There are six books in a stack,each with a weight of 3.0 N.The coefficient of friction between all the books is 0.20 as is the coefficient between the table and the bottom book.What horizontal push must I just exceed on the next to bottom book to start sliding the top five books off the bottom one?
A) 1.0 N
B) 5.0 N
C) 3.0 N
D) 7.0 N

Question

Quizplus · Accepted Answer

The force of friction between the bottom book and the table is:$$f_b=\mu_b n_b=\mu_b(5	imes3.0	ext{ N})=6.0	ext{ N}$$The force of friction between the next-to-bottom book and the bottom book is:$$f_2=\mu_2 n_2=\mu_2(4	imes3.0	ext{ N})=4.8	ext{ N}$$The force of friction between the third book and the second book is:$$f_3=\mu_3 n_3=\mu_3(3	imes3.0	ext{ N})=3.6	ext{ N}$$The force of friction between the fourth book and the third book is:$$f_4=\mu_4 n_4=\mu_4(2	imes3.0	ext{ N})=2.4	ext{ N}$$The force of friction between the fifth book and the fourth book is:$$f_5=\mu_5 n_5=\mu_5(1	imes3.0	ext{ N})=1.2	ext{ N}$$The total force of friction between the top five books and the bottom book is:$$f_t=f_b+f_2+f_3+f_4+f_5=6.0	ext{ N}+4.8	ext{ N}+3.6	ext{ N}+2.4	ext{ N}+1.2	ext{ N}=18.0	ext{ N}$$The horizontal push that must be just exceeded to start sliding the top five books off the bottom one is:$$F_p>f_t=\boxed{18.0	ext{ N}}$$

There Are Six Books in a Stack,each with a Weight