The spring force F and displacement x for a close-wound tension spring are measu

Question

The spring force F and displacement x for a close-wound tension spring are measured as shown in Fig. P1.2. The spring force F and displacement x satisfy the linear equation F = kx + F_i, where k is the spring constant and F_i is the preload induced during manufacturing of the spring. Using the given data in Fig. P1.2, find the equation of the line for the spring force f as a function of the displacement x, and determine the values of the spring constant k and preload F_i. Sketch the graph of F as a function 1 of x. Use appropriate axis scales 1 and clearly label the preload F_i the spring constant K, and both given data points on your graph.

Explanation / Answer

Solution

Given equation is: kx + Fi = F ....... .....(1)

Also given, F = 34.5 for x = 1.5 ...... ....(2)

and F = 57 for x = 3 ...... ....................(3).

(2) in (1): 1.5k + Fi = 34.5 ....... ...........(4)

(3) in (1): 3k + Fi = 57 ........................ (5)

2 x (4): 3k + 2Fi = 69 .......................(6)

(6) - (5): Fi = 12 ..................................(7)

(7) in (4): 1.5k + 12 = 34.5 or k = 15 .... (8)

(7) and (8) in (1) gives F as a function of x as: F = 12 + 15x ANSWER

The graph of F vs x is a straight line cutting y-axis at 12 and x-axis at - 0.8.

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