Solving a Crate Motion Problem: Find Time for 4m Movement

[homevolend]

Homework Statement

A woman pushes a crate with a force of 400N downward at a 35.2 angle down below horizontel. The crate weighs 300N. If coeffiecient of kenetic friction is 0.57, how much time does it take to move box 4m from rest.

Homework Equations

Fg=mg
Fk=(muk)mg

The Attempt at a Solution

I found fg by multiplying mass and gravity, I got 300N. Next I found Fk by multiplying micro by mass and gravity and got 171.1N.

Found gravity by doing 300/9.81 and got 30.6Kg.

Did

Fnety=Fn+Fay-Fg=0
0=Fn+400sin35.2-300
0=Fn+230.6-300
Fn=69.4

Fnetx=Fax-Fk
ma=Facostheta-Fk
30.6a=400cos35.2-171.1
30.6a=326.9-171.1
30.6a=155.9
a=5.1m/s²

Next i used d=V1t+.5at²
4=0t+.5(5.1)t²
4=2.55t²
t=1.57s

But I do not think I got the correct answer because I did not use the t² after the 2.55 in anyway to find the answer. Did I do the rest of the work correct and just did the calculating of the time wrong, or is my other work wrong?

thanks!

 

[jdc15]

I think the problem is with this part:

Fnetx=Fax-Fk
ma=Facostheta-Fk
30.6a=400cos35.2-171.1
30.6a=326.9-171.1
30.6a=155.9
a=5.1m/s2

Where does 171.1N come from? Normally frictional force is $$\mu F_N$$.

 

[homevolend]

Dont think so because I used the Fk= formula, and in the process I was trying to find Fn and I didnt know it so I used a different formula.

Fk=Ff

And Fk= muk x m x g

Fk= 0.57(30.6)(9.81)

I think it is in the ending but not sure, I just know the answer is wrong.