Respuesta :
Answer:
L = 7 cm
Step-by-step explanation:
Given,
natural length,L = 30 cm
Force to stretch the spring to 40 cm, F = 24 N
We know,
F = k Δ x
24 = k × (0.4 - 0.3)
0.1 k = 24
k = 240 N/m
now,
Work done calculation to stretch it from 30 cm to 35 cm
[tex]W =\dfrac{1}{2}kx^2[/tex]
[tex]W =\dfrac{1}{2}\times 240 \times 0.05^2[/tex]
W = 0.3 J
b) Work done to stretch from 9 cm to 11 cm
W = 0.6 J
Let L be the natural length
[tex]W =\dfrac{1}{2}kx^2[/tex]
[tex]0.6 = \dfrac{1}{2}k((11-L)^2-(9-L)^2)[/tex]
[tex]1.2 = k(40-4L)[/tex]
[tex]k = \dfrac{1.2}{40-4L}[/tex].........(1)
When spring is stretched from 11 cm to 13 cm
W = 1 J
[tex]W =\dfrac{1}{2}kx^2[/tex]
[tex]1 = \dfrac{1}{2}k((11-L)^2-(9-L)^2)[/tex]
[tex]2 = k(40-4L)[/tex]
[tex]k = \dfrac{2}{48-4L}[/tex]......(2)
Form equation (1) and (2)
[tex]\dfrac{1.2}{40-4L}=\dfrac{2}{48-4L}[/tex]
on solving
L = 7 cm
Hence, the natural length of the spring is equal to 7 cm.
