Chapter 10, Problem 2FC

To determine

The graph that correctly represents the restoring force F as a function of the displacement x.

Answer to Problem 2FC

The graph provided in option (c) correctly represents the restoring force F as a function of the displacement x.

Explanation of Solution

Description:

Write the expression for the restoring force of an ideal spring.

$F_x=-kx$ (1)

Here

$F_x$ is the restoring force,

k is the spring constant, and

x is the displacement.

From Expression (1), it is observed that the restoring force is always in a direction opposite to the displacement of the spring. That is, if the value of restoring force is positive, the displacement value must be negative.

In graph (c), the displacement value is positive whenever the force is negative and the displacement is negative whenever the force is positive. Hence option (c) is correct.

In graph (a), the both displacement and force have same sign. Hence, the option (a) is incorrect.

In graph (b), the force value is positive for both positive and negative values of the displacement. Hence, the option (b) is incorrect.

In graph (d), the force value is negative for both positive and negative values of the displacement. Hence, the option (d) is incorrect.

In graph (e), the displacement value is negative for both positive and negative values of the force. Hence, the option (e) is incorrect.

Conclusion:

Thus, the graph provided in option (c) correctly represents the restoring force F as a function of the displacement x.