Respuesta :
Answer:151.6 J
Explanation:
Given
Natural length of spring [tex]L_o=46\ cm[/tex]
Length after extension [tex]x'=57\ cm[/tex]
Force applied [tex]F=100\ N[/tex]
we know
[tex]F=k x[/tex]
where K=spring constant
[tex]100=k\times (0.57-0.46)[/tex]
[tex]k=\frac{100}{0.11}[/tex]
[tex]k=909.09\ N\m[/tex]
Work done require to stretch a spring x m is given by
[tex]W=\frac{1}{2}kx^2[/tex]
From [tex]x_1=61\ cm[/tex] to [tex]x=84\ cm[/tex] Work done is
[tex]W=\frac{1}{2}\times 909.09(0.84^2-0.61^2)[/tex]
[tex]W=151.59\ J[/tex]
The work required to stretch it from 61 cm to 84 cm is 151J.
Spring-mass system:
Length of the spring, L = 46cm = 0.46m
Force applied to the spring is, F = 100N
Stretch of the spring, x = 57-46 = 11cm = 0.11 m
The restoring force of the spring is given by:
F = kx
where k is the spring constant.
100 = k×0.11
k = 909 N/m
The potential energy of the spring-mass system is given by:
PE = ¹/₂kx²
According to the work-energy theorem, the work done is given by the difference in the initial and final potential energy of the spring-mass system:
W = PE(final) - PE(initial)
W = ¹/₂×909(0.84² - 0.61²)J
W = 151 J
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