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Homework Statement
A spring has an equilibrium length of 1m. The spring is compressed to a length of .5m and a mass of 2kg is placed at its free end on a frictionless slope which makes an angle of 41degree wrt the horizontal. The spring is then releases.
a. If the mass is NOT attached to the spring how far up the slope will the mass move before comming to rest.
Homework Equations
I thought since kinetic, restoring and gravitational energy is involved I start out with
1/2 mv_i^2 + mgy_1 + 1/2 kx_i^2 = 1/2 mv_f^2 + mgy_f + 1/2 kx_f^2
The Attempt at a Solution
Now I try to figure out what is actually active in my system.I first look at my
initial situation:
The spring is at rest, so v_i = 0 for my kinetic energy
The gravitational energy is present, since the block is present. My y_1 I need to calculate with y_1= 0.5m*sin41=.33m
I have potential energy of the spring also with x_i=-0.5m
Final situation:Here I do not know what acts in the system...
I have Kinetic energy with v_f
the potential energy of the spring is zero because x_f=0
But what to do with the gravitational energy? It says the block leaves the spring but is it still there in my final situation or not? Do I have to add it with the second hight y_f?
Then Part two when I found v_f of part one, I look again at
initial situation:
kinetic energy with v_i=v_f of part one
gravitational energy at y_i which I can set to zero
Final situation:
kinetic energy is zero, because the block comes to rest
gravitational energy at y_f which I need to find to find the distance.
Can someone please help me with this problem?
Thanks