A block with mass m = 17 kg rests on a frictionless table and is accelerated by a spring with spring constant k = 4201 N/m after being compressed a distance x1 = 0.556 m from the spring’s unstretched length. The floor is frictionless except for a rough patch a distance d = 2.3 m long. For this rough path, the coefficient of friction is μk = 0.45.

Question

1) What distance does the spring need to be compressed so that the block will just barely make it past the rough patch when released?

Answer 1

Your question makes no sense as typed. You gave the x1 = 0.556 and then asked what x1 =
Are there intermediate steps that you did not bother to type?

Answer 2

let x=2.3m be the distance the block is from the edge, distance before compressing.

energyincompressed spring=workdoneonFrictiontogetto edge
1/2 K (.556+d)^2=17*9.8*.45*2.3
solve for d.