In a pickup game of dorm shuffleboard,students crazed by final exams use a broom to propel a calculus book along the dorm hallway. If the 3.5 kg book is pushed from rest through a distance of 0.90 m by the horizontal 25 N force from the broom and then has a speed of 1.60 m/s,what is the coefficient of kinetic friction between the book and the floor?
Force with which the book is pushed, F = 25 N
Mass of the book, m = 3.5 kg
Let, µ be the coefficient of kinetic friction, so, frictional force experienced by the book is, f = µmg
=> f = µ(3.5)(10) [g = 10 m/s2]
=> f = 35µ
Net force that is responsible for accelerating the book is, F - f = 25 - 35µ
Acceleration of the book, a = (F - f)/m = (25 - 35µ)/3.3
After pushing through a distance 0.9 m the speed becomes 1.6 m/s.
So, using, v2 = u2 + 2as
=> 1.62 = 02 + 2[(25 - 35µ)/3.3](0.9)
=> µ = 0.58