What is the equation for the object's velocity after being pushed in spring?

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SUMMARY

The discussion centers on calculating the velocity of an object after it is released from a spring, specifically addressing the conversion of spring potential energy into kinetic energy. The equation used is final velocity squared = initial velocity squared + 2(acceleration)(distance), with the initial velocity being the velocity at the moment of release from the spring. The presence of friction, quantified at 30 N, introduces deceleration, which must be accounted for in the calculations. The kinetic energy at 4 meters was determined to be 30 J, leading to a calculated velocity of approximately 1.73 m/s.

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Homework Statement
Problem: A spring is compressed 50 cm from the equilibrium position. The spring constant is 12 N/cm. A 20 kg object is placed next to the spring initially at rest and it is released. After the object is released from the spring, the force of friction acting on the object is 30 N.

A) Calculate the force required to compress the spring by 50 cm. (Already got the answer which is 600N)

B) Calculate the energy that was stored in the spring. (Got this answer also which is 150 J)

C. Calculate the object's velocity 4m after it has left the spring. (This is where I stopped don't know what to do here)

What I tried: Unfortunately I don't know where to begin. I know what variables are which are work, spring constant, friction and potential energy in the spring which is the same as the work.

As for number 3, I'm totally lost but I do have a theory that I don't know if it would be true for this specific equation.

Theory: Would I have to find kinetic energy first.

The reason that I have such a theory is because of question D which I did not add since I did not attempt it as of yet but as of posting this, I will be attempting.
Relevant Equations
F=Kx and W=1/2FX
Et1+w=Et2
1/2mv+w=1/2mv
0+150=1/2 (20)
300=(20)v
15=v
I know this answer is wrong.
 
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When the object leaves the spring, the energy that was stored in the spring is converted into the kinetic energy of the object. So you can calculate the speed of the object at the time when it first leaves the spring. You are told that "After the object is released from the spring, the force of friction acting on the object is 30 N." Calculate the deceleration from that.
 
I did what would you said and got -1.5003 m/s^2 but when I use the formula final velocity squared=initial volocity+two (acceleration)(distance) I couldn't do it because I can't square root a negative number. Is the formula used wrong or am I on the right track but I just forgot a very key detail. Also, I did get the kinetic energy of the object at 4m which is 30J
 
Zero said:
I did what would you said and got -1.5003 m/s^2 but when I use the formula final velocity squared=initial volocity+two (acceleration)(distance) I couldn't do it because I can't square root a negative number. Is the formula used wrong or am I on the right track but I just forgot a very key detail. Also, I did get the kinetic energy of the object at 4m which is 30J
Can you show your equation? Just because the velocity is decreasing and doesn't reach zero, doesn't mean that you need to take the square root of a negative number...
 
Zero said:
final velocity squared=initial volocity+two (acceleration)(distance)
That should be
final velocity squared=initial velocity squared + two (acceleration)(distance)
What did you get for initial velocity?
Zero said:
I did get the kinetic energy of the object at 4m which is 30J
So deduce the velocity from that.
 
haruspex said:
That should be
final velocity squared=initial velocity squared + two (acceleration)(distance)
What did you get for initial velocity?

So deduce the velocity from that.
isn't initial velocity 0 so it wouldn't matter. Yes i know the kinetic energy is 30j and the velocity is 1.73 m/s but i just don't know how to get the answer for velocity unless you did a different formula than Ek=1/2mv^2 to find kinetic energy then that is possible to deduce that way
 
Zero said:
isn't initial velocity 0 so it wouldn't matter.
The acceleration in the equation you are using results from friction, and that does not start until the object leaves the spring. So for this equation the initial velocity is the velocity as it leaves the spring.
 
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haruspex said:
The acceleration in the equation you are using results from friction, and that does not start until the object leaves the spring. So for this equation the initial velocity is the velocity as it leaves the spring.
Got the answer thank you all for the effort
 
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berkeman said:
Can you show your equation? Just because the velocity is decreasing and doesn't reach zero, doesn't mean that you need to take the square root of a negative number...
Got the answer thank you all for the effort
 
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