a 60 kg boy on a sled reaches the bottom of a hill traveling at 8 m/s, if he comes to a stop at 20 m along this flat stretch of snow what is the coefficient of kinetic friction between the sled and the ground? (hint: find the acceleration first)
To find the coefficient of kinetic friction between the sled and the ground, we need to follow these steps:
Step 1: Find the acceleration of the boy and sled.
First, we need to find the initial velocity (u) of the boy and sled. The problem statement mentions that the boy reaches the bottom of the hill traveling at 8 m/s.
Initial velocity (u) = 8 m/s
The final velocity (v) is zero because the boy comes to a stop.
Final velocity (v) = 0 m/s
The distance traveled (s) is given as 20 m.
Distance (s) = 20 m
Now, we can use the kinematic equation to find the acceleration (a):
v² = u² + 2as
0 = (8)² + 2a(20)
64 = 40a
a = 64/40
a = 1.6 m/s²
Step 2: Calculate the force of friction acting on the sled.
The force of friction can be determined using Newton's second law of motion:
Force (F) = mass (m) × acceleration (a)
The mass of the boy and sled is given as 60 kg.
m = 60 kg
a = 1.6 m/s²
F = (60 kg) × (1.6 m/s²)
F = 96 N
Step 3: Determine the normal force.
The normal force (N) is equal to the weight of the boy and sled, which can be calculated as:
Weight = mass × gravity
mass = 60 kg
gravity = 9.8 m/s² (approximate value for gravity on Earth)
Weight = (60 kg) × (9.8 m/s²)
Weight = 588 N
Since the sled is on a flat surface, the normal force is equal to the weight (N = Weight).
N = 588 N
Step 4: Calculate the coefficient of kinetic friction.
The coefficient of kinetic friction (μ) is given by the formula:
μ = F/N
μ = (96 N) / (588 N)
μ ≈ 0.1633
Therefore, the coefficient of kinetic friction between the sled and the ground is approximately 0.1633.