Question

A vertical scale on a spring balance reads from 0 to 235 N . The scale has a length of 10.5 cm from the 0 to 235 N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.65 Hz .

Ignoring the mass of the spring, what is the mass m of the fish?

Express your answer in kilograms.

Answer 1

Given that :

spring force constant, F = 235 N

length of the scale, x = 10.5 cm = 0.105 m

using a hooke's law,      F = k x                                                     { eq.1 }

inserting the values in eq.1,

(235 N) = k (0.105 m)

k = (235 N) / (0.105 m)

k = 2238.1 N/m

Ignoring the mass of the spring, then the mass of the fish which will be given as :

using an equation,   f = [k / m ] / 2                                    { eq.2 }

2 f = k / m

squaring on both sides, we get

4 ² f² = k / m

Or        m = k / 4 ² f²                                                             { eq.3 }

where, f = oscillating frequency = 2.65 Hz

inserting the values in eq.3,

m = (2238.1 N/m) / 4 (3.14)² (2.65 Hz)²

m = [(2238.1) / (276.9)] kg

m = 8.08 kg