A spring is extended 15 cm from its equilibrium point. If the spring constant k is 75 N/m, the magnitude and direction of the elastic force F_el are described by which of the following?

Question

Quizplus · Accepted Answer

11ecba2d_1326_ff57_a3bf_23839806a119_MD0008_00 An elastic force (F_el) is generated when displacing a spring or other elastic object from its equilibrium point, which is the natural, nondisplaced position of an elastic object. According to Hooke's law, F_el is a function of the object displacement (x) and the elastic constant (k). This is expressed mathematically as: 11ecba2d_1326_ff58_a3bf_83e237988c56_MD0008_00 The value of k quantifies the relative elasticity of an object, which is attributable to its shape and the molecular structure of the material from which it is created. Although no material is perfectly elastic, Hooke's law is still useful in modeling the elastic forces generated by springs and other elastic objects. When applying Hooke's law, F_el is typically expressed as a negative (−) quantity because F_el acts counter to the direction of displacement. For example, extending a spring (ie, lengthening it) requires a displacing force (F) to perform some mechanical work on the spring over a positive (+) distance. Because the spring will rapidly return to its equilibrium position and undergo harmonic oscillations if F is withdrawn, F_el opposes F and is therefore expressed as a negative quantity. In this question, a spring with an elastic constant (spring constant) of 75 N/m is extended 15 cm from its equilibrium point. When converted to meters, the displacement of the object due to stretching is: 11ecba2d_1326_ff59_a3bf_eba0067983b1_MD0008_00 Using Hooke's law to calculate F_el gives: 11ecba2d_1326_ff5a_a3bf_635909dddc83_MD0008_00 11ecba2d_1326_ff5b_a3bf_d1668ffcf8f1_MD0008_00 Consequently, the magnitude of F_el is: 11ecba2d_1327_266c_a3bf_2df99f2f657a_MD0008_00 Furthermore, F_el points toward the equilibrium point because F_el acts to oppose the extension and restore the stretched spring back to its shorter natural position. Therefore, extending the spring 15 cm from its equilibrium point will generate an elastic force that has a magnitude of 1.1 × 10¹ N and is oriented toward the equilibrium point (Choice B). Educational objective: Hooke's law may be used to calculate the elastic forces generated by the compression and extension of springs and other elastic objects. The magnitude of the elastic force varies with displacement, but elastic forces are always oriented toward the equilibrium point.

A Spring Is Extended 15 Cm from Its Equilibrium Point