What is the Correct Force to Move a Package Up an Incline?

[srh]

Homework Statement

A 40-kg package is at rest on an inlcine when a force P is applied to it. Determine the magnitude of P if 4s is required for the package to travel 10 m up the incline. The static (us) and kinetic (uk) coefficients of friction between the package and the incline are 0.3 and 0.25 respectively.

Homework Equations

Newton's 2nd Law : sum of forces = mass x acceleration
x=x0+v0t+0.5at^2

The Attempt at a Solution

First I changed my coordinate system to make the x plane parallel w/ the incline. I then summed the forces in the y direction in equilibrium to find the value of the N, normal force. I found this to be 368.73 N. (N-mgcos(20)=0)

THen I summed the x forces and set equal to mass x acceleration:
Pcos(50)-(uk)(N)=ma

To find a I used the relation x=x0+v0t+0.5at^2:
x-x0 = 10m
v0=0
t=4s
I found a to be 1.25 m/s^2.

Plugging in all the known values I got P = 355.35 N. I know that P is supposed to be 612 N. I was wondering if it was obvious where I was going wrong?

 

[berkeman]

Thread moved from Engineering to Intro Physics.

Could you list all of the forces acting normal to the plane and parallel to it? I think you might be missing a term or two from the force pushing down and sideways on the block.