Work? maybe just kinematic ( I don't even know what it is)

AI Thread Summary
The discussion revolves around a physics problem involving a spring launching a 100 kg student up a frictionless incline after being compressed. The initial speed of the student after losing contact with the spring is calculated to be 14.1 m/s. The main challenge is determining how far the student travels up the incline, factoring in kinetic friction with a coefficient of 0.15 on a 30-degree slope. The user initially struggles with setting up the equations of motion correctly but ultimately resolves the issue. The conversation highlights the complexities of applying kinematic equations in the context of forces acting on an incline.
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Work?...maybe just kinematic...(please help! I don't even know what it is!)

The spring shown in the figure is compressed 50 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the 30 degree incline is 0.15.

http://session.masteringphysics.com/problemAsset/1000852/6/knight_Figure_11_54.jpg

What is the student's speed just after losing contact with the spring?

How far up the incline does the student go?

The v_initial is incredibly easy to find, 14.1, but I can't seem to find how far he travels up the incline.
I've set it up a few different ways, and each time I get the wrong answer.

if Fx = -F_f - F_w*sinθ = ma
Fy = n - F_w*cosθ = 0 -> n = m*g*cosθ

then shouldn't -umgcosθ - mgsinθ = ma
giving you a = -g(ucosθ + sinθ) ?

and then the distance could be solved using the v_initial and a using kinematics?
But it is wrong? Could someone please explain?
 
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