Question

A student measures the force required to stretch a spring by various amounts and makes the graph shown in Figure, which plots this force as a function 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 N/m? (c) What force would be needed to stretch the spring a distance of 17 cm from its unstretched length, assuming that it continues to obey Hooke’s law?

FIGURE 5.57

Answer 1

From Hooke’s law, the magnitude of spring force is directly proportional to the stretched distance.

Here, F is the spring force, k is the spring constant, and x is the stretched distance of spring.

The slope of the force vs distance graph gives the spring constant.

(a)

From the graph, as the force increases, the spring distance also increases. The graph is accordance with Hooke’s law.

Yes, the spring obeys the Hooke’s law. Because the graph of F vs x is a straight line.

(b)

Rearrange the equation for k.

From the graph, the distance at force 15 N is 10 cm.

Substitute 15 N for F, and 10 cm for x in .

Therefore, the spring constant is .

(c)

Calculate the force as follows:

Substitute 150 N/m for k, and 17 cm for x in .

Round off to two significant figures, the required force is .