Finding work done in compressing (forging) a solid cylinder

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SUMMARY

The discussion focuses on calculating the work done during the compression of an annealed copper cylinder, which is reduced from a height of 2 inches to 0.6 inches. The user has successfully determined the forging forces and has the necessary parameters, including a density of 0.37336 lb/in³ and a specific heat of 861 in-lb/lb°F. The challenge arises when incorporating the coefficient of kinetic friction, which complicates the work calculation. The user ultimately resolves their issue by correcting the bounds used in their Excel plotting, ensuring accurate results.

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  • Understanding of thermodynamics and work-energy principles
  • Familiarity with material properties, specifically for annealed copper
  • Proficiency in using Excel for data analysis and graphing
  • Knowledge of friction coefficients and their impact on mechanical work
NEXT STEPS
  • Study the principles of work done in thermodynamic processes
  • Learn about the effects of friction on work calculations in mechanical systems
  • Explore advanced Excel techniques for data visualization and analysis
  • Investigate the properties of different materials under compression
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Mechanical engineers, materials scientists, and students studying thermodynamics or materials processing who are involved in calculating work done during material deformation.

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Homework Statement


The problem is asking to find the change in temperature of forged cylinder. I know how to calculate this,
upload_2015-4-26_13-11-9.png
, however I am struggling to find the work done on the cylinder, which is required to solve this problem. The cylinder is annealed copper, which is compressed from a height on 2in to 0.6in. I was able to find the forging forces (attached below in excel screen shot), and they are correct. I am given the density: 0.37336lb/in^3, and the specific heat: 861in-lb/lb°F, now I just need to find the work done on the cylinder.

Homework Equations

The Attempt at a Solution


When the coefficient of friction is 0, the work is easy to find,
upload_2015-4-26_13-3-6.png

However once the coefficient of kinetic friction is non-zero, this equation no longer applies.

I tried finding the area under the curve by plotting in excel and extracting the equation, however the values I am getting are not even close, I'm pretty sure I'm making some conceptual mistake, any help is much appreciated.

upload_2015-4-26_13-5-14.png
 

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Figured it out, bounds were incorrect. X axis was in terms of percentage increase, not actual increase.
 

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