Block B has mass 6.00 kg and sits at rest on a horizontal, frictionless surface. Block A has mass 2.50 kg and sits at rest on top of block B. The coefficient of static friction between the two blocks is 0.400. A horizontal force P is then applied to block A. What is the largest value P can have and the blocks move together with equal accelerations?

Block A sits on block B and force is applied on block A. Block A will experience two forces 1) force P and 2) friction force in opposite direction of motion. Block B will experience one force that is force of friction in the direction of motion.

Let force on block A be P. friction force on it will be equal to kinetic friction, that is μ mg, where μ is coefficient of friction and m is mass of block A

friction force =.4 x 2.5 x 9.8

= 9.8 N

net force on block A = P - 9.8

acceleration = (P - 9.8) / 2.5

force on block B = 9.8

acceleration = force / mass

= 9.8 / 6

for common acceleration

(P - 9.8) / 2.5 = 9.8 / 6

(P - 9.8) / 2.5 = 1.63333

P = 13.88 N.