Question

A vertical scale on a spring balance reads from 0 to 245 N . The scale has a length of 10.0 cm from the 0 to 245 N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.55 Hz . Ignoring the mass of the spring, what is the mass m of the fish?

Answer 1

9.55 kg

Step-by-step explanation:

F = 245 N

Let K be te spring constant

F = K x

K = 245 / 0.1 = 2450 N/m

ω = 2 x π x f = 2 x 3.14 x 2.55 = 16.014 rad/s

`\omega =\sqrt{(K)/(m)}`

where m be the mass of fish

`16.014 =\sqrt{(2450)/(m)}`

m = 9.55 kg

Answer 2

mass m of the fish is 7.35 kg

Step-by-step explanation:

Given data

spring balance reads = 0 to 245 N

length = 10.0 cm

scale reading = 0 to 245 N

frequency f = 2.55 Hz

to find out

mass m of the fish

solution

we know the relation that is

ω = √(k/m) ......................1

here k = spring reading / length = 245 / 0.135

k = 1814.81 N/m

and

ω = 2π × f

ω = 2π × 2.5 = 15.71 rad/s

so put all value in equation 1 we get m

ω = √(k/m)

15.71 = √(1814.81/m)

so m = 7.35

mass m of the fish is 7.35 kg