How Long to Move a Box with Angled Force and Friction?

[starfish794]

A box of books weighing 320 N is shoved across the floor of an apartment by a force of 430 N exerted downward at an angle of 35.6° below the horizontal. If the coefficient of kinetic friction between box and floor is 0.57, how long does it take to move the box 3.90 m, starting from rest?

I found n to be 260.19 but now i don't know where to go with it. What formula should I use? I can't find one that includes time.

 

[Doc Al]

I found n to be 260.19 ...

What is "n" and how did you find this?

Hint: To calculate the normal force you must include all vertical forces acting on the books.

 

[Stonie]

I personally am having trouble with this exact same question only with different numbers.
I have found so far, the equations:

m*a[x] = F[applied]*cos(Θ) - force of friction.
m*a[y] = F[normal] - F[gravity] - F[applied]*sin(Θ)

and

m*a = F[applied]*cos(Θ) - mu *(m*g + F[applied]*sin(Θ))

However I continually get the wrong answer no matter how I go about it and have no clue what I'm doing wrong, or even if those equations are right.

Any help would also be appriciated by me, greatly.

 

[andrevdh]

Stonie, your equations are all correct so post the calculation.

 

[physics1234]

I solved those equations but I still don't understand how to find time from them. Help please?

 

[Doc Al]

Once you've solved for the acceleration, it becomes a kinematics problem.