A 0.51-kg crow lands on a slender branch and bobs up and down with a period of 1

Question

A 0.51-kg crow lands on a slender branch and bobs up and down with a period of 1.4 s . An eagle flies up to the same branch, scaring the crow away, and lands. The eagle now bobs up and down with a period of 3.7 s .

Part A

Treating the branch as an ideal spring, find the effective spring constant of the branch.

Express your answer to two significant figures and include the appropriate units.

Part B

Find the mass of the eagle.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A) mass of the crow = 0.51 kg

time period = 1.4 s

time period = 2pi *sqrt(m/K)

where m = mass of the object , K = spring constant

1.4 = 2*3.14*sqrt( 0.51/k)

k = 10.27 N-m

the spring constant of the branch if considered an ideal spring is 10.27 N/m

B) for the mass of eagle , we use the same formula for the time period

the time period of the eagle = 3.7 s

3.7 = 2*pi*sqrt(m/10.27)

m = 3.56 kg

mass of the eagle = 3.56 Kg

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