Question

Calculate the final volume (in cm3) of a 40 cm long cylindirical copper rod with a cross-sectional area of

1. 2 cm² when it is

stretched with a load of 4. 0×105 Newtons,

(ν= 0. 32, E= 70 GPa, σy = 300 GPa, σTS= 650 GPa, rCu = 120 pm)

Answer 1

The final volume of the cylindrical copper rod is 48.09143 cm³.

Step-by-step explanation:

To calculate the final volume of the cylindrical copper rod, we can use the formula:

Final volume = initial volume + change in volume

First, let's calculate the initial volume. The initial volume can be calculated using the formula:

Initial volume = cross-sectional area × length

Given that the cross-sectional area is 1.2 cm² and the length is 40 cm, the initial volume is:

Initial volume = 1.2 cm² × 40 cm = 48 cm³

Now, let's calculate the change in volume. The change in volume can be calculated using the formula:

Change in volume = (ν × load) / (E × cross-sectional area)

Given that ν is 0.32, the load is 4.0×105 Newtons, E is 70 GPa (70 × 10^9 Pa), and the cross-sectional area is 1.2 cm², the change in volume is:

Change in volume = (0.32 × 4.0×105 N) / (70 × 10^9 Pa × 1.2 cm²)

Change in volume = 0.09143 cm³

Now, we can calculate the final volume:

Final volume = 48 cm³ + 0.09143 cm³ = 48.09143 cm³

Therefore, the final volume of the cylindrical copper rod is 48.09143 cm³.