A 17-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 28 N. Starting from rest, the sled attains a speed of 2.3 m/s in 10 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 use the equation of motion relating force, mass, acceleration, and friction.
The equation is:
F_net = ma
Where:
F_net is the net force acting on the sled,
m is the mass of the sled, and
a is the acceleration of the sled.
In this case, the net force acting on the sled is the force of pulling minus the force of kinetic friction:
F_net = F_pull - F_friction
The force of pulling is given as 28 N.
The force of kinetic friction can be calculated using the following equation:
F_friction = µ_k * N
Where:
µ_k is the coefficient of kinetic friction, and
N is the normal force.
The normal force is equal to the weight of the sled, which can be calculated as:
N = mg
Where:
m is the mass of the sled, and
g is the acceleration due to gravity (9.8 m/s^2).
First, let's calculate the normal force:
N = (17 kg)(9.8 m/s^2) = 166.6 N
Substituting the values into the equation for the force of kinetic friction:
F_friction = µ_k * N
We can rearrange the equation to solve for the coefficient of kinetic friction (µ_k):
µ_k = F_friction / N
Now, let's calculate the force of kinetic friction using the equation of motion:
F_net = ma
The acceleration (a) can be calculated using the equation for average speed:
a = (v - u) / t
Where:
v is the final velocity (2.3 m/s),
u is the initial velocity (0 m/s), and
t is the time taken (10 m).
Substituting the values into the equation:
a = (2.3 m/s - 0 m/s) / 10 m = 0.23 m/s^2
Substituting the given values into the equation of motion:
F_net = ma
F_pull - F_friction = ma
Plugging in the known values:
28 N - µ_k * 166.6 N = (17 kg) * 0.23 m/s^2
Now, solve for µ_k:
µ_k = (28 N - (17 kg * 0.23 m/s^2)) / 166.6 N
µ_k = (28 N - 3.91 N) / 166.6 N
Therefore, the coefficient of kinetic friction between the runners of the sled and the snow is approximately 0.161.