Conservation of Energy object of mass

In summary, the conversation discusses a problem involving an object sliding down an incline and coming into contact with a spring. The goal is to find the initial separation between the object and the spring. The solution involves setting the work of the spring equal to the work of gravity, but this approach was incorrect and the correct solution was eventually found.
  • #1
Sheneron
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[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.
 
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  • #2
solved it, nevermind
 
  • #3
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!
 

Related to Conservation of Energy object of mass

1. What is the conservation of energy?

The conservation of energy is a fundamental principle in physics that states energy cannot be created or destroyed, only transferred or converted from one form to another.

2. Why is the conservation of energy important?

The conservation of energy is important because it allows us to predict and understand the behavior of objects and systems. It also helps us to develop more efficient and sustainable energy sources.

3. How does the conservation of energy apply to objects of mass?

The conservation of energy applies to objects of mass because they possess potential energy due to their position or location, and kinetic energy due to their motion. The total energy of the object remains constant unless acted upon by an external force.

4. Can the conservation of energy be violated?

No, the conservation of energy is a fundamental law of the universe and has been observed and tested in countless experiments. Any apparent violations are due to incomplete understanding or measurement errors.

5. How is the conservation of energy related to the first law of thermodynamics?

The first law of thermodynamics is a manifestation of the principle of conservation of energy. It states that the total energy of a closed system remains constant, and energy can only be transferred or converted, not created or destroyed. This law is essential in understanding the behavior of heat and work in thermodynamic systems.

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