A balsa wood block of mass 55g floats on a lake, bobbing up and down at a freque

Question

A balsa wood block of mass 55g floats on a lake, bobbing up and down at a frequency of 2.9Hz .

Part A What is the value of the effective spring constant of the water? Express your answer to two significant figures and include the appropriate units.

Part B A partially filled water bottle of mass 0.29kg and almost the same size and shape of the balsa block is tossed into the water. At what frequency would you expect the bottle to bob up and down? Assume SHM. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

A balsa wood block of mass 55 g floats on a lake, bobbing up and down at a frequency of 2.5 Hz

(a) What is the value of the effective spring constant of the water?

(a) T = 1/f
T = 2pi ( m/k )^1/2

f - frequency
m - mass
k - spring constant

1/f = 2pi ( m/k )^1/2
1/2.9 = 2pi ( 0.052/k )^1/2
k = 12.34 Nm^-1

(b) 1/f = 2pi ( 0.29/11.825 )^1/2
f = 1.21 Hz

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