Finding the speed of a book against a vertical wall

[Vanessa Avila]

Homework Statement

the main question asks: "If the book is initially at rest, what is its speed after it has traveled 0.400 m up the wall?"

Homework Equations

∑F = m*a
v_f² = v_i² + 2 * a * d , when initial velocity is 0.

The Attempt at a Solution

So here's my free body diagram:

and out of that FBD I got these equations:
∑Fx=N−Fcos(60)=0
∑Fy=fk+Fsin(60)=ma

I know that fk=μ(Fcos(60)) = μN

Should i solve for the acceleration and then plug it in the kinematics equation to solve for final velocity? And are my equations and FBD right?

 

[cnh1995]

Homework Statement

the main question asks: "If the book is initially at rest, what is its speed after it has traveled 0.400 m up the wall?"

Homework Equations

∑F = m*a
v_f² = v_i² + 2 * a * d , when initial velocity is 0.

The Attempt at a Solution

So here's my free body diagram:

and out of that FBD I got these equations:
∑Fx=N−Fcos(60)=0
∑Fy=fk+Fsin(60)=ma

I know that fk=μ(Fcos(60)) = μN

Should i solve for the acceleration and then plug it in the kinematics equation to solve for final velocity? And are my equations and FBD right?

The book is moving upward. Shouldn't the frictional force be downward then?

 

[Vanessa Avila]

The book is moving upward. Shouldn't the frictional force be downward then?

Oh okay so Fsin60 - mg - fk then? I forgot to add the mg on my equation up there.

 

[cnh1995]

Oh okay so Fsin60 - mg - fk then

Right.

 

[Vanessa Avila]

Right.

Ohh okay i didn't catch the "up" part on the question. So i can solve for acceleration now then given that equation?

 

[cnh1995]

Ohh okay i didn't catch the "up" part on the question. So i can solve for acceleration now then given that equation?

Yes. And then plug it in the kinematic equation

vf2 = vi2 + 2 * a * d

 

[Vanessa Avila]

Yes. And then plug it in the kinematic equation

Awesome. I did that and i got the right answer. Thanks a lot! :)