How much mass can a brass spring hold without becoming permanently bent?

In summary, the conversation is about solving a problem involving a brass spring with a mass attached to it. The problem asks for the distance the mass will drop before bouncing back, using conservation of energy and solving for the answer in terms of k, m, and g. The second part involves determining the maximum mass that can be used without permanently bending the spring, assuming the same value for k. The solution involves using the kinetic energy equation and setting it equal to the energy transferred by gravity minus the energy absorbed by the spring. This can be verified by finding the acceleration and integrating to find the velocity, setting it to zero.
  • #1
psruler
40
0
Hi, i need help on this problem:

A brass spring (with spring constant k) with no mass on it hangs vertically from fixed support bar, at rest. You attach a mass m to the free end and release it; how far does the mass drop before the spring brings it to a (brief) stop and it starts to bounce back: Use conservation of energy, and show your work. Solve for your answer in terms of k, m, and g. Ignore mass of the spring itself.

2) Your spring stretches more than 50 cm from its rest position, it will become permanently bent out of shape. What is the largest mass ( to 2 significant figures) that you would dare to use for your dropping experiment in part (a)? Assume the same value for k.
 
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  • #2
I'm going to have to venture a guess at this, since you haven't posted any of your work.

You need to establish a baseline for the potential energy. It doesn't matter where it is because only the change in potential energy is what's important, but you need to arbitrarily establish one never-the-less. I suggest using either the rest position of the spring or the (as yet unknown) lowest position of the mass.

From there, why don't you write the conservation of energy equation and see what you get?

cookiemonster
 
  • #3
Observe that the kinetic energy of the mass at a distance [tex]x[/tex] from rest equals the energy transferred by gravity ( [tex]mgx[/tex] ) minus the energy absorbed by the spring ( [tex]\frac{1}{2}kx^2 [/tex]). Use this info to solve for x when the kinetic energy is zero.

You can verify that result by setting up an equation for the acceleration ( [tex]g-(\frac{k}{m})x[/tex] ) and integrating it to find its velocity and setting that to zero.
 
Last edited:
  • #4
Thanks palpatine!
 

1. What is conservation of energy?

Conservation of energy is a fundamental law of physics which states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.

2. Why is conservation of energy important?

Conservation of energy is important because it has numerous practical applications, such as reducing energy waste, promoting sustainability, and improving efficiency in various systems. It also helps us to better understand and predict the behavior of physical systems.

3. How can I conserve energy in my daily life?

There are many ways to conserve energy in your daily life, such as turning off lights and electronics when not in use, using energy-efficient appliances, taking public transportation or carpooling, and using renewable energy sources like solar or wind power.

4. What role does conservation of energy play in addressing climate change?

Conservation of energy plays a crucial role in addressing climate change because the production and consumption of energy is a major contributor to greenhouse gas emissions. By conserving energy and using renewable sources, we can reduce our carbon footprint and mitigate the effects of climate change.

5. How can I get involved in conservation of energy efforts?

There are many ways to get involved in conservation of energy efforts, such as supporting legislation for renewable energy, participating in energy efficiency programs, volunteering with environmental organizations, and advocating for sustainable practices in your community.

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