A student, along with her backpack on the floor next to her, are in an elevator

Question

A student, along with her backpack on the floor next to her, are in an elevator that is accelerating upward with acceleration a. The student gives her backpack a quick kick at t = 0, imparting to it speed v and causing it to slide across the elevator floor. At time t, the backpack hits the opposite wall a distance L away from the student. Find the coefficient of kinetic friction µk between the backpack and the elevator floor. (Use any variable or symbol stated above along with the following as necessary: g.)

µk =

Explanation / Answer

assume the normal force from the floor on the backpack is N

from Newton's second law

N - mg = ma

so N = m(g+a)

the frictional force F = kN will cause a deceleration ax in horizontal motion

kN = max                          

k = max/ N = max / m(g+a) = ax /(g+a)                 (1)

for horizontal motion, we have

L = vt - (1/2)ax t2

so,

ax = 2(vt - L) /t2

substitute into eqn(1), we get

k = 2(vt-L)/[(g+a)t2]

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