How Does SHM Affect Apparent Weight on a Fish Scale in Water Waves?

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SUMMARY

The discussion focuses on calculating the apparent weight of a man floating in water while subjected to simple harmonic motion (SHM) due to wave action. The oscillation of the fish scale reading, ranging from 72kg to 178kg, is influenced by the wave parameters: a wave speed of 16 m/s, a wave height of 3 m, and a wavelength of 4 m. The solution involves determining the angular velocity (w = 25.13 rad/s) and using it to find the acceleration of the boat, which directly affects the apparent weight measured by the scale.

PREREQUISITES
  • Understanding of simple harmonic motion (SHM)
  • Knowledge of wave properties: speed, wavelength, and frequency
  • Familiarity with the concept of apparent weight in accelerating reference frames
  • Ability to apply trigonometric functions in physics equations
NEXT STEPS
  • Calculate the acceleration of the boat using the wave parameters
  • Explore the relationship between wave height and apparent weight
  • Study the effects of SHM on buoyancy and floating objects
  • Learn about the principles of oscillation in fluid dynamics
USEFUL FOR

Students in physics, particularly those studying wave mechanics and dynamics, as well as educators looking for practical examples of SHM and buoyancy effects in real-world scenarios.

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Homework Statement



A man floating in water was spotted by fishermen on a boat. Before taking him on board, the man was put on a fish scale to see how much he weighed. The reading on the scale oscillated between 72kg and 178kg. The wave speed was measured to be 16 m/s. The wave height was 3 m, and distance between two wave crests was 4m.

Assuming the boat rocks up and down in perfect SHM, find the reading of the scale when the boat passes, on the way down trough the middle between the highest and lowest points. Answer in kg.

Homework Equations


x=Acos(wt) (A = amplitude)
V=λ*f
w=2pi*f (w = angular velocity)

The Attempt at a Solution


V=λ*f (V=16, λ=the distance between two crests = 4 meters)
so f = V/λ = 16/4 = 4 (also T=1/f so T=1/4)

w = 2pi*f
so w = 2pi * 4 = 25.13

I don't know what to do with this information...Please help me out. Exam is tomorrow.
 
Last edited:
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Find the acceleration of the boat from the given parameters of the wave (speed, amplitude, wavelength). Then remember the apparent weight of a body in an accelerating system of reference.

ehild
 

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