Drew is walking back up the best hill in the neighborhood 24* grade. He's pulling on the empty 2.1kg sled with a force of 18N at an angle of 55* with the hill. He's walking with a constant velocity, what is the coefficient of friction?
To determine the coefficient of friction, we need to consider the forces acting on the sled and analyze the equilibrium condition.
First, let's break down the force applied by Drew into its components. The force vector can be split into two components: one parallel to the hill (F_parallel) and one perpendicular to the hill (F_perpendicular).
F_parallel = 18N * cos(55°)
F_perpendicular = 18N * sin(55°)
Next, we need to consider the forces acting on the sled. The forces involved are the gravitational force (mg), the normal force (N) exerted by the hill, and the force of friction (F_friction). Since Drew is walking with a constant velocity, the force of friction must be equal to the force applied by Drew pulling the sled.
Now, let's write the equilibrium equations for the motion of the sled in the vertical and horizontal directions:
Vertical equilibrium:
N - mg = 0
Horizontal equilibrium:
F_friction + F_parallel = 0
Since the sled is sliding up the hill, we need to treat the coefficient of friction as kinetic friction (μ_k). The equation for the force of friction is given by:
F_friction = μ_k * N
Substituting the equations and solving for the coefficient of friction (μ_k):
μ_k * (N - mg) = -F_parallel
μ_k = -F_parallel / (N - mg)
To calculate the normal force (N), we need to find the gravitational force acting on the sled. The gravitational force is given by:
mg = mass * acceleration due to gravity
= 2.1kg * 9.8 m/s^2
Now, substituting all the given values, we can solve for the coefficient of friction (μ_k).