Answer:
mass of the fish m= 5.567 Kg
Explanation:
Assuming we have to find the mass of the fish m.
F_max on the vertical spring = 250 N
length of scale x = 14 cm
frequency of oscillation f= 2.85 Hz
for a spring F= Kx
k= spring constant
x= length of scale
K= F/x
=[tex]\frac{250}{14\times10^{-2}}[/tex]
= 1785. 71 N/m
Since, [tex]f= \frac{1}{2\pi} \sqrt{\frac{K}{m} }[/tex]
putting values we get
[tex]2.85= \frac{1}{2\pi} \sqrt{\frac{1785.71}{m} }[/tex]
solving the above equation we get
m= 5.567 Kg
Answer:
The mass of the fish is 5.56 kg.
Explanation:
Given that,
Force = 250 N
Length = 14.0 cm
Frequency = 2.85 Hz
Suppose ignoring the mass of the spring, what is the mass m of the fish?
We need to calculate the spring constant
Using formula of spring constant
[tex]k=\dfrac{F}{x}[/tex]
Where, F = force
x = length
Put the value into the formula
[tex]k=\dfrac{250}{14.0\times10^{-2}}[/tex]
[tex]k=1785.7\ N/m[/tex]
We need to calculate the mass of the fish
Using formula of frequency
[tex]f=\dfrac{1}{2\pi}\times\sqrt{\dfrac{k}{m}}[/tex]
[tex]m=\dfrac{k}{f^2\times4\pi^2}[/tex]
Put the value into the formula
[tex]m=\dfrac{1785.7}{2.85^2\times4\times\pi^2}[/tex]
[tex]m=5.56\ kg[/tex]
Hence, The mass of the fish is 5.56 kg.
