Block B has mass 4.00 kg and sits at rest on a horizontal, frictionless surface. Block A has mass 2.00 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 P⃗ is then applied to block A.

What is the largest value P can have and the blocks move together with equal accelerations?

P = 12 N

Explanation:

Given that

Mass of B block m = 4 kg

Mass of A block m' = 2 kg

μ = 0.4

Given that block B is on friction less surface. If these blocks moves together with same acceleration only if the this acceleration will be equal to the acceleration of block B which produce by friction force.

Lets take acceleration is a m/s²

For block A

fr = μ m' g

fr = 0.4 x 2 x 10 N

fr = 8 N

For block B

fr = m a

8 = 4. a

a = 2 m/s²

If they moves together

P = (m+m') a

P = (4 + 2) x 2

P = 12 N

P = 12 N