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A 10 kg brass load suspended by a brass wire 10 m long is observed to vibrate vertically in simple harmonic motion at a frequency of 10 Hz. What is the cross-sectional area of the wire?

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Final answer:

The cross-sectional area of the brass wire can be determined by using the formula for the frequency of a vibrating string or wire under tension, along with the weight of the 10 kg load and properties of brass.

Step-by-step explanation:

The question involves determining the cross-sectional area of a brass wire from which a 10 kg brass load is suspended. The wire is 10 m long and vibrates at a frequency of 10 Hz in simple harmonic motion (SHM). To calculate the cross-sectional area, we must use the formula for the frequency of a vibrating string or wire under tension:

f = (1/2L)√(T/μ), where f is the frequency, L is the length, T is the tension, and μ is the linear mass density.

The tension in the wire (T) is equal to the weight of the 10 kg load, which can be found using T = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.81 m/s²).

We also need to express the linear mass density (μ) as the mass per unit length, which depends on the cross-sectional area (A) and the density of brass (ρ): μ = ρA.

By arranging the formula to solve for A and substituting known values, we can solve for the cross-sectional area of the wire.

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