2D kinematics and vectors

1. The problem statement, all variables and given/known data

A book of mass M = .55 kg rests on a table where the coefficient of static friction us = .45. A force, F = 4 N acts on the book at an angle of 15 degrees above the surface of the table. What is the acceleration of the book if the coefficient of kinetic friction uk = .23?

2. Relevant equations

ΣFx = ma
ΣFy = ma

Ff = Fn(uk)

3. The attempt at a solution

I drew free body diagrams.

ΣFx = Fx – Ff
Fx – Ff = ma(x)
Fx – Fn(uk) = ma(x)

ΣFy = ma
Fn – Fy – mg = ma(y)

I’m not sure where to go from here. I know that I need to use Pythagoras theorem when I have the values of a(x) and a(y) but I don’t know how to get that far.

Please help, I’ve been working on this for 2+ hours.


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