A 17-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 20 N. Starting from rest, the sled attains a speed of 2.2 m/s in 8.4 m. Find the coefficient of kinetic friction between the runners of the sled and the snow.
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To find the coefficient of kinetic friction, we need to analyze the forces acting on the sled.
First, let's calculate the acceleration of the sled using the given information about its initial and final speeds, as well as the distance traveled.
Acceleration (a) can be calculated using the formula:
a = (vf - vi) / t
Where:
vf = final velocity = 2.2 m/s
vi = initial velocity = 0 m/s (starting from rest)
t = time taken = 8.4 m
Plugging in the given values, we get:
a = (2.2 m/s - 0 m/s) / 8.4 s
a = 0.26 m/s^2
Next, let's analyze the forces acting on the sled. There are two main forces:
1. The horizontal applied force pulling the sled forward (20 N).
2. The kinetic friction force opposing the motion of the sled.
We can now calculate the net force acting on the sled using Newton's second law:
Net force (Fnet) = mass (m) * acceleration (a)
Fnet = 17 kg * 0.26 m/s^2
Fnet = 4.42 N
Since the sled is moving at a constant speed, we know that the net force is zero. This means that the force of kinetic friction is equal in magnitude but opposite in direction to the applied force. Therefore, the force of kinetic friction is 20 N.
The force of kinetic friction can be calculated using the equation:
Force of kinetic friction = coefficient of kinetic friction (μ) * normal force (N)
The normal force (N) is the force exerted by the ground on the sled and is equal to the weight of the sled (mg), where g is the acceleration due to gravity (9.8 m/s^2). In this case, N = 17 kg * 9.8 m/s^2.
Now, we can calculate the coefficient of kinetic friction:
20 N = μ * (17 kg * 9.8 m/s^2)
Rearranging the equation, we get:
Coefficient of kinetic friction (μ) = 20 N / (17 kg * 9.8 m/s^2)
Calculating this expression, we find:
μ ≈ 0.117
Therefore, the coefficient of kinetic friction between the runners of the sled and the snow is approximately 0.117.