What is d if kinetic friction is present?
Use D0EL.
Step 1: Define/draw diagram and coordinate system.
Step 2: Choose a consistent zero.
Step 3: Energy conservation
Step 4: Losses.
The previous energy conservation equation:
mgdsin θ = ½ kX^{2}
becomes: E_{f} = E_{i}  losses
→ mgdsin θ = ½ kX^{2}  f_{k} d
The friction force f_{k} = μ_{k} N = μ_{k} mg cos θ
The energy equation becomes: ½ kX^{2} = mgdsin θ + μ_{k} mg dcos θ
Solving for d gives:
d  = 
