Conservation of energy hard problem.

1. Dec 12, 2016

Neon32

1. The problem statement, all variables and given/known data
An object of mass m starts from rest and slides a distance d down a frictionless incline of angle (theata). While sliding, it contacts an unstressed spring of negligible mass as shown in the Figure below. The object slides an additional distance x as it is brought momentarily to rest by compression of the spring (of force constant k). Find the initial separation d between object and spring. (Use theta for (theta), g for acceleration due to gravity, and m, k and x as necessary.)

http://www.webassign.net/pse/p8-10.gif

2. Relevant equations
Initial energy=finnl energy
K.Ei+P.Ei=K.Ef+P.Ef
3. The attempt at a solution
Here is how I tried to solve it:

Initial energy=0+mgh1
Final energy=0+mgh2+1/2kx²

intial energy=Final energy
mgh1=mgh2+1/2kx²
mgh1-mgh2=1/2kx²
mg(h1-h2)=1/2kx² (1)
since h1-h2=(d+x)sin(theta)
By substituation in equation (1):

mg(d+x)sin(theta)=1/2kx²
then we can solve for d

I found a bit different answer in the answers sheet.

2. Dec 12, 2016

Elvis 123456789

Your method looks good. The answer should be correct.

3. Dec 12, 2016

CWatters

I agree. Perhaps post what the answer sheet says. The usual mistake is to forget the PE due to "x" but you got that right.

4. Dec 12, 2016

Neon32

Here is the answer in answer sheets. He made it in less steps than mine and didn't mention h1 and h2.
http://imgur.com/a/SdrlK

5. Dec 12, 2016

Elvis 123456789

That is the same result you derived; he just went ahead and actually solved for "d".

6. Dec 12, 2016

Delta²

Just a note, in the answer sheet it shows clearly that your teacher choses another level of zero potential energy (you consider 0 potential energy at the base of the inclined, while your teacher puts the zero potential energy at height h2). But the answer should be independent of where we choose the zero potential energy to be and indeed both yours and your teacher method lead to the same result for d. (another note, your teacher uses $\Delta x$ instead of $x$).

7. Dec 12, 2016

Neon32

I understood the first part about choosing zero potential energy but I don't get the second part. Does it matter if he say ##\Delta X or just X? In this problem it's just a symbol. As far as I can see it didn't affect the problem.

8. Dec 12, 2016

Delta²

Nope it doesn't matter its just a symbol as you say for the displacement of the spring.

9. Dec 12, 2016

Neon32

Thanks. Appreciated :).

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