Conservation/Conversion of energy

  • Thread starter drkidd22
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In summary, a 4.5kg mass is dropped from a height of 3.3m above a spring with a spring constant of 25N/cm. Using the equations for force, potential energy, and velocity, it is determined that the spring will compress approximately 0.7m. However, in order to accurately solve for the compression, the spring energy must also be taken into account. By setting the initial energy equal to the final energy and considering the spring energy, the correct value for the spring compression can be calculated.
  • #1
drkidd22
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Homework Statement


A mass of 4.5kg is dropped from a height of 3.3m above a spring. spring const is 25N/cm. How much is the spring compressed.


Homework Equations



F = 4.5*9.8 = 44.1

PE = mgh = 4.5*3.3*9.8 = 145.53

v = sqrt(2(9.8)(3.3)) = 8.04m/s

The Attempt at a Solution



The above are the few things I was able to grab out of the given information. The issue I'm having is plugging this into an equation to find the spring
 
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  • #2
Energy is conserved in this problem. If you write
initial energy = final energy
and then fill in the details of the kinds of energy involved you will be able to solve for the spring compression.
 
  • #3
so I get that mgh = 1/2mv^2+mgh?

145.53 = .5(4.5)(8.04)^2+(4.5)(9.8)h

.7m?

I don't think I did it right
 
  • #4
Well I looked into a few of the formulas on the book and I get to a quadratic equation, but I'm still missing something here and I'm not sure what it is.

.5(.25)Y^2-(4.5)(9.8)Y+4.5(9.8)(-3.3)
0.125Y^2-44.1Y+145.53.

356? That's not possible so any adive on this will be appreciated.

Thnsx
 
  • #5
Got it done. My equation above is right, the only problem was that I had to convert N/cm to N/m.

Thanks
 
  • #6
You didn't consider the spring!
Initially you have the mgh. When the mass hits the spring, it comes to a stop and you only have spring energy ½kx².
 

What is conservation of energy?

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

What is conversion of energy?

Conversion of energy is the process of transforming energy from one form to another. This can occur naturally, such as the conversion of sunlight into chemical energy through photosynthesis, or through human-made devices like generators and batteries.

Why is conservation of energy important?

Conservation of energy is important because it is a fundamental law of nature that governs how energy behaves. It allows us to understand and predict the behavior of physical systems, and it is the basis for many technological advancements.

How does energy conversion affect the environment?

Energy conversion can have both positive and negative impacts on the environment. For example, the use of renewable energy sources can reduce harmful emissions, while the extraction and use of fossil fuels can contribute to air and water pollution and climate change.

What are some examples of energy conservation?

There are many ways to conserve energy, including turning off lights and electronics when not in use, using energy-efficient appliances, and using public transportation or carpooling instead of driving alone. Conserving energy can also involve using renewable energy sources and reducing our overall energy consumption.

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