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

AI Thread Summary
The discussion revolves around a physics problem involving a man floating in water and the apparent weight measured by a fish scale as the boat undergoes simple harmonic motion (SHM). The scale reading fluctuates between 72kg and 178kg due to the boat's oscillation, with the wave characteristics provided: speed of 16 m/s, wave height of 3 m, and distance between crests of 4 m. The user is tasked with calculating the scale reading when the boat is at the midpoint of its oscillation. Key equations for wave motion and SHM are mentioned, including the relationship between wave speed, frequency, and angular velocity. The final goal is to determine the acceleration of the boat and how it affects the apparent weight during the oscillation.
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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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