Find velocity of a cart using a spring at an angle

[PhilEWCC]

I have to find the velocity of the cart when it lands right under the spring at 90 degrees. The spring is at an angle. I am not getting the right numbers though, can anyone help? This is my first post here BTW. This community looks awesome!

2. Equations
You can use anything, but I used both Conservation of Energy (change in total energy = 0) and Work-Force equation (Work = int(F*ds))

3. Attempt at a solution
You can see my attempt, variables and work here. Thanks in advance.

https://imgur.com/a/alJ4Q

More variables and work in imgur album.

 

[DEvens]

Your work is kind of hard to follow. What does "Vf = 0.5 recorded" mean? Is that the result of an experiment?

I don't see the length of the spring under zero tension anywhere. Did I miss it? Your picture is confusing. I can't quite figure out the relation between h and Delta Xf. And you have something equal to 0.006, and labeled negligible. I can't figure out what that is supposed to be. Does it mean the cart starts very nearly at rest?

Try to be more careful in labelling things so that it is easier to figure out what they correspond to.

 

[PhilEWCC]

Your work is kind of hard to follow. What does "Vf = 0.5 recorded" mean? Is that the result of an experiment?

I don't see the length of the spring under zero tension anywhere. Did I miss it? Your picture is confusing. I can't quite figure out the relation between h and Delta Xf. And you have something equal to 0.006, and labeled negligible. I can't figure out what that is supposed to be. Does it mean the cart starts very nearly at rest?

Try to be more careful in labelling things so that it is easier to figure out what they correspond to.

Sorry if it's a little confusing.
The length of the spring under zero tension is .085m, h is the height from the pivot point of the top of the spring to the cart. Delta Xf is the distance in zero tension of the bottom of the spring to stretched position on the cart once at 90 degrees. And yes, the cart starts at rest.

 

[DEvens]

If I followed your data and your diagram correctly I get the same answer you do. Where did the "recorded" value of 0.5 m/s come from?

Check all your values. Make sure you have got the right value, and that you are interpreting it correctly.

 

[PhilEWCC]

That's what I was thinking. I don't know how else to find velocity other than these two methods, which seem correct. I will try and rerecord some data when I get back in the lab again.

The velocity was recorded with a calibrated motion sensor. I can upload logger pro data if you want, too. Let me know haha :). This is for a challenge for extra points in our class.

 

[PhilEWCC]

Just wondering DEvens, what equation did you use to get the same answer as I did?