A vertical scale on a spring balance reads from 0 to 200 / rm{N}. The scale has a length of 10.0 / rm{cm} from the 0 to 200 / rm{N} reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.05 / rm{Hz}.

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

Question

Physics

Salty

23 June, 22:33

A vertical scale on a spring balance reads from 0 to 200 / rm{N}. The scale has a length of 10.0 / rm{cm} from the 0 to 200 / rm{N} reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.05 / rm{Hz}.

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

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Answers (1)

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Gabriel Sherman · Answer 1

m = 12.05 kg

Explanation:

Spring constant in K, N/m

K = 200/10 * 100

K = 2000 N/m

Angular Frequency = sqrt (Spring constant / (Mass)

ω = 2 π f

ω = 2π * 2.05 Hz = 12.8805 rad/s

ω^2 = Spring constant / Mass

Mass = Spring constant / ω^2

ω^2 = 165.907 rad^2/s^2

m = 2000 (N/m) / 165.907 (rad^2/s^2)

m = 12.05 kg