∙A student measures the force required to stretch a spring...

$\bullet$ A student measures the force required to stretch a spring by various amounts and makes the graph shown in Figure 5.57 which plots this force as a func- tion of the distance the spring has stretched. (a) Does this spring obey Hooke's law? How do you know? (b) What is the force constant of the spring, in $\mathrm{N} / \mathrm{m}$ ? (c) What force would be needed to stretch the spring a distance of 17 $\mathrm{cm}$ from its unstretched length, assuming that it continues to obey Hooke's law?

$\bullet$ A student measures the
force required to stretch a spring
by various amounts and makes
the graph shown in Figure 5.57
which plots this force as a func-
tion of the distance the spring
has stretched. (a) Does this
spring obey Hooke's law? How
do you know? (b) What is the
force constant of the spring, in $\mathrm{N} / \mathrm{m}$ ? (c) What force would
be needed to stretch the spring a distance of 17 $\mathrm{cm}$ from
its unstretched length, assuming that it continues to obey
Hooke's law?

Key Concepts

Hooke's Law

Hooke's law is a fundamental principle in mechanics which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position, provided the deformation is within the elastic limit of the spring. This relationship is typically expressed as F = kx, where F is the force, k is the spring constant, and x is the displacement.

Spring Constant

The spring constant, denoted by k, quantifies the stiffness of a spring. It is defined as the ratio of the force applied to the displacement produced, and it can be determined experimentally as the slope of the force versus displacement graph. A higher spring constant indicates a stiffer spring that requires more force to produce the same displacement.

Graphical Analysis of Force-Extension Relationships

Graphical analysis is used to determine the relationship between force and displacement in experiments involving springs. By plotting the applied force against the displacement, one can determine if the relationship is linear, which is a key indicator that Hooke's law is being followed. The slope of this linear graph represents the spring constant, making it a crucial method for analyzing the elastic properties of the spring.

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