For the following problems, consider a 1.0 kg book resting on top of a table. The coefficients of static and kinetic friction are, respectively, _S = 0.80 and _k = 0.60. The box is pushed in the positive x-direction.

(a) Draw the scenario described above. Include the frame of reference and the expected direction of the applied and friction forces.

(b) Based on the coefficients of friction given, redraw the figure shown in the "Static vs. kinetic firction" section with appropriate values on the friction force axis for a range applied force from 0 N to 15 N.

(c) What are the magnitudes and directions of (1) the friction force acting on the book and (2) the acceleration of the book for the following applied forces. Assume that the book is initially at rest when the force is applied, and all the forces are in the +x direction unless otherwise noted.

i. F_P = 1 N

ii. F_P = 6 N

iii. F_P = 10 N

iv. F_P = 10 N initially, and then a second force (F_P,2 = 3 N) in the negative x-direction is added shortly afterwards.

(d) Briefly describe what happens to the magnitudes of the friction force and the acceleration of the book as the applied force is increased linearly in time.

(e) Draw a graph showing the acceleration of the book as a function of the applied force as the force is gradually increased from 0 N to 15 N.