Newton's Laws Practice Problem: Finding Force on Book During Braking

[mp1019]

Homework Statement

Your 3.10 kg physics book is next to you on the horizontal seat of your car. The coefficient of static friction between the book and the seat is 0.640, and the coefficient of kinetic friction is 0.540. Suppose you are traveling at 79.2 km/h = 22.0 m/s and brake at a constant rate to a stop over a distance of 65.4 m.

The answer is 35.2 N and 65.3 degrees with the horizontal.

What force does the seat exert on the book in this process?

(Upward Force in N, and the backwards angle for it)

Homework Equations

F=m*a

The Attempt at a Solution

I am having trouble visualizing though because I know the F is not solely in the y direction (from the seat) but I don't know how I should go about finding it. I tried to break it up into components and solve for theta using arctan, but this did not work either.

 

[tiny-tim]

Welcome to PF!

Hi mp1019! Welcome to PF!

(have a theta: θ )

F=m*a
…
I am having trouble visualizing though because I know the F is not solely in the y direction (from the seat) but I don't know how I should go about finding it. I tried to break it up into components and solve for theta using arctan, but this did not work either.

Well, that should have worked …

type out what you did, and then we'll be able to help.

 

[mp1019]

Sorry about the θ!

Well, since I got the answer wrong when I tried to say that the upward force was simply the Fn, I tried to break it up into components. I thought that I should look at the m*g*cos(θ) as the x component and m*g*sin(θ) as the y component. So, I tried to use arctan(y/x) to get θ; and I thought that I would use that to solve for the upward force by finding the vector sum of the two components.