Add Friction

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 kX2
becomes:   Ef = Ei - losses → mgdsin θ = ½ kX2 - fk d

The friction force fk = μk N = μk mg cos θ

The energy equation becomes:   ½ kX2 = mgdsin θ + μk mg dcos θ

Solving for d gives:
d =
2mg [sin θ + μkcos θ]