Question

which graph correctly shows the relationship between force and the amount of deformation an object will experience? amount of deformation (cm) force applied (n) amount of deformation (cm) force applied (n) amount of deformation (cm) force applied (n)

Explanation:

Step1: Recall Hooke's Law

According to Hooke's Law, within the elastic - limit, the force applied to a spring (or an elastic object) is directly proportional to the amount of deformation. The formula is $F = kx$, where $F$ is the force applied, $x$ is the amount of deformation, and $k$ is the spring - constant. A direct - proportional relationship is represented by a straight - line graph passing through the origin ($y = mx$ form, here $y = F$, $x$ is the deformation, and $m = k$).

Step2: Analyze the graphs

Graph A shows a straight - line with a positive slope, indicating that as the force applied increases, the amount of deformation increases in a linear fashion. This is consistent with Hooke's Law. Graph B shows a vertical line, which is not a valid representation of the relationship as it implies that for different forces, the deformation is the same. Graph C shows a negative slope, which means that as the force increases, the deformation decreases, which is not possible according to Hooke's Law for elastic objects under normal circumstances.

Answer:

A