Question

A vertical scale on a spring balance reads from 0 to 250 N . The scale has a length of 14.0 cm from the 0 to 250 N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.85 Hz .

Answer 1

The mass of the fish is 5.56 kg.

Step-by-step 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

`k=(F)/(x)`

Where, F = force

x = length

Put the value into the formula

`k=(250)/(14.0*10^(-2))`

`k=1785.7\ N/m`

We need to calculate the mass of the fish

Using formula of frequency

`f=(1)/(2\pi)*\sqrt{(k)/(m)}`

`m=(k)/(f^2*4\pi^2)`

Put the value into the formula

`m=(1785.7)/(2.85^2*4*\pi^2)`

`m=5.56\ kg`

Hence, The mass of the fish is 5.56 kg.

Answer 2

mass of the fish m= 5.567 Kg

Step-by-step 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

=
`(250)/(14*10^(-2))`

= 1785. 71 N/m

Since,
`f= (1)/(2\pi) \sqrt{(K)/(m) }`

putting values we get

`2.85= (1)/(2\pi) \sqrt{(1785.71)/(m) }`

solving the above equation we get

m= 5.567 Kg