Calculate the Coefficient of Friction

Question

You are at the top of a track that is 15 meters high and 80 meters long when your sled begins to slide down the track. When you reach the bottom of the track, you continue to slide, but hit a rough patch for 4 meters. What is the coefficient of Kinetic Friction for the rough part if you find that your speed after the rough patch is 5 m/s? The total mass of the car and the people is 2000 kg.

Answer 1

h = initial height

If the sled went down the track without friction, its speed at the bottom is

v₀ = √(2gh)

x = length of rough patch

v = final speed at the end of the rough patch

a = acceleration along the rough patch

From kinematics,

v² - v₀² = 2ax

a = f/m = -μmg/m = -μg

v² - v₀² = -2μgx ⇒

μ = (v₀² - v²) / (2gx)

μ = (2gh - v²) / (2gx)

Now plug in the following values and get μ:

g = 9.8 m/s²

h = 15 m

v = 5 m/s

x = 4 m

You finish from here.