(6%) Problem 7: The force required to compress a non-standard spring as a functi
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Question
(6%) Problem 7: The force required to compress a non-standard spring as a function of displacement from, equilibrium x is given by the equation F(x) = ar. bx, where a spring. 55 N/m2, b = 18 N/m, and the positive x direction is in the compression direction of the 33% Part (a) Write a general equation in terms of the given variables for the work required to compress this spring frorn equilibrum to any point xp 33% Part (b) Calculate the work done, in joules, on the spring as it is compressed from x :0 tox,-58 cm. 33% Part (c) Calculate the work done, in joules, on the spring as it is compressed from x,-58 cm to x,-98 cm. 2=Explanation / Answer
here,
F = a x^2 - bx
a)
work done , W = integration( F .dx)
W = a x^3 /3 - b * x^2 /2
b)
for x = 0 m to x = 0.58 m
W = 55 * 0.58^3 /3 - 18 * 0.58^2 /2 - 0
W = 0.55 J
c)
for x = 0.58 m to x = 0.98 m
W = 55 * 0.98^3 /3 - 18 * 0.98^2 /2 - (55 * 0.58^3 /3 - 18 * 0.58^2 /2 )
W = 8.06 J
here,
F = a x^2 - bx
a)
work done , W = integration( F .dx)
W = a x^3 /3 - b * x^2 /2
b)
for x = 0 m to x = 0.58 m
W = 55 * 0.58^3 /3 - 18 * 0.58^2 /2 - 0
W = 0.55 J
c)
for x = 0.58 m to x = 0.98 m
W = 55 * 0.98^3 /3 - 18 * 0.98^2 /2 - (55 * 0.58^3 /3 - 18 * 0.58^2 /2 )
W = 8.06 J
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