Ask question

Ask question

All categories

4 years ago

10

Atoms in a solid are not stationary, but vibrate about their equilibrium positions. Typically, the frequency of vibration is abo

ut f = 4.11 x 1012 Hz, and the amplitude is about 1.23 x 10^-11 m. For a typical atom, what is its (a) maximum speed and (b) maximum acceleration

1 answer:

hoa [83]4 years ago

4 0

To develop this problem it is necessary to use the equations of description of the simple harmonic movement in which the acceleration and angular velocity are expressed as a function of the Amplitude.

Our values are given as

$f = 4.11 *10^{12} Hz$

$A = 1.23 * 10^{-11}m$

The angular velocity of a body can be described as a function of frequency as

$\omega = 2\pi f$

$\omega = 2\pi 4.11 *10^{12}$

$\omega=2.582*10^{13} rad/s$

PART A) The expression for the maximum angular velocity is given by the amplitude so that

$V = A\omega$

$V =( 1.23 * 10^{-11})(2.582*10^{13})$

$V = = 317.586m/s$

PART B) The maximum acceleration on your part would be given by the expression

$a = A \omega^2$

$a =( 1.23 * 10^{-11})(2.582*10^{13})^2$

$a= 8.2*10^{15}m/s^2$

You might be interested in

Water is diffrent from other substances because:

sergeinik [125]

Its B.hope this helps

8 0

3 years ago

Read 2 more answers

An open 1-m-diameter tank contains water at a depth of 0.7 m when at rest. As the tank is rotated about its vertical axis the ce

Mamont248 [21]

Answer:

Explanation:

To find the angular velocity of the tank at which the bottom of the tank is exposed

From the information given:

At rest, the initial volume of the tank is:

$V_i = \pi R^2 h_i --- (1)$

where;

height h which is the height for the free surface in a rotating tank is expressed as:

$h = \dfrac{\omega^2 r^2}{2g} + C$

at the bottom surface of the tank;

r = 0, h = 0

∴

$h = \dfrac{\omega^2 r^2}{2g} + C$

0 = 0 + C

C = 0

Thus; the free surface height in a rotating tank is:

$h=\dfrac{\omega^2 r^2}{2g} --- (2)$

Now; the volume of the water when the tank is rotating is:

dV = 2π × r × h × dr

Taking the integral on both sides;

$\int \limits ^{V_f}_{0} \ dV = \int \limits ^R_0 \times 2 \pi \times r \times h \ dr$

replacing the value of h in equation (2); we have:

$V_f} = \int \limits ^R_0 \times 2 \pi \times r \times ( \dfrac{\omega ^2 r^2}{2g} ) \ dr$

$V_f = \dfrac{ \pi \omega ^2}{g} \int \limits ^R_0 \ r^3 \ dr$

$V_f = \dfrac{ \pi \omega ^2}{g} \Big [ \dfrac{r^4}{4} \Big]^R_0$

$V_f = \dfrac{ \pi \omega ^2}{g} \Big [ \dfrac{R^4}{4} \Big] --- (3)$

Since the volume of the water when it is at rest and when the angular speed rotates at an angular speed is equal.

Then $V_f = V_i$

Replacing equation (1) and (3)

$\dfrac{\pi \omega^2}{g}( \dfrac{R^4}{4}) = \pi R^2 h_i$

$\omega^2 = \dfrac{4g \times h_i }{R^2}$

$\omega =\sqrt{ \dfrac{4g \times h_i }{R^2}}$

$\omega = \sqrt{\dfrac{4 \times 9.81 \ m/s^2 \times 0.7 \ m}{(0.5)^2} }$

$\omega = \sqrt{109.87 }$

$\mathbf{\omega = 10.48 \ rad/s}$

Finally, the angular velocity of the tank at which the bottom of the tank is exposed = 10.48 rad/s

6 0

3 years ago

For a home sound system, two small speakers are located so that one is 52 cm closer to the listener than the other. What is the

alekssr [168]

You'll get destructive interference if both waves are the same frequency but the peaks of one wave overlap the troughs of the other wave.

That can only happen if one wave has to travel (1/2 wavelength) farther than the other one to reach your ears. So we want to find the lowest frequency for which 52 cm is 1/2 of a wavelength ... the wavelength is 104 cm.

Frequency = (speed) / (wavelength)

Frequency = (344 m/s) / (104 cm)

Frequency = (344 m/s) / (1.04 meter)

Frequency = (344 / 1.04) per second

Frequency = 330.8 Hz .

7 0

3 years ago

A uniform magnetic field is perpendicular to the plane of a wire loop. If the loop accelerates in the direction of the field, wi

Nataly [62]

Answer:

No

Explanation:

If the coil is accelerated parallel to the magnetic field, it means also that the force on the coil acts parallel to the field. For current to be induced in a coil, a basic condition must be met which is that the directions of force (acceleration) and the magnetic field must be perpendicular to each other. This brings about current being induced in a direction perpendicular to bothering the directions of the force acting on the coil and the that of the magnetic field. This current would flow through the coil in either a clockwise or anticlockwise manner.

Since the coil is accelerated parallel to the magnetic field, no current is induced in it.

3 0

3 years ago

Which term is the product of force and distance?

lesya [120]

Answer:

work

Explanation:

it is a scalar quantity. it is equal to product of force and distance if the direction of motion is in direction of force in straight line

4 0

3 years ago