1 kg mass sliding down 30° ramp, across friction surface, compressing spring

[Addie]

An object with mass 1 kg slides down a frictionless inclined plane of length 4 m set at an angle of 30 degrees. It then slides across a flat surface of length 1 m. While sliding across this surface the object experiences sliding friction with the coefficient of sliding friction being .6. It then strikes a spring with a spring constant of 1000 N/m. There is no friction present during the compression of the spring.

What is the maximum compression of the spring, assuming that the object does not stop before hitting the spring?

What is the speed of the object half way across the flat surface?

My answers just don't seem right... but here is my work maybe somebody out there can help...

State 1 is the ramp, there i got
F1= (mg)(sin30)=4.92 N

State 2 is the flat surface:
Etotal= Wc +Wnc
Etot=(F1 x 1 m) + (-Ffr x 1)
Et=(4.92 J) - (1kg x 9.81 m/s^2 x 1m x .6)
Et= -.981 J

State 3 is the spring:
W=1/2 k x^2
-.981 J= 1/2 (1000 Nm) x^2
x= ? because you can't square root negative obviously, so I did somethign wrong and suposeably the correct answer is x=.1655 m and v=5.77 m/s...but I want to figure out how to do the problem, because it seems I am not doing it right please help someone thanks...

 

[learningphysics]

State 2 is the flat surface:
Etotal= Wc +Wnc
Etot=(F1 x 1 m) + (-Ffr x 1)

Here's your mistake. It should be:
Etot=(F1 x 4 m) + (-Ffr x 1)

The question says the inclined plane is 4m long, so F1 works through 4 m.

 

[Addie]

I thought that at first, but as the the block is moving along the the flat surface doesn't that force act on the 1 m flat surface not the incline surface?

 

[Doc Al]

Think in terms of energy. The initial energy is potential: $mgh = mgd sin\theta$. That's the energy the block has as it begins its horizontal slide.