If a titanium bar with a mass of 2 kg and a length of 3 m shortens by 0.02 mm under a compressive load of 3,900 kN, what is the strain?

To determine the strain in the titanium bar, we first need to understand the definition of strain, which is the ratio of the change in length (deformation) to the original length of the material. The formula to calculate strain is:

[ \text{Strain} = \frac{\Delta L}{L_0} ]

where:

• ( \Delta L ) is the change in length (which will be negative for a shortening scenario)

• ( L_0 ) is the original length

In this scenario:

• The original length ( L_0 ) is 3 m, which is equivalent to 3000 mm (to match the units of change in length).

• The change in length ( \Delta L ) is -0.02 mm (negative because the bar shortens).

Substituting these values into the strain formula gives us:

[ \text{Strain} = \frac{-0.02 , \text{mm}}{3000 , \text{mm}} = -0.0000066667 ]

This value can also be expressed in scientific notation as -6.666 * 10⁻⁶, which corresponds exactly to the choice given.