The value of "k" for spring constant, is the book answer incorrect?

[SShep71]

Homework Statement

1-3. The spring force F and displacement y for a close-wound tension spring are measured as shown in Fig. P1.3 The spring force and displacement satisfy the linear equation y=((1/k)F-(Fi/k)
, where k is the spring constant and Fi is the preload induced during manufacturing of the spring.

(a) Determine the spring constant k and the pre-load F using the given data in Fig. P1.3. (b) Sketch the graph of the line y(F) and clearly indicate both the spring constant k and preload Fi using the given data.

Relevant Equations

y=((1/k)F-(Fi/k))

There is some discussion currently and I was hoping to get some opinions here. The question is in regard to a Hook's law problem. The text gives the problem as seen below. The text says the answer is 50lb/in. Several people have tried from several different approaches. Factoring the "y" equation to solve for Fi, straight method, etc.

In case the image does not work, here are the specifics:
k= spring constant
Fi=preload at manufacturing
F=spring force
y=displacement

Observations:
F(lbf) y(in)
100 1.0
75 0.5

The students are to determine the "Fi" and "k" values. The book states 50lb/in as the answer

 

[PeroK]

Observations:
F(lbf) y(in)
100 1.0
75 0.5

The students are to determine the "Fi" and "k" values. The book states 50lb/in as the answer

If the relationship between (total) applied force and (total) displacement is linear, then (using that data) an additional extension of 0.5 inches requires an additional force of 25 lbf. Hence $k = 50$ lbf per inch.

 

[SShep71]

No disagreement from me, the logic is sound. I guess it's the method of algebraically solving it that seems to have a few "twisted-under britches" in this group.

 

[PeroK]

No disagreement from me, the logic is sound. I guess it's the method of algebraically solving it that seems to have a few "twisted-under britches" in this group.

Note that your relevant equation:

Relevant Equations: y=((1/k)F-(Fi/k))

Can be simplified to:
$$\Delta y = \frac{\Delta F}{k}$$Which may help to straighten out your britches.