Finding work done in compressing (forging) a solid cylinder

In summary, the problem involves finding the change in temperature of a forged cylinder made of annealed copper. The necessary information, such as the density and specific heat, is provided. However, the work done on the cylinder is also required, which has proven difficult due to the presence of a non-zero coefficient of kinetic friction. Attempts to find the work using an excel graph have been unsuccessful, but the mistake was identified and corrected.
  • #1
MechEngrStdnt
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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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  • #2
Figured it out, bounds were incorrect. X axis was in terms of percentage increase, not actual increase.
 

1. How is work done calculated in compressing a solid cylinder?

The work done in compressing a solid cylinder can be calculated using the formula W = F x d, where W is the work done, F is the force applied, and d is the distance the cylinder is compressed.

2. What factors affect the work done in compressing a solid cylinder?

The work done in compressing a solid cylinder is affected by the force applied, the distance the cylinder is compressed, and the properties of the material being compressed, such as its elasticity and strength.

3. How does the shape of the cylinder affect the work done in compressing it?

The shape of the cylinder can affect the work done in compressing it, as cylinders with larger diameters require more force to compress than cylinders with smaller diameters. This is because the surface area of the cylinder increases with its diameter, resulting in a larger force being needed to compress it.

4. What is the relationship between work done and energy in compressing a solid cylinder?

The work done in compressing a solid cylinder results in the conversion of mechanical energy to potential energy, as the compression increases the potential energy stored in the material. The amount of energy stored is equal to the work done in the compression process.

5. How does temperature affect the work done in compressing a solid cylinder?

The temperature of the cylinder can affect the work done in compressing it, as higher temperatures can cause the material to become more pliable and easier to compress. This can result in less work being done to achieve the same amount of compression compared to a cylinder at a lower temperature.

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