A fisherman's scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant (b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5cm more and released so that it vibrates up and down ...

Question

Mathematics

Dario Macias

14 October, 23:48

A fisherman's scale stretches 3.6 cm when a 2.7-kg fish hangs from it. (a) What is the spring stiffness constant (b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5cm more and released so that it vibrates up and down ...

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Anika Bradley · Answer 1

Hooke's law states that F = - kx, so

k = - F/x = - ma / x = - 2.6kg · (-9.8m/s²) / (0.041m) = 621 N/m ← (a)

(b) f = (1/2π) · sqrt (k/m) = (1/2π) · sqrt (621N/m / 2.6kg) = 2.46/s = 2.46Hz

Amplitude is simply 2.1cm