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 5.0 kg book is pushed from rest through a distance of 0.62 m by the horizontal 30 N force from the broom and then has a speed of 1.5 m/s, what is the coefficient of kinetic friction between the book and floor?

μ_k=0.58

Explanation:

First, we state the givens and required in our example here, then we will proceed through our solution steps  

m_book=5.0 kg

d= 0.62 m

F_horizontal= 30 N

v_f=1.5 m/s

μ_k=??

Now, we will put our motion equations due to force, according to Newton's Second Law  

∑F=ma

Vertical-->W-N=0                                        (1)

Horizontal-->F_horizontal-μ_k=ma            (2)

So now, let's solve for μ_k from the second equation  

F_horizontal-μ_k*N=ma

μ_k=F_horizontal-ma/N                               (3)

Then, we need to calculate N, a to get the value of μ_k

From equation Number (1), we can calculate N like this  

N=W=mg

N=34.3 N

Second, by using kinematics we will find the value of a  

v_f^2=v_o^2+2a*d

Solving for a, we get  

a=v_f^2-v_o^2/2d

a=1.42 m/s^2

Finally, we plug in our calculated values in equation number (3)  

μ_k=(F_horizontal-ma)/N

μ_k=0.58