Acceleration of Book on Incline: Forces & Friction Analysis

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The discussion revolves around calculating the acceleration of a physics book on an incline connected to a coffee cup. The book's mass is 3.91 kg, and it is pushed up a slope with a speed of 3.99 m/s, while the incline is at 21.7° with given coefficients of friction. The user attempts to solve the problem by analyzing the forces acting on both the book and the coffee cup separately, using equations for net force and tension. A specific point of confusion arises regarding the calculation of the force component, specifically the 8.152 N value. Clarification is sought on how this force was derived to resolve the discrepancies in the calculations.
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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...
 
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can you describe how you got the 8.152N?
 

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