Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

256 Chapter 10 Force and Force-Related Parameters

where

Fapplied force (N or lb)

kspring constant (N/mm or N/cm or lb/in.)

xdeformation of the spring ( mm or cm or in.— use units that are consistent withk)

Byelastic rangewe mean the range over which if the applied force is removed the internal spring

force will return the spring to its original unstretched shape and size and do so with no per-

manent deformation. Note the spring force is equal to the applied force. The value of the spring

constant depends on the type of material used to make the spring. Moreover, the shape and

winding of the spring will also affect itskvalue. The spring constant can be determined

experimentally.

Example 10.1 For a given spring, in order to determine the value of the spring constant, we have attached dead

weights to one end of the spring, as shown in Figure 10.5. We have measured and recorded the

deflection caused by the corresponding weights as given in Table 10.1(a). What is the value of the

spring constant? We have plotted the results of the experiment using Excel (shown in Figure 10.6).

The spring constantkis determined by calculating the slope of a force-deflection line

(recall that the slope of a line is determined from slope rise /run, and for this problem,

the slope change in force /change in deflection). This approach leads to a value of

k0.54 N/mm.

Often, when connecting experimental force-deflection points, you may not obtain a

straight line that goes through each experimental point. In this case, you will try to come up

with the best fit to the data points. There are mathematical procedures (including least-squares

techniques) that allow you to find the best fit to a set of data points. We will discuss curve

fitting using Excel in Section 14.8, but for now just draw a line that you think best fits the data

points. As an example, we have shown a set of data points in Table 10.1(b) and a good corre-

sponding fit in Figure 10.7.

25

20

15

10

5

0

0 102030

Deflection (mm)

Force-deflection

40

Force (load) (N)

■Figure 10.6

The force-deflection diagram for the spring in Example 10.1.

■Figure 10.5

The spring setup.

TABLE 10.1(a) The Results of the

Experiment for Example 10.1

The Deflection

Weight (N) of the Spring (mm)

4.9 9

9.8 18

14.7 27

19.6 36

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