# Conservation of energy hard problem.

#### 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

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#### Elvis 123456789

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

#### CWatters

Homework Helper
Gold Member
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.

#### Neon32

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.
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

#### Elvis 123456789

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

#### Delta2

Homework Helper
Gold Member
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 $x$).

#### Neon32

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 $x$).
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.

#### Delta2

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

#### Neon32

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

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"Conservation of energy hard problem."

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