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 floor?
Question
Answer:
Coefficient of friction between the book and floor is 0.582.
Explanation:
Using the velocity formula;
v^2 = 2as
a = v^2/(2s)
a = 1.6^2/(2*0.9)
a = 2.56/1.8
a = 1.42 m/s^2
the force necessary to give the book the acceleration is
F = ma = 3.5*1.42 (m is mass of the book i.e. 3.5 kg)
F = 4.98 N
The difference in the force is the friction force, which is
Ff = 25 – 4.98 = 20 N
Ff = mgμ
where μ is coefficient of friction and g is acceleration due to gravity that is 9.8 m/s^2
μ = Ff/mg
μ = 20/(3.5*9.81)
μ = 0.582
Coefficient of friction between the book and floor is 0.582.