# ± The Fish Scale (mastering physics)?

A vertical scale on a spring balance reads from 0 to 220N . The scale has a length of 15.0cm from the 0 to 220N reading. A fish hanging from the bottom of the spring oscillates vertically at a frequency of 2.45Hz .

Part A

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

Relevance

k = 200N / 0.15m = 1333 N/m

for simple harmonic motion

f = ω / 2π

where ω = √(k/m)

2πf = √(k/m)

(2πf)² = k/m

m = k / (2πf)²

m = 1333 / (2π2.45)²

m = 5.63 kg

Edit

Jully Wum is correct. I erred on the force value. (I really dislike the new Answers format which makes this type of error easier to make)

m = (220 / 0.15) / (2π2.45)²

m = 6.19 kg

• Login to reply the answers
• Spring force constant .. k = 220N /0.15m .. .. k = 1466.70 N/m

Frequency of a loaded spring .. f = 1/T = 1 / {2π√(m/k)}

f = 2.45 Hz = (1/2π) x √(k/m)

2.45² = (1/4π²) x k/m

m = (1/4π²) 1466.7 / 2.45² .. .. ►m = 6.20 kg

Damon has used an equivalent method .. but the wrong force (200N)

• Login to reply the answers