A mass m = 11.0 kg rests on a frictionless table and accelerated by a spring with spring constant k = 5008.0 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μk = 0.46. The mass leaves the spring at a speed v = 2.8 m/s.
3) The mass is measured to leave the rough spot with a final speed vf = 1.5 m/s.
How much work is done by friction as the mass crosses the rough spot?
What is the length of the rough spot?
In a new scenario, the block only makes it (exactly) half-way through the rough spot. How far was the spring compressed from it

Question

A mass m = 11.0 kg rests on a frictionless table and accelerated by a spring with spring constant k = 5008.0 N/m. The floor is frictionless except for a rough patch. For this rough path, the coefficient of friction is μk = 0.46. The mass leaves the spring at a speed v = 2.8 m/s. 
3) The mass is measured to leave the rough spot with a final speed vf = 1.5 m/s.
 How much work is done by friction as the mass crosses the rough spot? 
What is the length of the rough spot? 
In a new scenario, the block only makes it (exactly) half-way through the rough spot. How far was the spring compressed from it