Solving Friction Force and Acceleration Problems

[pttest]

Homework Statement

A block of mass m lies on a horizontal table. The coefficient of static friction between the block and the table is mu_s. The coefficient of kinetic friction is mu_k. (mu_k<mu_s)
a: Suppose you push horizontally with half the force needed to just make the block move. What is the magnitude of the friction force?
b: Suppose you push horizontally with precisely enough force to make the block start to move, and you continue to apply the same amount of force even after it starts moving. Find the acceleration a of the block after it begins to move? {Express your answer in terms of some or all of the variables mu_s, mu_k, and m, as well as the acceleration due to gravity g}

Homework Equations

F_k = mu_k.N (N is normal force)
F_s = mu_s.N

The Attempt at a Solution

I was wondering a: 1/2.mu_k.m.g
b: mu_k.g
could anybody please expalin this problem?

Thanks in advance

 

[rl.bhat]

With in the limit, the frictional force is a self adjusting force.
So in a: frictional force is f/2, because the block is not moving.
In b: Net force acting on the block is f - μk*mg. Now find the acceleration.