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?

 

[m2003]

I would suggest checking your calculations and making sure that all units are consistent. It is also important to consider the direction of forces and accelerations, as well as the angles involved in the problem. Additionally, you may want to double check the values for the coefficients of friction and make sure they are correct. It may also be helpful to draw a free body diagram to visually represent the forces acting on the book and coffee cup.