Question

The results of a test of a metal are shown in the table, with strain in meters per meter, andstress in units called megapascals, or MPa. Stress is a measure of how much force is applied tothe metal, and strain is a measure of how far the metal bends under that force.a. Make a graph of the data with strain on the horizontal axis.b. Hooke's law states that stress is directly proportional to strain. Does the metal obey Hooke'slaw for in any part of its domain? Explain your reasoning.c. Write a function that models this material over the domain you found in part b.d. The ultimate tensile strength is the maximum value on the stress-strain curve. What are thestress and strain values for this material's ultimate tensile strength?

Answer 1

a.

b.

The metal obey this law for values of strain until 0.05, where we have a linear relationship (each increase of 0.01 in the strain causes an increase of 100 in the stress). After this point, we don't have a linear relationship anymore.

c. Since an increase of 0.01 in the strain causes an increase of 100 in the stress, the slope is:

$m=\frac{100}{0.01}=10000$

Now, calculating the coefficient b (y-intercept), we have:

$\begin{gathered} (0.01,100)\colon \\ 100=0.01\cdot10000+b \\ 100=100+b \\ b=0 \end{gathered}$

So the equation is:

$y=10000x$

d.

The maximum value of stress is 560, and occurs at strain = 0.07.