A 17-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 34 N. Starting from rest, the sled attains a speed of 2.9 m/s in 9.9 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 following steps:
Step 1: Calculate the net force acting on the sled.
The net force is equal to the horizontal force minus the force of kinetic friction. Since the sled is moving at a constant speed, the net force will be zero. Therefore, net force = 0.
Step 2: Calculate the force of kinetic friction.
The force of kinetic friction can be determined using the equation:
Force of friction = coefficient of kinetic friction * normal force
The normal force is the force exerted by the surface perpendicular to the object. In this case, since the sled is on a flat surface, the normal force will be equal to the weight of the sled, which can be calculated as:
Weight = mass * acceleration due to gravity
Given that the mass of the sled is 17 kg and the acceleration due to gravity is approximately 9.8 m/s², we can find the weight of the sled.
Weight = 17 kg * 9.8 m/s²
Weight ≈ 166.6 N
Substituting the weight into the equation for the force of friction, we have:
Force of friction = coefficient of kinetic friction * 166.6 N
Step 3: Calculate the force applied to the sled.
The force applied to the sled is given as 34 N.
Step 4: Determine the equation for the net force.
Using the equation for the net force:
Net force = force applied - force of friction
Since the net force is zero (because the sled is moving at a constant speed), we have:
0 = 34 N - force of friction
Step 5: Solve for the coefficient of kinetic friction.
To find the coefficient of kinetic friction, we rearrange the equation to solve for it:
force of friction = 34 N - 0
force of friction = 34 N
Substituting this into the equation for the force of friction:
34 N = coefficient of kinetic friction * 166.6 N
Simplifying the equation:
coefficient of kinetic friction = 34 N / 166.6 N
Calculating the coefficient of kinetic friction:
coefficient of kinetic friction ≈ 0.204
Therefore, the coefficient of kinetic friction between the runners of the sled and the snow is approximately 0.204.