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2 years ago

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Two or more velocities add by

1 answer:

forsale [732]2 years ago

6 0

Two or more velocities add by vector sum.
In fact, velocity is a vector, with its own intensity, direction and verse. Therefore, we cannot simply add two velocities by algebraic sum, but we need to decompose them on two axes (if we are in a 2D-plane) and calculate the resultant on each axis, and then calculate the total resultant of the two vectors, which will have its intensity, direction and verse.

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Consider a spherical tank full of water with radius 3 m (plus a spout on top 1m high). Set up an integral expression for the wor

sweet-ann [11.9K]

Answer:

The answer to the question is

4433.416 kJ

See explanation below

(3-y)²+r² = 3² or

6y-y² = r²

r =√(6y-y²)

The volume of a small section of height Δy = Δy ×(√(6y-y²))²×π

For water with density of 1000 kg/m³, the mass of the slice

= 1000×Δy ×(√(6y-y²))²×π and since force = mass × acceleration we have

1000×Δy ×(√(6y-y²))²×π ×g = 1000×Δy ×(√(6y-y²))²×π ×9.81

The work done to move a unit height of y+1 = Force × Distance

W = 1000×Δy ×(√(6y-y²))²×π ×9.81 × (y+1)

Integrating the entire section of the sphere that is 2×r high, or from 0 to 6 we get

W = $\int\limits^6_0 {1000*(6y-y^{2} ) *\pi *9.81 * (y+1)} \, dy$

= $9810*\pi \int\limits^6_0 {5y^{2} -y^{3} +6y \, dy$

$= 9810*\pi *[\frac{5y^{3} }{3} -\frac{y^{4} }{4} +3y^{2} ]^{6} _{0}$

=9810×π×144 =4433416 J

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3 years ago

Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. When properly tuned, the note

mote1985 [20]

Answer:

Frequency = 658 Hz

Explanation:

The third harmonics of A is,

$f_{A}=(3)(440Hz)=1320Hz$

The second harmonics of E is,

$f_{E}=(2)(659Hz)=1318Hz$

The difference in the two frequencies is,

delta_f = 1320 Hz - 1318 Hz = 2 Hz

The beat frequency between the third harmonic of A and the second harmonic of E is,

delta_f = $3f_{A}-2f_{E}$

$f_{E}=\frac{3f_{A}-delta_f}{2}$

We have calculate the frequency of the E string when she hears four beats per second, then

delat_f = 4 Hz

$f_{E}=\frac{3(440Hz)-4Hz}{2}$

$f_{E}=658Hz$

Hope this helps!

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