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2 years ago

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A harmonic wave on a string with a mass per unit length of 0.050 kg/m and a tension of 60 N has an amplitude of 5.0 cm. Each sec

tion of the string moves with simple harmonic motion at a frequency of 8 Hz. Find the power propagated along the string.

1 answer:

Dennis_Churaev [7]2 years ago

6 0

Answer:

Power of the string wave will be equal to 5.464 watt

Explanation:

We have given mass per unit length is 0.050 kg/m

Tension in the string T = 60 N

Amplitude of the wave A = 5 cm = 0.05 m

Frequency f = 8 Hz

So angular frequency $\omega =2\pi f=2\times 3.14\times 8=50.24rad/sec$

Velocity of the string wave is equal to $v=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{60}{0.050}}=34.641m/sec$

Power of wave propagation is equal to $P=\frac{1}{2}\mu \omega ^2vA^2=\frac{1}{2}\times 0.050\times 50.24^2\times 34.641\times 0.05^2=5.464watt$

So power of the wave will be equal to 5.464 watt

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A baseball, which has a mass of 0.685 kg., is moving with a velocity of 38.0 m/s when it contacts the baseball bat duringwhich t

Evgen [1.6K]

Answers:

a) $65.075 kgm/s$

b) $10.526 s$

c) $61.82 N$

Explanation:

<h3>a) Impulse delivered to the ball</h3>

According to the Impulse-Momentum theorem we have the following:

$I=\Delta p=p_{2}-p_{1}$ (1)

Where:

$I$ is the impulse

$\Delta p$ is the change in momentum

$p_{2}=mV_{2}$ is the final momentum of the ball with mass $m=0.685 kg$ and final velocity (to the right) $V_{2}=57 m/s$

$p_{1}=mV_{1}$ is the initial momentum of the ball with initial velocity (to the left) $V_{1}=-38 m/s$

So:

$I=\Delta p=mV_{2}-mV_{1}$ (2)

$I=\Delta p=m(V_{2}-V_{1})$ (3)

$I=\Delta p=0.685 kg (57 m/s-(-38 m/s))$ (4)

$I=\Delta p=65.075 kg m/s$ (5)

<h3>b) Time </h3>

This time can be calculated by the following equations, taking into account the ball undergoes a maximum compression of approximately $1.0 cm=0.01 m$ :

$V_{2}=V_{1}+at$ (6)

$V_{2}^{2}=V_{1}^{2}+2ad$ (7)

Where:

$a$ is the acceleration

$d=0.01 m$ is the length the ball was compressed

$t$ is the time

Finding $a$ from (7):

$a=\frac{V_{2}^{2}-V_{1}^{2}}{2d}$ (8)

$a=\frac{(57 m/s)^{2}-(-38 m/s)^{2}}{2(0.01 m)}$ (9)

$a=90.25 m/s^{2}$ (10)

Substituting (10) in (6):

$57 m/s=-38 m/s+(90.25 m/s^{2})t$ (11)

Finding $t$ :

$t=1.052 s$ (12)

<h3>c) Force applied to the ball by the bat </h3>

According to Newton's second law of motion, the force $F$ is proportional to the variation of momentum $\Delta p$ in time $\Delta t$ :

$F=\frac{\Delta p}{\Delta t}$ (13)

$F=\frac{65.075 kgm/s}{1.052 s}$ (14)

Finally:

$F=61.82 N$

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3 years ago

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An electron in a vacuum is first accelerated by a voltage of 81700 V and then enters a region in which there is a uniform magnet

Vilka [71]

Answer:

Magnetic force is equal to $1.37\times 10^{-11}N$

Explanation:

We have given electron is accelerated with a potential difference of 81700 volt.

Magnetic field B = 0.508 T

Angle between magnetic field and velocity $\Theta =90^{0}$

Mass of electron $m=9.11\times 10^{-31}kg$

Charge on electron $e=1.6\times 10^{-19}C$

By energy conservation.

$\frac{1}{2}mv^2=qV$

$\frac{1}{2}\times 9.11\times 10^{-31}\times v^2=1.6\times 10^{-19}\times 81700$

$v=169.4\times 10^6m/sec$

Magnetic force on electron

$F=qvBsin\Theta$

$F=1.6\times 10^{-19}\times 169.4\times 10^6\times 0.508\times sin90^{\circ}$

$=1.37\times 10^{-11}N$

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How to find the volume of a cylinder? This question is specifically for physics.

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The formula for finding the volume of a cylinder is V=πr2h

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The root-mean-square value of an alternating current of S0Hz frequency is 10 ampere. The time taken by the alternating current i

stealth61 [152]

Answer:

(D ) $5\times10^{-3} sec$ and $14.14 amp.$

Explanation:

Given that, the rms value of current is 10 ampere and its frequency is 50 Hz.

Now maximum value of current can be calculated as,

$I_{max}=\sqrt{2}I_{rms}\\I_{max}=10\times \sqrt{2} \\I_{max}=14.14 amp.$

The time period is defined as,

$T=\frac{1}{f}\\ T=\frac{1}{50}\\ T=0.02 sec$

Now the time taken by alternating current going from zero to maximum value is,

$t=\frac{T}{4}\\ t=\frac{0.02}{4}\\ t=5\times 10^{-3}sec$

Therefore, the time taken by alternating current to reach maximum value is $t=5\times 10^{-3}sec$ and the peak value of current is $14.14 amp.$ .

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3 years ago

Arrange the following events in the mantle convection process. Use numbers 1-5.

finlep [7]

Answer:

1) Lithospheric plates move in the asthenosphere due to rising and sinking of materials is 1.

2) The decomposition of radioactive elements causes heat in the interior part of the Earth

3) Heat slowly rises to the mantle and creates convection current.

4). Heat moves to the core

5) The process repeats as cycle.

Explanation:

Mantle convection is the gradual slow creeping of movement of the Earth's mantle which is as a result of convection current which transfer heat from the interior to the surface of the Earth .

The process of mantle convection start with

1. Lithospheric plates move in the asthenosphere due to rising and sinking of materials is and thus form the two component of the mantle.

2) The decomposition of radioactive elements causes heat in the interior part of the Earth. This is as a result of accretion which is associated to sea flooding

3) Heat slowly rises to the mantle and creates convection current.

4). Heat moves to the core, cools down by conduction and convection of heat.

5) The process repeats as cycle.

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