Final answer:
The coefficient of kinetic friction between the runners of the sled and the snow is approximately 0.153.
Step-by-step explanation:
To find the coefficient of kinetic friction between the runners of the sled and the snow, we first need to calculate the net force acting on the sled. We can use Newton's second law of motion, which states that the net force is equal to the mass of the object multiplied by its acceleration.
Given: mass of the sled (m) = 16 kg, force applied (F) = 24 N, initial speed (v0) = 0 m/s, final speed (v) = 2.0 m/s, and distance (d) = 8.0 m.
Using the equation:
F = ma
we can rearrange it to:
a = F/m
Substituting the given values:
a = 24 N / 16 kg
a = 1.5 m/s2
Next, we can use the equation:
v2 = v02 + 2ad
Substituting the given values:
(2.0 m/s)2 = (0 m/s)2 + 2 * (1.5 m/s2) * (8.0 m)
Simplifying the equation:
4.0 m2/s2 = 24 m2/s2
Now, we can find the coefficient of kinetic friction (μk) using the equation:
μk = (Force of friction) / (Normal force)
Since the sled is on a horizontal surface, the normal force is equal to the weight of the sled, which can be calculated using:
Weight = mass * acceleration due to gravity
Weight = 16 kg * 9.8 m/s2
Substituting the values:
Weight = 156.8 N
The force of friction can be calculated using:
Force of friction = μk * Normal force
Substituting the values:
24 N = μk * 156.8 N
Simplifying the equation:
μk = 24 N / 156.8 N
μk ≈ 0.153