Question

6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring (in centimeters)

Answer 1

9.8 cm

Step-by-step explanation:

x = natural length

k*[(12 - x)² - (10 - x)²]/2 = 6 (1)

k*[(14 - x)² - (12 - x)²]/2 = 6 + 10 (2)

(1): k(144 + x² - 24x - 100 - x² + 20x) = 12

k(44 - 4x) = 12,

divide by 4, k(11 - x) = 3, k = 3/(11 - x)

(2): k(196 + x² - 28x - 144 - x² + 24x) = 32

k(52 - 4x) = 32

divide by 4, k(13 - x) = 8

3/(11 - x) * (13 - x) = 8

3(13 - x) = 8(11 - x)

39 - 3x = 88 - 8x

5x = 49

x = 9.8 cm