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nekit [7.7K]
3 years ago
11

An unstable atomic nucleus of mass 1.82 10-26 kg initially at rest disintegrates into three particles. One of the particles, of

mass 5.18 10-27 kg, moves in the y direction with a speed of 6.00 106 m/s. Another particle, of mass 8.50 10-27 kg, moves in the x direction with a speed of 4.00 106 m/s. (a) Find the velocity of the third particle.
Physics
1 answer:
Rainbow [258]3 years ago
3 0

Answer:

Explanation:

Using Conservation of momentum (total final momentum of system is)

m1•v1f + m2•v2 f + m3•v3 f=0

and it must be zero to equal the original momentum( since the original body is at rest).

Given that

original mass M=1.82×10^-26

First disintegrate mass m1=5.18×10^-27kg

In y direction V1f=6×10^6 I'm/s

Second disintegrate mass m2=8.5×10^-27kg

In x direction V2f=4×10^6 im/s

Then the third disintegrate will be

m3=M-m1-m2

m3=1.82×10^-26-5.18×10^-27-8.5×10^-27

m3=4.52×10^-27

And the velocity is unknown

Now using the formula above

m1•v1f + m2•v2 f + m3•v3 f=0

m3•V3f= - m1•v1f - m2•v2 f

4.52E-27V3f=-5.18E-27×6E6j - 8.5E-27×4E6 i

Divide thorough by 4.52E-27

V3f= - 6.88×10^6j - 7.52×10^6i

V3f= - 7.52×10^6i - 6.88×10^6j

The final velocity of the third mass disintegrate is 6.88×10^6j - 7.52×10^6i m/s

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A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that radiate in phase. Antenna B is
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Correct question:

A radio transmitting station operating at a frequency of 120 MHz has two identical antennas that radiate in phase. Antenna B is 9.05 m to the right of antenna A. Consider point P between the antennas and along the line connecting them, a horizontal distance x to the right of antenna A.

For what values of x will constructive interference occur at point P?

Answer:

values of x in which constructive interference will occur at point P are; 0.775 m, 2.025 m, 3.275 m, 4.525 m, 5.775 m, 7.025 m, 8.275 m

Explanation:

Given;

frequency, F = 120 MH = 120 x 10⁶ Hz

distance between A and B = 9.05 m

make a sketch of this antenna

A-------------------P------------------B

         x                      9.05 - x

Now, we calculate the wavefront between the two antenna

λ = v/f

where;

v is speed of light = 3 x 10⁸ m/s

λ = (3 x 10⁸) / (120 x 10⁶)

λ = 2.5 m

Thus, the constructive interference = n(2.5)

For constructive interference to occur at point P, then

the path difference = constructive interference

Path difference = 9.05 - x - x

                          = 9.05 -2x

∴ 9.05 - 2x = n(2.5)

2x =  9.05 - n(2.5)

x = 4.525 - n(1.25)

Finally, determine the value of x for which n = -1, -2, -3 and 0, 1, 2, 3

when n = -1

x = 4.525 + 1(1.25)

x = 5.775m

when n = -2

x = 4.525 + 2(1.25)

x = 7.025m

when n = -3

x = 4.525 + 3(1.25)

x = 8.275m

when n = 0

x = 4.525 - 0(1.25)

x = 4.525m

when n = 1

x = 4.525 - 1(1.25)

x = 3.275m

when n = 2

x = 4.525 - 2(1.25)

x = 2.025m

when n = 3

x = 4.525 - 3(1.25)

x = 0.775m

Thus, values of x in which constructive interference will occur at point P are; 0.775 m, 2.025 m, 3.275 m, 4.525 m, 5.775 m, 7.025 m, 8.275 m

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A sinusoidal wave traveling in the negative x direction (to the left) has an amplitude of 20.0 cm , a wavelength of 35.0 cm , an
SOVA2 [1]

The expression for the wave function describing this wave is y(x,t) = 0.02 sin(17.95x + 75.4t - 0.00198).

The angular frequency of a wave  is 75.4 rad/s.

<h3>What is wave function?</h3>

A wave function is a mathematical equation for the motion of the wave.

y(x, t) = A sin(kx + ωt + Φ)

where;

  • ω is angular speed
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  • Φ is phase angle

The angular wave number of the wave is calculated as follows;

k = 2π/λ

where;

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k = 2π / 0.35

k = 17.95/m

<h3>Angular speed</h3>

ω = 2πf

ω = 2π(12)

ω = 75.4 rad/s

<h3>Phase angle</h3>

75.4(0.2) sin(Φ) = -0.03

sin(Φ) = -0.001989

Φ = arc sin(-0.001989)

Φ = -0.00198

<h3>Wave function</h3>

y(x,t) = 0.02 sin(17.95x + 75.4t - 0.00198)

Thus, the expression for the wave function describing this wave is y(x,t) = 0.02 sin(17.95x + 75.4t - 0.00198).

Learn more about wave function here: brainly.com/question/22675050

#SPJ4

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