Interpretation:
The percent cold work (% CW) for the given two cases should be determined.
Concept Introduction:
The general relationship between the percentage cold working and area is based on the formula:
For the above equation,
Answer to Problem 8.25P
The value of percent cold working for 2-inch diameter reduced to 1.5 in. and then to 1 in. diameter is
The value of percent cold working for 2inches to 1-inch diameter is
Explanation of Solution
Given Information:
A copper rod is reduced from 2 inches diameter to 1.5-inchdiameter and on further reduction attaining the value of final diameter as 1 inch.
For the next case, the diameter is reducing in a single step that is from a value of 2 inches to 1 inch
As,
On substituting the value of area in the above formula of percentage cold working,
Now, on substituting the value of initial diameter and final diameter,
Calculation of percent cold working when the initial diameter of 2 inches is further reduced to 1 inch
As given,
Initial diameter
Reducing diameter
On substituting the values of diameter in the above equation of cold working,
For third case, calculation of percent cold working when the initial diameter of 2-inch is reduced to 1-inch
As given:
Initial diameter
Reducing diameter
On substituting the values of diameter in the above equation of cold working,
The value of percent cold working for a diameter change of 2inch to 1.5 inch is 43.75%.
The value of percent cold working for a diameter change of 2inch to 1 inch is 75%.
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