Conservation of mechanical energy question

[jgray]

Homework Statement

A block of mass 2.5 kg is placed against a compressed spring (k = 2900 N/m) at the bottom of an inclined plane (angle = 28 degrees). When the spring is released the block is projected up the incline and the spring expands by 14 cm to its normal length.
a.Calculate the maximum distance traveled by the block up the incline without friction.
b.Repeat the calculation with friction, taking µk = 0.22.

Homework Equations

E=1/2kx^2
E=1/2mv^2
E=mgy + 1/2kx^2

The Attempt at a Solution

Stuck on part a since I'm not sure its right.. :
E1=E2
mgh=1/2kx^2
(2.5)(9.8)h=1/2(2900)(.14)^2
24.5h=28.42
h=1.16m
So since I have one side of the triangle and the angle, I should be able to find the distance:
d= h/sin28 = 1.16/0.469471562= 2.47 m

Am I on the right track so far?? Thanks for any advise!

 

[SammyS]

Homework Statement

A block of mass 2.5 kg is placed against a compressed spring (k = 2900 N/m) at the bottom of an inclined plane (angle = 28 degrees). When the spring is released the block is projected up the incline and the spring expands by 14 cm to its normal length.
a.Calculate the maximum distance traveled by the block up the incline without friction.
b.Repeat the calculation with friction, taking µk = 0.22.

Homework Equations

E=1/2kx^2
E=1/2mv^2
E=mgy + 1/2kx^2

The Attempt at a Solution

Stuck on part a since I'm not sure its right.. :
E1=E2
mgh=1/2kx^2
(2.5)(9.8)h=1/2(2900)(.14)^2
24.5h=28.42
h=1.16m
So since I have one side of the triangle and the angle, I should be able to find the distance:
d= h/sin28 = 1.16/0.469471562= 2.47 m

Am I on the right track so far?? Thanks for any advise!

That looks like the right result.

Your energy equations are inconsistent.

PE_SPRING = (1/2)kx² .

PE_GRAVITY = mgh

E = KE + PE