Question

A vertical scale on a spring balance reads from 0 to 250 N. The scale has a length of 15.0 cm from the 0 to 250 N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.60 Hz. Ignoring the mass of the spring, why is the mass m of the fish?

Answer 1

Answer:

Mass of fish=6.252 kg

Explanation:

Force F=0 N to 250 N

Length x=15.0 cm=0.15 m

Frequency f=2.60 Hz

To find

Mass of fish m

Solution

First we need to find spring constant

$k=Force/distance\\k=F/x\\k=250/0.15\\k=1666.7 N/m$

As we know that the time period is given as

$T=2\pi\sqrt{\frac{m}{k} }\\ And\\f_{Frequency} =1/T\\So\\1/f=2\pi\sqrt{\frac{m}{k} }\\1/f^{2}=4\pi^{2}\frac{m}{k}\\ k/f^{2}=4\pi^{2}m\\m=\frac{k}{4\pi^{2}f^{2} } \\m=\frac{1666.7}{4\pi^{2} (2.60)^{2} }\\ m=6.252kg$