A quartz crystal vibrates with a frequency of 35,621 Hz. What is the period of the crystal's motion?

Answers

Answer 1

Period = 1 / frequency

Period = 1 / (35,621 /s)

Period = 2.8073... x 10⁻⁵ sec

Period = 28.07 microseconds

or

Period = 0.0281 millisecond

Answer 2

The period (T) of the crystal's motion is equal to [tex]2.81 \times 10^{-5}\;seconds[/tex].

Given the following data:

Frequency of quartz crystal = 35,621 Hertz.

To calculate the period of the crystal's motion:

The formula for the period of oscillation.

Mathematically, the period of oscillation of an object is given by this formula:

[tex]T=\frac{1}{F}[/tex]

Where:

T is the period of oscillation.F is the frequency.

Substituting the given parameters into the formula, we have;

[tex]T=\frac{1}{35621} \\\\T=2.81 \times 10^{-5}\;seconds[/tex]

Therefore, the period (T) of the crystal's motion is equal to [tex]2.81 \times 10^{-5}\;seconds[/tex].

Read more on period here: https://brainly.com/question/14024265


Related Questions

Two identical loudspeakers 2.30 m apart are emitting sound waves into a room where the speed of sound is 340 m/s. Abby is standing 3.00 m in front of one of the speakers, perpendicular to the line joining the speakers, and hears a maximum in the intensity of the sound. Part A What is the lowest possible frequency of sound for which this is possible

Answers

Answer:

1089.74 Hz

Explanation:

Using Pythagoras theorem, we can find the distance from the point to the second speaker.

Thus;

d2 = √(3² + 2.3²)

d2 = √(9 + 5.29)

d2 = √14.29

d2 = 3.78 m

Then, the path distance which is the extra distance travelled would be;

Δd = d2 - d1

Δd = 3.78 - 3

Δd = 0.78 m

Now, the destructive interference condition is given by the formula;

Δd = (m + ½)λ

λ is the wavelength

m is a non - negative integer.

In this case, m = 2

Thus;

0.78 = (2 + ½)λ

λ = 0.78/(2½)

λ = 0.312 m

Now the formula for frequency of a wave is given by;

f = v/λ

Where v is speed of sound.

Thus;

f = 340/0.312

f = 1089.74 Hz

gg The sound source of a ship’s sonar system operates at a frequency of 22.0 kHzkHz . The speed of sound in water (assumed to be at a uniform 20∘C∘C) is 1482 m/sm/s . What is the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling straight toward the ship at 4.95 m/sm/s ? Assume that the ship is at rest in the water.

Answers

Answer:

Δf = 73.72Hz

Explanation:

In order to calculate the difference in frequency between the direct waves and the reflected waves, you first take into account the Doppler's effect for an observer getting closer to the source:

[tex]f'=f(\frac{v+v_o}{v-v_s})[/tex]         (1)

You can assume that the reflected waves come from a source "the whale". Then you have:

f': frequency of the reflected waves = ?

f: frequency of the source = 22.0*kHz = 22.0*10^3 Hz

v: speed of the sound in water = 1482m/s

vs: speed of the source = 4.95m/s

vo: speed of the observer = 0m/s

You replace the values of the parameters in the equation (1):

[tex]f'=(22.0*10^3Hz)(\frac{1482m/s}{1482m/s-4.95m/s})=22073.72Hz[/tex]

Then, the difference in frequency is:

[tex]\Delta f = f'-f=22000Hz-22073.72Hz=73.72Hz[/tex]

The pressure exerted by a phonograph needle on a record is surprisingly large. If the equivalent of 0.600 g is supported by a needle, the tip of which is a circle 0.240 mm in radius, what pressure is exerted on the record in N/m2?

Answers

Answer:

[tex]P=3.25x10^{4}\frac{N}{m^2}[/tex]

Explanation:

Hello,

In this case, since pressure is defined as the force applied over a surface:

[tex]P=\frac{F}{A}[/tex]

We can associate the force with the weight of the needle computed by using the acceleration of the gravity:

[tex]F=0.600g*\frac{1kg}{1000g}*9.8\frac{m}{s^2} =5.88x10^{-3}N[/tex]

And the area of the the tip (circle) in meters:

[tex]A=\pi r^2=\pi (0.240mm)^2=\pi (0.240mm*\frac{1m}{1000mm} )^2\\\\A=1.81x10^{-7}m^2[/tex]

Thus, the pressure exerted on the record turns out:

[tex]P=\frac{5.88x10^{-3}N}{1.81x10^{-7}m^2} \\\\P=3.25x10^{4}\frac{N}{m^2}[/tex]

Which is truly a large value due to the tiny area on which the pressure is exerted.

Best regards.

Which of the following biotic organisms makes its own energy from inorganic substances?
producers
consumers
decomposers
minerals

Answers

Answer:

producers make its own energy frominorganic substances.

A hollow conducting spherical shell has radii of 0.80 m and 1.20 m, The radial component of the electric field at a point that is 0.60 m from the center is closest to

Answers

Complete Question

The complete question is  shown on the first uploaded image  

 

Answer:

The electric field at that point is  [tex]E = 7500 \ N/C[/tex]

Explanation:

From the question we are told that  

       The  radius of the inner circle is [tex]r_i = 0.80 \ m[/tex]

        The  radius of the outer circle is  [tex]r_o = 1.20 \ m[/tex]

       The  charge on the spherical shell [tex]q_n = -500nC = -500*10^{-9} \ C[/tex]

      The magnitude of the point charge at the center is  [tex]q_c = + 300 nC = + 300 * 10^{-9} \ C[/tex]

        The  position we are considering is  x =  0.60 m  from the center

Generally  the  electric field  at the distance x =  0.60 m  from the center  is mathematically represented as

                 [tex]E = \frac{k * q_c }{x^2}[/tex]

substituting values  

                  [tex]E = \frac{k * q_c }{x^2}[/tex]

where  k is  the coulomb constant with value [tex]k = 9*10^{9} \ kg\cdot m^3\cdot s^{-4} \cdot A^{-2}.[/tex]

     substituting values

                  [tex]E = \frac{9*10^9 * 300 *10^{-9}}{0.6^2}[/tex]

                 [tex]E = 7500 \ N/C[/tex]

A 25.0 kg block is initially at rest on a horizontal surface. A horizontal force of 75 N is required to set the block in motion, after which a horizontal force of 60 N is required to keep the block in moving with constant speed. Find the coefficient of static and kinetic friction between the block and the surface.

Answers

Answer:

μs = 0.30

μk = 0.24

Explanation:

In order to calculate the kinetic friction and static friction between the block and the surface, you take into account that the kinetic friction is important when the block is moving and the static friction when the block is at rest.

You use the following formula to find the coefficient of static friction:

[tex]F_1=\mu_s Mg[/tex]       (1)

F1 = 75N

μs: coefficient of static friction = ?

M: mass of the block = 25.0kg

g: gravitational acceleration = 9.8m/s^2

You solve for μs in the equation (1):

[tex]\mu_s=\frac{F_1}{Mg}=\frac{75N}{(25.0kg)(9.8m/s^2)}=0.30[/tex]

For the coefficient of kinetic friction you have:

[tex]F_2=\mu_k Mg[/tex]       (2)

F2 = 60N

μk: coefficient of kinetic friction = ?

You solve for μk in the equation (2):

[tex]\mu_k=\frac{F_2}{Mg}=\frac{60N}{(25.0kg)(9.8m/s^2)}=0.24[/tex]

Then, you have:

coefficient of static friction = 0.30

coefficient of kinetic friction = 0.24

A passenger jet flies from one airport to another 1,233 miles away in 2.4 h. Find its average speed. = ____ m/s

Answers

Speed = (distance) / (time)

Speed = (1,233 mile) / (2.4 hour)

Speed = 513.75 mile/hour

Speed = (513.75 mi/hr) x (1609.344 meter/mi) x (1 hr / 3600 sec)

Speed = (513.75 x 1609.344 / 3600) (mile-meter-hour/hour-mile-second)

Speed = 229.7 meter/second

Bromine, a liquid at room temperature, has a boiling point

Answers

Yes it does !  The so-called "boiling point" is the temperature at which Bromine liquid can change state and become Bromine vapor, if enough additional thermal energy is provided.  The boiling point is higher than room temperature.

When the charges in the rod are in equilibrium, what is the magnitude of the electric field within the rod?

Answers

Answer: If we have equilibrium, the magnitude must be zero.

Explanation:

If the charges are in equilibrium, this means that the total charge is equal to zero.

And as the charges must be homogeneously distributed in the rod, we can conclude that the electric field within the rod must be zero, so the magnitude of the electric field must be zero

An accelerating voltage of 2.25 103 V is applied to an electron gun, producing a beam of electrons originally traveling horizontally north in vacuum toward the center of a viewing screen 36.4 cm away. (a) What is the magnitude of the deflection on the screen caused by the Earth's gravitational field

Answers

Answer:

s= 8.28×10⁻¹⁶m

Explanation:

given

V= 2.25×10³V

from conservation of energy

mv²/2=qΔV

v=√(2qΔV/m)

v= √(2×1.6×10⁻¹⁹×2.25×10³/9.1×10⁻³¹)

=√7.9×10¹⁴m/s

=2.8×10⁷m/s

the deflection of electron beam is

S= gt²/2

recall t= d/v

s=g([tex]\frac{d}{v}[/tex])²/2

s= [tex]\frac{1}{2}[/tex]×9.8×(0.364/2.8×10⁷)²

s= 8.28×10⁻¹⁶m

A d'Arsonal meter with an internal resistance of 1 kohm requires 10 mA to produce full-scale deflection. Calculate thew value of a series

Answers

Question:

A d’Arsonval meter with an internal resistance of 1 kΩ requires 10 mA to produce full-scale deflection. Calculate the value of a series resistance needed to measure 50 V of full scale.

Answer:

4kΩ

Explanation:

Given;

internal resistance, r = 1kΩ

current, I = 10mA = 0.01A

Voltage of full scale, V = 50V

Since there is full scale voltage of 50V, then the combined or total resistance (R) of the circuit is given as follows;

From Ohm's law

V = IR

R = [tex]\frac{V}{I}[/tex]                 [substitute the values of V and I]

R = [tex]\frac{50}{0.01}[/tex]

R = 5000Ω = 5kΩ

The combined resistance (R) is actually the total resistance of the series arrangement of the series resistance([tex]R_{S}[/tex]) and the internal resistance (r) in the circuit. i.e

R = [tex]R_{S}[/tex] + r

[tex]R_{S}[/tex] = R - r                 [Substitute the values of R and r]

[tex]R_{S}[/tex] = 5kΩ - 1kΩ

[tex]R_{S}[/tex] = 4kΩ

Therefore the series resistance is 4kΩ

A particle of charge = 50 µC moves in a region where the only force on it is an electric force. As the particle moves 25 cm, its kinetic energy increases by 1.5 mJ. Determine the electric potential difference acting on the partice​

Answers

Answer:

nvbnncbmkghbbbvvvvvvbvbhgggghhhhb

a. Using the information below, calculate the cyclotron period of an electron that is launched into a magnetic field of strength 1 Gauss with a speed 200 m/s.

Electron Mass = 9.11 x 10^-31 kg
Proton Mass = 1.67 x 10^-27 kg
Elementary Charge = 1.602 x10^9 Nm/C

b. Using the same information from above, calculate the net work done on the charged particle by the magnetic field as it makes one full rotation.

Answers

Answer:

Explanation:

In cyclotron charged particle moves in a circular path in a magnetic field .

for rotation  

mv² / R = Bqv where m is mass and q be charge of the particle which moves on circular path of radius R with velocity v .

v = BqR / m  

Time period of rotation  

T = 2πR / v  

= 2πR m / BqR

= 2π m / Bq

For electron  

T = 2π x 9.1 x 10⁻³¹ / (1 x 10⁻⁴ x 1.602 x 10⁻¹⁹)

= 35.67 x 10⁻⁸ s  

b )  

work done on the charged particle will be zero because force on charged particle is perpendicular to its movement so work done will be zero

A student has made the statement that the electric flux through one half of a Gaussian surface is always equal and opposite to the flux through the other half of the Gaussian surface. This is:_______.

a. never true.

b. never false.

c. true whenever enclosed charge is symmetrically located at a center point, or on a center line or centrally placed plane

d. true whenever no charge is enclosed within the Gaussian surface.

e. true only when no charge is enclosed within the Gaussian surface.

Answers

Answer:

E.true only when no charge is enclosed within the Gaussian surface.

Explanation:

Because Gauss’s law states that the net flux of an electric field in a closed surface is directly proportional to the enclosed electric charge.

You walk into an elevator, step onto a scale, and push the "down" button to go directly from the tenth floor to the first floor. You also recall that your normal weight is w= 635 N. If the elevator has an initial acceleration of magnitude 2.45 m/s2, what does the scale read? Express your answer in newtons.

Answers

Answer: 479. 425 N

Explanation: the calculation of a body in an elevator obeys Newton law. When it is accelerating upward, the scale reading is greater than the true weight of the person.

It is given by N= m(g+a)

When it is accelerating downward, the scale reading is less than the true weight.

It so given by N = m(g-a)

The answer to the above questions is in the attached photo

Answer:

the scale will read 476.414 N

Explanation:

Weight = 635 N

mass = (weight) ÷ (acceleration due to gravity 9.81 m/^2)

mass m = 635 ÷ 9.81 = 64.729 kg

initial acceleration of the elevator a = 2.45 m/s^2

the force produced by the acceleration of the elevator downwards = ma

your body inertia force try to counteract this force, by a force equal and opposite to the direction of this force, leading to an apparent weight loss

apparent weight = weight - ma

apparent weight = 635 - (64.729 x 2.45)

apparent weight =  635 - 158.586  = 476.414 N


An ac circuit consist of a pure resistance of 10ohms is connected across an ae supply
230V 50Hz Calculate the:
(i)Current flowing in the circuit.

(ii)Power dissipated

Answers

Plz check attachment for answer.

Hope it's helpful

When moving to a new apartment, you rent a truck and create a ramp with a 244 cm long piece of plywood. The top of the moving ramp lies on the edge of the truck bed at a height of 115 cm. You load your textbooks into a wooden box at the bottom of the ramp (the coefficient of kinetic friction between the box and ramp is = 0.2). Then you and a few friends give the box a quick push and it starts to slide up the ramp. A) What angle is made by the ramp and the ground?B) Unfortunately, after letting go, the box only tables 80cm up the ramp before it starts coming back down! What speed was the box initially traveling with just after you stopped pushing it?

Answers

Answer:

A)    θ = 28.1º , B)         v = 2.47 m / s

Explanation:

A) The angle of the ramp can be found using trigonometry

         sin θ = y / L

         Φ = sin⁻¹ y / L

         θ = sin⁻¹ (115/244)

         θ = 28.1º

B) For this pate we can use the relationship between work and kinetic energy

       W =ΔK

where the work is

       W = -fr x

the negative sign is due to the fact that the friction force closes against the movement

Lavariacion of energy cineta is

         ΔEm = ½ m v² - mgh

        -fr x = ½ m v² - m gh

the friction force has the equation

         fr = very N

           

at the highest part there is no speed and we take the origin from the lowest part of the ramp

To find the friction force we use Newton's second law. Where one axis is parallel to the ramp and the other is perpendicular

             

Axis y . perpendicular

            N- Wy = 0

            cos tea = Wy / W

            Wy = W cos treaa

             N = mg cos tea

we substitute

   

- (very mg cos tea) x = ½ m v²2 - mgh

            v2 = m (gh- very g cos tea x)

   let's calculate

           v = Ra (9.8 0.80 - 0.2 9.8 0.0 cos 28.1)

           v = RA (7.84 -1.729)

           v = 2.47 m / s

Light from a helium-neon laser (? = 633 nm) is used to illuminate two narrow slits. The interference pattern is observed on a screen 3.2m behind the slits. Eleven bright fringes are seen, spanning a distance of 60mm .

What is the spacing (in mm) between the slits?

Answers

Answer:

0.3376 mm

Explanation:

The computation of the spacing in mm between the slits is shown below:

As we know that

[tex]d = \frac{m\lambda L}{\Delta y}[/tex]

where,

[tex]\lambda[/tex] = wavelength

L = distance from the scrren

[tex]\Delta y[/tex] = spanning distance

As there are 11 bright fingers seen so m would be

= 11 - 1

= 10

Now placing these values to the above formula

So, the spacing is

[tex]= \frac{(10)(633 \times 10^{-9})(3.2m)}{60 \times 10^{-3}}[/tex]

= 0.3376 mm

We simply applied the above formula.

Answer:

Explanation:

Maximum occurs when the path difference is an integral multiple of wavelength

Here [tex]\lambda[/tex] - Wavelength, [tex]d-[/tex] slit separation and [tex]m-[/tex] Order of pattern

Rearrange the equation for

[tex]\begin{aligned}d &=\frac{m \lambda}{\sin \theta} \\

\text { Here, } \sin \theta &=\frac{y}{L} \quad\left(\begin{array}{l}

\text { Here, } L-\text { separation between slit and screen } \\

y-\text { Distance between respective fringe from center on screen }\end{array}\right)[/tex]

[tex]d=\frac{m \lambda}{\left(\frac{y}{L}\right)} \\

&=\frac{m \lambda L}{y}[/tex]

Here, order

Due to the fact that there are 11 bright fringes seen, you take [tex]11-1=10[/tex]

since starts from 0,1,2,3

Substitute given values

[tex]\begin{aligned}d &=\frac{(10)\left(633 \times 10^{-9} \mathrm{m}\right)(3.2 \mathrm{m})}{60 \times 10^{-3} \mathrm{m}} \\&=\left(3.376 \times 10^{-4} \mathrm{m}\right)\left(\frac{1 \mathrm{mm}}{10^{-3} \mathrm{m}}\right) \\&=0.3376 \mathrm{mm}\end{aligned}[/tex]


3. Which is a general chemical equation for an endothermic, double-replacement reaction?

O AB+ CD + energy-> AD+ CB
O AB+ CD AD + CB + energy
O AB+ C + energy - A+ CB
O AB+C- A+ CB + energy

Answers

The correct answer is A.  AB+ CD + energy-> AD+ CB

Explanation:

In chemistry, a reaction is endothermic if the reaction involves absorption of heat or energy and this is necessary for the reaction to start. In terms of the chemical equation, this implies energy is part of the reactants or initial substances. Besides this, if the reaction is a double-replacement reaction this means two ions of the original substances are swapped or replaced, which means new substances in the products.

According to this, option A is the correct chemical equation because energy is part of the reactants, which shows the reaction is endothermic and the reactants AB + CD lead to the products AD + CB which shows two ions of the compounds were replaced (double replacement).

Answer:

The proper Answer is A) AB+CD + Energy --> AD + CB

Explanation:

A block is attached to a horizontal spring and it slides back and forth in simple harmonic motion on a frictionless horizontal surface. At one extreme end of the oscillation cycle, where the block comes to a momentary halt before reversing the direction of its motion, another block is placed on top of the first block without changing its zero velocity. The simple harmonic motion then continues. What happens to the amplitude and the angular frequency of the ensuing motion of the two-block system

Answers

Answer:

A = A₀ ,   w = w₀/√2

Explanation:

This is a problem that we must solve with Newton's second law. They indicate that at the end of the initial movement where the speed is zero, add a mass to the block, we assume that it has the same mass, therefore the total mass is m_total = 2 m. Let's write Newton's second law at this point

                   [tex]F_{e}[/tex] = m_total a

the elastic force is

                   F_{e} = - k x

acceleration is

                   a = d²x / dt²

we substitute

                   - k x = m_total   d²x / dt²

                     d²x / dt² + (k / m_total) x = 0

we substitute

                     d²x / dt² + (k /2m) x = 0

the solution to this differential equation is

                    x = A cos (wt + Ф)

where

                  w = √ (k / 2m)

to find the constant Ф we use the velocity

                    v = dx / dt = - Aw sin (wt + Ф)

                   

At the most extreme point and when the new movement begins (t = 0) they indicate that v = 0

                   0 = - A w sin Ф

for this expression to be zero the sine must be zero therefore Ф = 0

when replacing

                  x = A cos (wt)

                  w = 1 /√2  √ (k / m)

if we want to relate to the initial movement (before placing the block)

                 w₀ = √ (k / m)

                 w = w₀ /√ 2

The amplitude of the movement is the distance from the equilibrium point to where the movement begins, in this case it is the same as in the initial movement

                  A = A₀

the subscript is used to refer to the oscillations before placing the second block

we substitute to have the final equation

                 x = A₀ cos (w₀ t /√2)

                     

                 A = A₀

                 w = w₀/√2

Stress is a factor that contributes to heart disease risk.true or false

Answers

The answer for this question would be True

what tools use cut wood

Answers

Answer:

hand saws

power saws

Circular Saw

Explanation:

that is all that i know

Check Your UnderstandingSuppose the radius of the loop-the-loop inExample 7.9is 15 cm and thetoy car starts from rest at a height of 45 cm above the bottom. What is its speed at the top of the loop

Answers

Answer:

v = 1.7 m/s

Explanation:

By applying conservation of energy principle in this situation, we know that:

Loss in Potential Energy of Car = Gain in Kinetic Energy of Car

mgΔh = (1/2)mv²

2gΔh = v²

v = √(2gΔh)

where,

v = velocity of car at top of the loop = ?

g = 9.8 m/s²

Δh = change in height = 45 cm - Diameter of Loop

Δh = 45 cm - 30 cm = 15 cm = 0.15 m

Therefore,

v = √(2)(9.8 m/s²)(0.15 m)

v = 1.7 m/s

Based on what you know about electricity, hypothesize about how series resistors would affect current flow. What would you expect the effective resistance of two equal resistors in series to be, compared to the resistance of a single resistor?

Answers

Answer:

Effective resistance of two equal resistors in series is twice that of a single resistor and in essence will reduce the amount of current flowing in the circuit.

Explanation:

When two resistors are connected in series, their effective resistance is the sum of their individual resistances. For example, given two resistors of resistance values R₁ and R₂, their effective resistance, Rₓ is given by;

Rₓ = R₁ + R₂            --------------(1)

If these resistors have equal resistance values, say R, then equation 1 becomes;

Rₓ = R + R

Rₓ = 2R

This means that their effective resistance is twice of their individual resistances. In other words, when two equal resistors are in series, their effective resistance is twice the resistance of each single one of those resistors.

Now, according to Ohm's law, voltage(V) is the product of current (I) and resistance (R). i.e

V = IR

I = [tex]\frac{V}{R}[/tex]

We can deduce that current increases as resistance decreases and vice-versa.

So, if the two equal resistors described above are connected in series, the amount of current flowing will be reduced compared to having just a single resistor.

The resonance tube used in this experiment produced only one resonance tone. What length of tube would be required to produce a second tone under the same experimental conditions? Explain your answer.

Answers

Answer:

the length that would produce a sound tone under the same experimental contditions must be increased by  Δl = [tex]\frac{v}{2f}[/tex]

Explanation:

Recall

V = f ×λ

where λ is ⁴/₃l₂ for second resonance

f = [tex]\frac{3v}{4l_{2} }[/tex]

l₂ = [tex]\frac{3v}{4f}[/tex]

where λ is 4l₁ for 1st resonance

f = [tex]\frac{v}{4l_{1} }[/tex]

l₁ = [tex]\frac{v}{4f}[/tex]

∴ Δl = l₂ - l₁ =  [tex]\frac{3v}{4f}[/tex] ⁻  [tex]\frac{v}{4f}[/tex]

Δl=  [tex]\frac{2v}{4f}[/tex]

Δl = [tex]\frac{v}{2f}[/tex]

Therefore, the length should increase by [tex]\frac{v}{2f}[/tex]

A sunbather stands waist deep in the ocean and observes that six crests of periodic surface waves pass each minute. The crests are 16.00 meters apart. What is the wavelength, frequency, period, and speed of the waves

Answers

Answer:

Wavelength = 16 m

Frequency = 0.1 Hz

Period = 10 s^-1

speed of the wave = 1.6 m/s

Explanation:

The crests of the wave is 16.00 m apart

Also, 6 crests pass per minute

The wavelength of this wave is the distance between consecutive corresponding troughs or crests. This means that the wavelength λ is 16 m

Frequency is defined as a number of cycles per seconds.

A minute has 60 sec, therefore, the frequency of this wave is

==> f =  6/60 = 0.1 Hz

Period is the inverse of the frequency, therefore period of the wave is

==> T = 1/0.1 = 10 s^-1

Speed of the wave is the frequency times the wavelength

v = λf = 16 x 0.1 = 1.6 m/s

The Huka Falls on the Waikato River is one of New Zealand's most visited natural tourist attractions. On average, the river has a flow rate of about 300,000 L/s. At the gorge, the river narrows to 20-m wide and averages 20-m deep.
(a) What is the average speed of the river in the gorge?
(b) What is the average speed of the water in the river downstream of the falls when it widens to 60 m and its depth increases to an average of 40 m?

Answers

Answer:

(a) V = 0.75 m/s

(b) V = 0.125 m/s

Explanation:

The speed of the flow of the river can be given by following formula:

V = Q/A

V = Q/w d

where,

V = Speed of Flow of River

Q = Volume Flow Rate of River

w = width of river

d = depth of river

A = Area of Cross-Section of River = w d

(a)

Here,

Q = (300,000 L/s)(0.001 m³/1 L) = 300 m³/s

w = 20 m

d = 20 m

Therefore,

V = (300 m³/s)/(20 m)(20 m)

V = 0.75 m/s

(b)

Here,

Q = (300,000 L/s)(0.001 m³/1 L) = 300 m³/s

w = 60 m

d = 40 m

Therefore,

V = (300 m³/s)/(60 m)(40 m)

V = 0.125 m/s

If the person is shaking her hand up-and-down 12 times per second, what is the wave speed?

Answers

Welllll, first of all, it would take incredible muscular development and control to be able to do that, and I don't believe it's actually humanly possible.

But for Math and Physics problems, that's OK.  We don't mind suspending our disbelief, accepting a temporary alternate reality, and working with the hand that is dealt.

The speed of a wave doesn't depend on how the wave is created.  A puppy wagging its tail, a fly batting its wings, or a person shaking her hand up and down, are moving the air.  The wave that travels away from the vibration is a sound wave in air.  Its speed depends only on the characteristics of the air it travels through.

For some typical combination of temperature, pressure, and humidity, this speed (of sound) is taken to be 343 meters per second.

Notice that the 'sound' of shaking her hand up and down will not be 'heard' by anyone, no matter how close she stands to them.  12 Hz (12 per second) is not a fast-enough wiggle to be sensed as sound by human ears.  If the person senses the wave at all, it will only be as some kind of pulsating breeze.

In a ballistic pendulum experiment, a small marble is fired into a cup attached to the end of a pendulum. If the mass of the marble is 0.0215 kg and the mass of the pendulum is 0.250 kg, how high h will the pendulum swing if the marble has an initial speed of 5.15 m/s? Assume that the mass of the pendulum is concentrated at its end so that linear momentum is conserved during this collision.

Answers

Answer:

h = 8.48*10^-3m

Explanation:

In order to calculate the height reached by the pendulum with the marble, you first take into account the momentum conservation law, to calculate the speed of both pendulum and marble just after the collision.

The total momentum of the system before the collision is equal to the total momentum after:

[tex]m_1v_1+m_2v_2=(m_1+m_2)v[/tex]        (1)

Here you used the fact that the pendulum has its total mass concentrated at the end of the pendulum.

m1: mass of the marble = 0.0215kg

m2: mass of the pendulum concentrated at its end = 0.250kg

v1: horizontal speed of the arble before the collision = 5.15m/s

v2: horizontal speed of the pendulum before the collision = 0m/s

v: horizontal speed of both marble and pendulum after the collision = ?

You solve the equation (1) for v, and replace the values of the other parameters:

[tex]v=\frac{m_1v_1+m_2v_2}{m_1+m_2}\\\\v=\frac{(0.0215kg)(5.15m/s)+(0.250kg)(0m/s)}{0.0215kg+0.250kg}=0.40\frac{m}{s}[/tex]

Next, you use the energy conservation law. In this case the kinetic energy of both marble and pendulum (just after the collision) is equal to the potential energy of the system when both marble and pendulum reache a height h:

[tex]U=K\\\\(m_1+m_2)gh=\frac{1}{2}(m_1+m_2)v^2\\\\h=\frac{v^2}{2g}[/tex]

v = 0.40m/s

g: gravitational acceleration = 9,8m/s^2

[tex]h=\frac{(0.40m/s)^2}{2(9.8m/s^2)}=8.48*10^{-3}m[/tex]

Then, the height reached by marble and pendulum is 8.48*10^-3m

A uniform electric field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate, 1.60 cm distant from the first, in a time interval of 3.20×10−6s3.20×10 −6 s. (a) Find the magnitude of the electric field. (b) Find the speed of the proton when it strikes the negatively charged plate.

Answers

Answer:

E = 326.17 N/C

Explanation:

(a) In order to calculate the magnitude of the electric field between the parallel plates you first calculate the acceleration of the proton. You use the following formula:

[tex]x=v_ot+\frac{1}{2}at^2[/tex]         (1)

vo: initial speed of the proton = 0m/s

t: time that the proton takes to cross the space between the plates = 3.20*10^-6 s

a: acceleration of the proton = ?

x: distance traveled by the proton = 1.60cm = 0.016m

You solve the equation (1) for a, and replace the values of all parameters:

[tex]a=\frac{2x}{t^2}=\frac{2(0.016m)}{(3.20*10^{-6}s)^2}=3.125*10^{10}\frac{m}{s^2}[/tex]

Next, you use the Newton second law for the electric force, to find the magnitude of the electric field:

[tex]F_e=qE=ma[/tex]           (2)

q: charge of the proton = 1.6*10^-19C

m: mass of the proton = 1.77*10^-27kg

You solve the equation (2) for E:

[tex]E=\frac{ma}{q}=\frac{(1.67*10^{-27}kg)(3.125*10^{10}m/s^2)}{1.6*10^{-19}C}\\\\E=326.17\frac{N}{C}[/tex]

The magnitude of the electric field in between the parallel plates is 326.17N/C

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