U Physics 12E 7.71 Conservation of Energy: An experimental apparatus with mass

In summary, the question is asking for the force constant and initial compression distance of a spring in order to launch an animal without damaging it. This is achieved by using Conservation of Energy and Newton's Second Law, merging them using the compression distance x, and relating it to height h from gravitational potential energy and acceleration a from Newton's Second Law. The objective is to limit the forces so the animal is not harmed, which is achieved by pulling out x from the equation kx^2=ma and then plugging it into the equation for elastic potential energy. Once the final equation is obtained, a suitable k and x can be chosen to meet the objective.
  • #1
NamaeKana
16
0
The question is shown below the --- or this question and answerbook is from U Physics 12E #7.71. I uploaded a JPG that can be seen at http://i43.tinypic.com/35j9jja.jpg

I don't understand this problem. I see that to solve this Conservation of Energy and N2L are merged using x, and that h from Ugrav, and a from F=ma are thus related, but why ? I understand the algebra, but how does this merger model the problem ?

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An experimental apparatus with mass m is placed on a vertical spring of negligible mass and pushed down until the spring is compressed a distance x. The apparatus is then released and reaches its maximum height at a distance h above the point where it is released. The apparatus is not attached to the spring, and at its maximum height it is no longer in contact with the spring. The maximum magnitude of acceleration the apparatus can have without being damaged is a, where a > g.
(a) What should the force constant of the spring be?
(b) What distance x must the spring be compressed initially?
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  • #2
o.k. i get it now. we are propagating a to limit the forces so the block/animal launched doesn't break/die. so that's why we pull out x from kx^2=ma then plug x into Uel=Ug. the objective again it to limit. then after we get the final equation, we can pick a k and an x-compression that will work.
 

1. How does the experimental apparatus demonstrate conservation of energy?

The experimental apparatus with mass is designed to show the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another. The apparatus first has potential energy due to its position, then converts to kinetic energy as it falls, and finally converts back to potential energy when it reaches the bottom of the apparatus. The total energy remains the same throughout the process, demonstrating the conservation of energy.

2. What is the purpose of using an experimental apparatus to demonstrate conservation of energy?

An experimental apparatus is used because it allows for a controlled and measurable demonstration of the principle of conservation of energy. It provides a visual representation of how energy can be transferred and transformed, making it easier to understand and demonstrate the concept.

3. How does the mass of the apparatus affect the demonstration of conservation of energy?

The mass of the apparatus does not affect the demonstration of conservation of energy. The principle of conservation of energy applies to all objects, regardless of their mass. The only factor that affects the demonstration is the initial height of the apparatus, as this determines the potential energy at the start of the experiment.

4. Can the experimental apparatus be used to demonstrate other energy concepts?

Yes, the experimental apparatus can be used to demonstrate other energy concepts, such as potential and kinetic energy, as well as the relationship between work and energy. By adjusting the height and mass of the apparatus, different energy concepts can be explored and demonstrated.

5. How can the accuracy of the demonstration be improved?

To improve the accuracy of the demonstration, the apparatus should be designed with minimal friction and air resistance. This can be achieved by using smooth surfaces and reducing the size and weight of the apparatus. Additionally, multiple trials should be conducted and the results should be averaged to minimize any potential errors.

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