A child pushes a 5 kilogram machine along a horizontal floor with a force, P, which makes an angle, theta=30o below the horizontal. The coefficients of kinetic and static friction between the floor and the machine are 0.3 and 0.5 correspondingly. The machine is initially at rest.
a) Compute the maximum force of static friction that must be overcome by the applied before the machine moves.
b) Find what is the value of the force P needed to move the machine at a constant acceleration of 1.5 m/s^2 along the floor?
c) Assume he pushes the machine with just enough force to move the machine, and continues to push with the same force after the machine starts moving, find the acceleration of the machine while in motion.