A vertical scale on a spring balance reads from 0 to 185N . The scale has a leng

Question

A vertical scale on a spring balance reads from 0 to 185N . The scale has a length of 13.0cm from the 0 to 185N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.90Hz .Ignoring the mass of the spring, what is the mass of the fish in kg? A vertical scale on a spring balance reads from 0 to 185N . The scale has a length of 13.0cm from the 0 to 185N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.90Hz .Ignoring the mass of the spring, what is the mass of the fish in kg?

Explanation / Answer

when a weight of 195 N is put on the scale, the spring extends by 13.5 cm. From Hooke's Law, that means the spring constant, k, is given by:

F = -k*delta-x

185 N = -k * (-0.130 m)

k = 1.423 *10^3 kg/s^2

A massless spring with a nonzero mass (M) attached to it will oscillate with a natural frequency, in Hz, of:

f = (sqrt(k/M))/(2*pi)

Plugging in the appropriate values for this problem, and solving for M, we have:

M = k/(2*pi*f)^2

M = (1.423 *10^3 kg/s^2)/(2*pi*2.9 s^-1)^2

M = 4.286 kg

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