A problem about Work and Energy :(

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SUMMARY

The discussion centers on a physics problem involving a 1-kg block sliding down a frictionless curved ramp and subsequently moving across a rough horizontal surface. The block gains 60 J of kinetic energy, achieving a speed of 10.9545 m/s at the end of the ramp. Key calculations include determining the height of the ramp (6.1224 m), the coefficient of kinetic friction on the rough surface (0.3316), and the length of the inclined plane (3.0768 m) when the coefficient of kinetic friction is 0.25. The maximum compression of the spring was not determined.

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Jettro Ulanday
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Moved from a technical forum, so homework template missing
Starting from rest, 1-kg block slides down a frictionless curved ramp, which is one quadrant of a circle, and gains 60 J of kinetic energy at the end of the curved path. The block then slides on a 6-m long rough horizontal surface and acquires a speed of 9 m/s just before going up a rough plane inclined at an angle 10 degrees with the horizontal. It continues moving with a constant speed of 6 m/s on a smooth horizontal surface where it hits and compresses a horizontal spring (k= 300 N/m) before coming to rest.
Questions:
a.) Height of the Curved ramp
b.) Speed of the block at the end of the curved path
c.) Coefficient of Kinetic Friction between the block and the rough horizontal surface
d.) Length of the inclined plane when the coefficient of kinetic friction between the block and inclined plane was 0.25
e.) Maximum compression of the string

Tried my best answering, and these are my answers:
a.) 6.1224 m
b.) 10.9545 m/s
c.) 0.3316
d.) 3.0768 m
e.) NONE as of now

Can anyone help? I'm not quite sure of my answers, Thanks.
 
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You should now show your work. How did you answer a) ? We will start from there.
 

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