Conservation of Energy object of mass

[Sheneron]

[SOLVED] Conservation of Energy

Homework Statement

An object of mass m starts from rest and slides a distance d down a frictionless incline of angle . While sliding, it contacts an unstressed spring of negligible mass as shown in Figure P8.10. 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 , g for acceleration due to gravity, and m, k and x as necessary.)

http://img214.imageshack.us/my.php?image=p810uu0.gif

Homework Equations

Wspring = 1/2kx^2
W = F*d

The Attempt at a Solution

I thought that the work of the spring would equal the work of gravity. so I set the two equations equal to one another, but apparently that is wrong.

 

[Sheneron]

solved it, nevermind

 

[Moetasim]

I also tried setting the potential energy of the object at the top of the incline equal to the potential energy of the object at the bottom of the incline plus the potential energy of the compressed spring, but that didn't work either. I'm not sure where to go from here.

It seems like you are on the right track by considering the conservation of energy principle. However, there are a few things to keep in mind when using this principle. First, make sure that the energy terms you are using are all for the same object. In this case, the work done by the spring is for the object of mass m, while the work done by gravity is for the same object. So, your initial equation should be: Wspring = Wgravity.

Next, remember that the work done by gravity is equal to the change in potential energy of the object. So, you can write Wgravity as mgh, where h is the vertical height change of the object.

For the spring, you correctly identified the work-energy equation, but you need to be careful with the variables. The distance x in this equation is the distance that the spring is compressed, not the distance that the object slides down the incline. So, you can write Wspring as 1/2kx^2, where x is the distance of compression of the spring.

Now, you can set these two equations equal to each other and solve for x. This will give you the distance of compression of the spring. Then, you can use this value of x to find the initial separation d between the object and the spring.

Hope this helps!