force applied is double of that found in part a. Findthe accelerations of the two masses.

Explanation

Both upper block andlower block will have acceleration `2m/s^2`

`R_1=mg F=mu R_1-T=0`
`rarr T-muR_1=0`
`and `F--mu mg =T` …..ii
`rarr T=mu mg`
Putting `T=mu mg`
`F=mu mg +mu mg = 2mu mg`
b. `2F=T-mumg -ma`
=0.........i
`T-ma-mu mg =0 [:.R=mg]`
`rarr T=ma+mumg`
Putting value of T in i. we have
`2F-Mamu mg +mu mg-ma=0`
Putting `F=2mumg`
2(2mumg)-2mumg=a(M+m)`
`rarr4mu mg-2mumg=a(M+m)`
`rarr a=(2mu mg)/(M+m)`
Both blocks move with this acceleration a in opposite direction.