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Force, Transverse Traveling and Natural Frenquency of a System

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4. A 70 kg ancient statue lies at the bottom of the sea (fresh water). Its volume is 3.0*10^4 (cm)^3.
a) How much force is required to lift it up at constant velocity through the water? (A force diagram would prove helpful in this problem).
b) If the statue was in salt water instead of fresh water, would the force required to lift the statue be greater or less than in fresh water? Explain.

5. A transverse traveling wave on a string is represented by

y(x,t) = 0.15 m sin [(0.393/m)x + (12.57rad/s)t]

where standard notation is used. For this wave, determine the

a) wavelength
b) frequency
c) velocity
d) amplitude
e) angular frequency and wave vector
f) magnitude of the maximum speed of particles on the string
g) magnitude of the maximum acceleration of particles on the string
h) direction of propagation of the wave
i) particle velocity and particle acceleration of the particle at x = 6m when t = 0.250s

6. a) Explain what characterizes a natural frequency of a system.
b) Explain what is meant by resonance, or driving the system at resonance.
c) Give an example of a system that has only one natural frequency and a system that has an infinite number of natural frequencies.
d) Explain what is meant by the principle of superposition.

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Solution Preview

Please refer to the attachment.




a) This problem is solved using Archimedes' principle according to which an object immersed in a liquid experiences an upward force (thrust) which is equal to the weight of the liquid displaced by the body. Hence, the forces experienced by the statue are i) the weight mg acting downwards and ii) the Upward thrust f of sea water, as shown in the fig..

Net downward force acting on the statue = mg - f

Hence, a minimum force F = mg - f is required to lift the statue off the sea bed.

Volume of the water displaced by the statue = Volume of the statue = 3x104 cu.cm = 3x104x10-6 or 3x10-2 m3

Density of fresh water = 1000 kg/m3

Mass of the water displaced by the statue = 3x10-2x1000 = 30 kg

Weight of the water displaced by the statue = 30 x 9.8 = 294 N

Weight of the statue = mg = 70 x 9.8 = 686 N

Minimum force required to lift the statue = F = 686 - 294 = 392 N

b) As the density of salt water is slightly greater than the fresh water, the upward thrust f will ...

Solution Summary

The solution discusses questions regarding force, transverse traveling and natural frequency of a system.