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 0.87 m by the horizontal 25 N force from the broom and then has a speed of 1.58 m/s, what is the coefficient of kinetic friction between the book and floor?
To find the coefficient of kinetic friction between the book and the floor, we need to use the following equation:
μk = (Fk) / (N)
Where:
μk is the coefficient of kinetic friction,
Fk is the force of kinetic friction, and
N is the normal force.
First, let's calculate the normal force acting on the book. The normal force is the force exerted by the floor on the book, perpendicular to the surface.
In this case, since the book is on a horizontal surface and there is no vertical acceleration, the normal force is equal in magnitude but opposite in direction to the force due to gravity (weight).
The weight of the book can be calculated using the equation:
Weight = m * g
Where:
m is the mass of the book, and
g is the acceleration due to gravity.
In this case, the mass of the book is 3.5 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Weight = 3.5 kg * 9.8 m/s^2 = 34.3 N
Now, let's calculate the force of kinetic friction acting on the book. The force of kinetic friction can be calculated using the equation:
Fk = μk * N
We know the force of kinetic friction acting on the book is equal in magnitude but opposite in direction to the horizontal force applied by the broom, which is 25 N.
25 N = μk * N
Substituting the value of the normal force (34.3 N) into the equation, we can solve for the coefficient of kinetic friction (μk).
25 N = μk * 34.3 N
μk = 25 N / 34.3 N
μk ≈ 0.728
Therefore, the coefficient of kinetic friction between the book and the floor is approximately 0.728.