How to Solve for Force Needed to Move a Box on a Ramp with Kinetic Friction

[Funkmaster W]

Homework Statement

Find the force(F) needed to move a 50kg box up a ramp angled at 40 degrees with an acceleration of 1m/(s^2) while pulling at an angle of15 degrees above parallel to the ramp. the ramp has a frictional constant of .1
a=1m/(s^2)
m=50kg
angle of ramp=40 degrees
angle pulling box at = 15 degrees
mu(sub k) = .1
g(gravity)=9.8

Homework Equations

F=ma
F=(mu)N

The Attempt at a Solution

i drew a fbd then split things up into components and found m*g*cos(40)=375.362 and m*g*sin(40)=314.966
then to find force i combined the vectors and equations

50 = F*cos(15) - (314.966 + .1N)
N= -F*sin(15) + 375.362

from here i solved for F by plugging in for N since i had the same two variables in each equation.

50 = F*cos(15) - (314.966 + .1((-F*sin(15)) + 375.362))
50 = .966F - (314.966 -0.026F + 37.536)
402.502 = .992F
F = 405.748
now i solved this however my physics teacher said that F is around 356 but i am unable to find my mistake and was wondering if someone could help me

 

[True Cherokee]

It looks like all of your math checks out to me. I think your physics teacher may have gotten his signs mixed up somewhere. I don't see where you could have gotten a magically different number.

 

[True Cherokee]

Edit to may above post: Your teacher could have accidentally done 314.966-37.536 instead of addition. Then it end up around 348.33, which is just a difference in rounding.