A 1-liter root beer bottle is immersed halfway in water.What is the buoyant force on the bottle?
1 answer:
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Answer:
(A) 0.2306 m
(B) 1.467 Hz
(C) 0.1152 m
Explanation:
spring constant (K) = 16.4 N/m
mass (m) = 0.193 kg
acceleration due to gravity (g) = 9.8 m/s^{2}
(A) force = Kx, where x = extension
mg = Kx
0.193 x 9.8 = 16.4x
x = 0.1153 m
now the mass actually falls two times this value before it gets to its equilibrium position ( turning point ) and oscillates about this point
therefore
2x = 0.2306 m
(B) frequency (f) = \frac{1}{2π} x
frequency (f) = \frac{1}{2π} x
frequency = 1.467 Hz
(C) the amplitude is the maximum position of the mass from the equilibrium position, which is half the distance the mass falls below the initial length of the spring
= \frac{0.2306}{2} = 0.1152 m