Question

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 0.74 m by the horizontal 21 N force from the broom and then has a speed of 1.2 m/s, what is the coefficient of kinetic friction between the book and floor?

Answer 1

0.51

Step-by-step explanation:

m = mass of the book = 3.5 kg

F = force applied by the broom on the book = 21 N

a = acceleration of the book

v₀ = initial speed of the book = 0 m/s

v = final speed of the book = 1.2 m/s

d = distance traveled = 0.74 m

Using the equation

v² = v₀² + 2 a d

1.2² = 0² + 2 a (0.74)

a = 0.973 m/s²

f = kinetic frictional force

Force equation for the motion of the book is given as

F - f = ma

21 - f = (3.5) (0.973)

f = 17.6 N

μ = Coefficient of kinetic friction

Kinetic frictional force is given as

f = μ mg

17.6 = μ (3.5 x 9.8)

μ = 0.51