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## 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. When the spring is released the block is projected up the incline and the spring expands by 14 cm to its normal length.

Calculate the maximum distance traveled by the block up the incline.

** the angle of the incline is 28 degrees.

a.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

sin(theta)=opp/hyp

xtotal= x1+x3

## The Attempt at a Solution

for a) I seperated the question into 3 situations: the compressed block, the block at normal length, and the block at its highest point

Situation 1: let y=0m here

E1= 1/2kx^2

Situation 2: let x=0m here

E2=1/2mv^2

Situation 3:

E3= mgy + 1/2kx^2

I used Situation 1 and 3...

E1=E3

1/2kx

_{1}^2 = mgy

_{3}+ 1/2kx

_{3}^2

I used trig ratios to find that y

_{3}= 0.14sin28

I solved: x

_{1}= 0.0207 , then added it with x

_{3}:

xtotal= x1+x3 = 0.14m - 0.0207m

I feel like I'm doing this completely wrong. Can someone explain step-by-step the correct way to solve for this?

b) I know there has to be non-conservative work done, but I have no clue which situation to use... I'm confused, please help !!

& THANK YOU

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