According to Newton's second law, provided F is directed horizontally,
• the net horizontal force acting on the larger block is
F - µmg = 3mA
where µmg represents the friction experienced by the larger block from contact with the smaller block, µ is the static friction coefficient between both blocks, and A indicates the acceleration of the block;
• the net vertical force on the larger block is
4mg - 3mg - mg = 0
where 4mg denotes the magnitude of the normal force exerted by the surface on the combined mass of both blocks, 3mg corresponds to the weight of the larger block, and mg indicates the weight of the smaller block;
• the net horizontal force acting on the smaller block is
µmg = ma
where µmg again signifies the friction between both blocks; however, it is important to note that this force aligns in the same direction as F. It is the sole force influencing the smaller block in the horizontal direction, thus (b) static friction causes the smaller block's acceleration;
• the net vertical force on the smaller block is
mg - mg = 0
where mg represents the force of both the normal force from the larger block pushing up against the smaller one, and the weight of the smaller block.
(You should be able to create your own free-body diagrams based on the forces discussed.)
(c) Solve the equations stated above to find A and a:
A = (F - µmg) / (3m)
a = µg
