F-2 A hockey puck leaves a player’s stick with a velocity of 10 m/s and slides 40 m before coming to rest. Find the coefficient of friction between the puck and the ice.

At face value, this problem seems easy enough to do; in fact, it is quite difficult.
The coefficient of friction shows up in only one equation, namely, F
F = uFN

.

 
Red = Friction force
Blue = normal force
Green = gravitational force

Violet = velocity vector

 Looking in the y-direction

(+ ) FN + (-) mg = Fnet = ma = 0

FN - mg = 0

FN= mg

Looking in the x - direction 
(-) F
F = FNET = ma
-F
F = ma
-uF
N = ma
-umg = ma
u = - a/g

 Note that there is no force in the + X direction.

Note also that the velocity vector is not part of the calculation in the box above right because it is not a force vector

 We can calculate the acceleraton from the kinematics where
VF = 0
Vi = + 10 m/s
d = 40 m
a = ?

V^2 =Vi^2 + 2 a d
0 = 100 m^2/s^2 + a (80m)

a = -1.25 m/s^2

 u = -a/g

u = - (-1.25 m/s^2) / 9.8 m/s^2

u = .127

pubished 06/25/07