How can we calculate the ultimate tensile strength if we have the maximum load and cross-sectional area of a sample?

Ultimate tensile strength (UTS) is a measure of the maximum amount of tensile stress that a material can withstand before failure. To calculate UTS, you need two key pieces of information: the maximum load that the material can bear and the cross-sectional area over which that load is applied.

The correct approach to find the ultimate tensile strength is to divide the maximum load by the cross-sectional area of the sample. This division results in a value that reflects the stress, typically measured in units like megapascals (MPa) or pounds per square inch (psi). The formula can be represented as:

[ \text{UTS} = \frac{\text{Maximum Load}}{\text{Cross-sectional Area}} ]

This indicates how many pounds (or newtons) are held on each square inch (or square millimeter) of the material. It provides insight into the material's ability to withstand tension before failure.

The other options suggest incorrect methods of calculation that do not align with the established formula for determining tensile strength. For instance, using the original area or manipulating loads in ways that do not pertain to the ultimate tensile strength calculation would not yield an accurate representation of the material's strength.