A 16-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 27 N. Starting from rest, the sled attains a speed of 2.2 m/s in 9.6 m. Find the coefficient of kinetic friction between the runners of the sled and the snow.
To find the coefficient of kinetic friction between the runners of the sled and the snow, we can start by calculating the net force acting on the sled.
First, we need to find the acceleration of the sled. We can use the formula:
v^2 = u^2 + 2as
where v is the final velocity (2.2 m/s), u is the initial velocity (0 m/s since the sled starts from rest), a is the acceleration, and s is the displacement (distance covered by the sled, 9.6 m).
Rearranging the formula, we can solve for acceleration:
a = (v^2 - u^2) / (2s)
a = (2.2^2 - 0) / (2 * 9.6)
a ≈ 0.523 m/s^2
Next, we can calculate the net force acting on the sled using Newton's second law:
F_net = ma
where F_net is the net force, m is the mass of the sled (16 kg), and a is the acceleration (calculated above).
F_net = (16 kg) * (0.523 m/s^2)
F_net ≈ 8.368 N
Finally, we can calculate the force of friction using the equation:
F_friction = μ * F_normal
where F_friction is the force of friction, μ is the coefficient of kinetic friction, and F_normal is the normal force. In this case, the normal force is equal to the weight of the sled, which can be calculated using:
F_normal = m * g
where m is the mass of the sled (16 kg) and g is the acceleration due to gravity (9.8 m/s^2).
F_normal = (16 kg) * (9.8 m/s^2)
F_normal ≈ 156.8 N
Substituting the values into the equation for force of friction:
8.368 N = μ * 156.8 N
Simplifying the equation:
μ = 8.368 N / 156.8 N
μ ≈ 0.053
Therefore, the coefficient of kinetic friction between the runners of the sled and the snow is approximately 0.053.