Acceleration of Book on Incline: Forces & Friction Analysis

[Vii]

Homework Statement

The 3.91 kg physics book shown is connected by a string to a 519.0 g coffee cup. The book is given a push up the slope and released with a speed of 3.99 m/s. The coefficients of friction are μs = 0.457 and μk = 0.330. What is the acceleration of the book if the slope is inclined at 21.7°?

Homework Equations

$$F_N_E_T=ma$$

The Attempt at a Solution

I've tried splitting the equation into two: the book and the coffee mug.

COFFEE MUG:

$$F_N_E_T=\vec{F}_g - \vec{F}_T$$
$$ma=mg - T$$
$$0.519a=(0.519)(9.8)-T$$
$$T=5.0862-0.519a$$

BOOK:

I've split weight into its x and y components.

$$F_N_E_T = T + W_x - F_k_i_n_e_t_i_c$$
$$ma = T + W_x - F_k_i_n_e_t_i_c$$
$$3.91a = T + 8.152$$
$$T = 3.91a - 8.152$$

Then I equated T and solved for a. But I'm still getting the wrong answer...

 

[learningphysics]

can you describe how you got the 8.152N?