Two block of masses `m_(1)` and `m_(2)` connected by a light spring rest on a horizontal plane. The coefficient of friction between the block and the surface is equal to `mu`. What minimum constant force has to be applied in the horizontal direction to the block of mass `m_(1)` in order to shift the other block?

Explanation

`F.x=mum_(1)gx-1/2kx^(2)=0" "...(i)`
But `Kx=mu_(2)g.` (for just moving body of mass `m_(2))`
Put the value of K in (i) to get F.
F.x `-mum_(1)gx-1/2kx^(2)=0`
But `kx=mum_(2)g` (for moving body of mass `m_(2)`)
`Fx-mum_(1)gx-1/2((mum_(2)g)/(x))x^(2)=0`
`F=mum_(1)g+1/2mum_(2)g`
`=mu(m_(1)+(m_(2))/(2))g`
`=0.5(10+10/2)10`
`=75N`