Poly(methyl acrylate) (PMA) is a rubbery polymer in most conditions, as its glass transition tem- perature T, ñ 10 °C. PMA has a Kuhn length b = 15 Å and a Kuhn molar mass of Mo 495 g/mol. (a) If the entanglement molecular weight of PMA is Me ~ 11 kg/mol, estimate its tube diameter a. (b) PMA has a mass density P 1.11 g/cm². Estimate the volume of the Kuhn monomer vo. How does this compare to the published value of vo ~ 0.740 nm3? On the basis of the value Pe - 21, estimate the entanglement molecular weight. (c) The length of the confining tube can be expressed as L ~bN/Ne. Calculate the length of the tube, as well as the reptation time for the polymer chain if it has a monomer friction coefficient so = 3 x 10-10 g/s

Answers

Answer 1

a. 58.7 Å its tube diameter a.

b. we get v₀ ≈ 0.446 nm³. This is smaller than the published value of v₀ ~ 0.740 nm³.

c. The length of the confining tube L can be expressed as L ≈ bN/Ne.

(a) To estimate the tube diameter a for poly(methyl acrylate) (PMA) with an entanglement molecular weight Me of ~11 kg/mol, we can use the relation Me = πa^2/ρ, where ρ is the mass density. Rearranging for a, we get a = sqrt(Me * ρ/π). Substituting the given values (Me = 11,000 g/mol and ρ = 1.11 g/cm³), we get a ≈ 58.7 Å.
(b) To estimate the volume of the Kuhn monomer v₀, we can use the formula v₀ = M₀/ρ, where M₀ is the Kuhn molar mass (495 g/mol). Substituting the given values,  Using the value Pe = 21, we can estimate the entanglement molecular weight Me' = Pe * M₀ ≈ 10,395 g/mol, which is close to the given Me ~ 11 kg/mol.
(c) To calculate the reptation time τ for the polymer chain, we can use the formula τ = ξ₀N²b²/Ne, where ξ₀ is the monomer friction coefficient (3 x 10⁻¹⁰ g/s). We don't have the values for N and Ne in the given problem, but the formulas provide a method to determine the length of the tube and the reptation time for the polymer chain once those values are known.

To know more about molecular weight visit:

brainly.com/question/27988184

#SPJ11


Related Questions

astronomers can use ground-based telescopes to observe large portions of what regions of the electromagnetic spectrum?

Answers

Astronomers can use ground-based telescopes to observe large portions of the electromagnetic spectrum, including radio waves, infrared, visible light, and limited portions of ultraviolet radiation.

However, observations of X-rays and gamma rays typically require space-based telescopes due to the absorption properties of Earth's atmosphere.

1. Radio Waves: Ground-based radio telescopes are specifically designed to detect and study radio waves emitted by celestial objects. Radio waves have long wavelengths and can easily pass through Earth's atmosphere, allowing ground-based telescopes to observe a wide range of radio frequencies. These observations provide insights into phenomena such as pulsars, quasars, and cosmic microwave background radiation.

2. Infrared: Infrared radiation has wavelengths longer than visible light but shorter than radio waves. Ground-based infrared telescopes can detect and analyze infrared emissions from objects in space. While some infrared wavelengths are absorbed by Earth's atmosphere, there are specific atmospheric windows where infrared radiation can penetrate, allowing astronomers to study various celestial objects, including cool stars, planetary atmospheres, and dust clouds.

3. Visible Light: Ground-based telescopes are primarily designed to observe visible light, which is the portion of the electromagnetic spectrum that human eyes can detect. These telescopes utilize mirrors or lenses to collect and focus visible light for observation. Visible light observations are crucial for studying stars, galaxies, and other astronomical objects, providing detailed information about their colors, spectra, and structures.

4. Ultraviolet: Ultraviolet (UV) radiation has shorter wavelengths than visible light. While a significant portion of UV radiation is absorbed by Earth's atmosphere, certain UV wavelengths can be observed using ground-based telescopes at high altitudes or in specific locations. Ground-based UV telescopes can study objects like hot stars, active galactic nuclei, and interstellar medium, shedding light on processes such as stellar evolution and galaxy formation.

5. X-rays and Gamma Rays: X-rays and gamma rays have very short wavelengths and are highly energetic forms of electromagnetic radiation. Due to their high energy, these types of radiation are mostly absorbed by Earth's atmosphere. Therefore, observations of X-rays and gamma rays require specialized telescopes located in space, such as the Chandra X-ray Observatory and the Fermi Gamma-ray Space Telescope. However, some ground-based observatories use techniques like atmospheric Cherenkov radiation to detect very high-energy gamma rays indirectly.

To know more about ground-based telescopes, please click on:

https://brainly.com/question/14392320

#SPJ11

Determine the op-amp cutoff-frequency for a device whose unity-gain bandwidth is 2 MHz and the differential-gain is 200 V/mV A. 150 Hz B. 50 Hz C. 5 Hz D. 10 Hz

Answers

The cutoff-frequency of the op-amp is 10 Hz.


To determine the cutoff-frequency of an op-amp with a unity-gain bandwidth of 2 MHz and differential-gain of 200 V/mV, we can use the formula:

Cutoff Frequency = Unity-Gain Bandwidth / Differential-Gain

Plugging in the values, we get:

Cutoff Frequency = 2 MHz / 200 V/mV = 10 Hz

Therefore, the correct answer is D) 10 Hz.

This means that the op-amp's frequency response starts to decrease at 10 Hz, and signals with frequencies lower than 10 Hz are amplified with less gain than higher frequencies.

It's important to note that the cutoff-frequency is a key parameter in designing filter circuits and understanding the limitations of an op-amp's frequency response.

For more such questions on op-amp, click on:

https://brainly.com/question/30890598

#SPJ11

The cutoff-frequency of the op-amp is 10 Hz.

To determine the cutoff-frequency of an op-amp with a unity-gain bandwidth of 2 MHz and differential-gain of 200 V/mV, we can use the formula:

Cutoff Frequency = Unity-Gain Bandwidth / Differential-Gain

Plugging in the values, we get:

Cutoff Frequency = 2 MHz / 200 V/mV = 10 Hz

Therefore, the correct answer is D) 10 Hz.

This means that the op-amp's frequency response starts to decrease at 10 Hz, and signals with frequencies lower than 10 Hz are amplified with less gain than higher frequencies.

It's important to note that the cutoff-frequency is a key parameter in designing filter circuits and understanding the limitations of an op-amp's frequency response.

Visit to know more about Op-amp:-

brainly.com/question/30890598

#SPJ11

the mass of a string is 1.00 10-3 kg, and it is stretched so the tension in it is 155 n. a transverse wave traveling on this string has a frequency of 260 hz and a wavelength of 0.60 m. what is the length of the string?

Answers

The length of the string is approximately 1.56 meters.

To find the length of the string, we need to first determine the wave speed on the string. We can use the formula for wave speed:

v = sqrt(T/μ)

where v is the wave speed, T is the tension (155 N), and μ is the linear mass density of the string (mass per unit length).

Given the mass of the string as 1.00 x 10^-3 kg, we need to find the length of the string (L) to determine μ. Since we know the wavelength (λ) and the frequency (f) of the transverse wave, we can use the wave equation:

v = λf

Substituting the known values, we get:

v = 0.60 m * 260 Hz = 156 m/s

Now, using the formula for wave speed:

156 m/s = sqrt(155 N / μ)

Squaring both sides and rearranging the equation, we get:

μ = 155 N / (156 m/s)^2 ≈ 6.41 x 10^-4 kg/m

Now, we can find the length of the string using the linear mass density:

L = (mass of the string) / μ = (1.00 x 10^-3 kg) / (6.41 x 10^-4 kg/m) ≈ 1.56 m

Learn more about length here:-

https://brainly.com/question/32232199

#SPJ11

Light of frequency 1.42 × 1015 hz illuminates a sodium surface. the ejected photoelectrons are found to have a maximum kinetic energy of 3.61 ev. Calculate the work function of sodium. Planck’s constant is 6.63 × 10−34 J · s. Your answer must be exact.

Answers

The  work function of sodium is:

φ = E - Kmax = (9.44 × 10^-19 J) - (5.79 × 10^-19 J) = 3.65 × 10^-19 J

So the work function of sodium is 3.65 x 10^-19 J.

We can use the equation relating the energy of a photon to its frequency and Planck's constant:

E = hf

where E is the energy of the photon, h is Planck's constant, and f is the frequency of the light.

The work function, denoted by φ, is the minimum energy required to remove an electron from the surface of the metal. The maximum kinetic energy of the photoelectrons, denoted by Kmax, is related to the energy of the photons and the work function by:

Kmax = E - φ

where E is the energy of the photon.

We can rearrange this equation to solve for the work function:

φ = E - Kmax

Substituting the given values, we have:

E = hf = (6.63 × 10^-34 J·s)(1.42 × 10^15 Hz) = 9.44 × 10^-19 J

Kmax = 3.61 eV = (3.61 eV)(1.602 × 10^-19 J/eV) = 5.79 × 10^-19 J

Therefore, the work function of sodium is:

φ = E - Kmax = (9.44 × 10^-19 J) - (5.79 × 10^-19 J) = 3.65 × 10^-19 J

So the work function of sodium is 3.65 x 10^-19 J.

Visit to know more about Sodium:-

brainly.com/question/25597694

#SPJ11

An ideal neon sign transformer provides 9530 v at 59.0 ma with an input voltage of 110 v. calculate the transformer's input power and current.

Answers

The input current of the neon sign transformer is 5.12 amperes

To calculate the input power and current of the neon sign transformer, we can use the following formulas:

Input power = Output voltage x Output current

Input current = Input power / Input voltage

Given values:

Output voltage (V) = 9530 V

Output current (I) = 59.0 mA = 0.059 A

Input voltage (V) = 110 V

Using the formula for input power, we have:

Input power = Output voltage x Output current

Input power = 9530 V x 0.059 A

Input power = 562.87 W

Therefore, the input power of the neon sign transformer is 562.87 watts.

Using the formula for input current, we have:

Input current = Input power / Input voltage

Input current = 562.87 W / 110 V

Input current = 5.12 A

To know more about transformer refer here

https://brainly.com/question/29435094#

#SPJ11

Consider a circular loop of wire, placed next to a straight wire carrying an electric current, I. Which of the following is true about the induced current of the circular loop?
a) For a constant current I that does not change with time, a smaller I will lead to a larger induced current in the circular loop.
b) The induced current will increase if the current I changes faster with time.
c) The induced current will increase if we shrink the size of the circular loop.
d) None of the above.
e) For a constant current I that does not change with time, a larger I will lead to a larger induced current in the circular loop.

Answers

The correct answer is d) None of the above.  The induced current in the circular loop depends on the rate of change of the magnetic field passing through the loop. It is not directly related to the current in the straight wire. Therefore, options a) and e) are incorrect.

Option b) may seem like a plausible answer, but it is not always true. The induced current depends on the rate of change of the magnetic field, which is affected by both the magnitude and direction of the current in the straight wire.

Option c) is also incorrect. The size of the loop may affect the strength of the magnetic field passing through it, but it does not directly affect the induced current.

Therefore, the correct answer is d) None of the above.

You can learn more about induced current at: brainly.com/question/31686728

#SPJ11

a long wire is connected to a battery of 1.5 v and a current flows through it. by what factor does the drift velocity change if the wire is connected to a dc electric source of 7.0 v ?

Answers

Drift velocity is the average velocity of charge carriers (usually electrons) moving in a conductor in the direction opposite to the electric field. It is directly proportional to the strength of the electric field applied to the conductor and inversely proportional to the resistance of the conductor. Therefore, the drift velocity of the charge carriers in a wire changes when the electric field or resistance changes.

In this case, the wire is initially connected to a 1.5 V battery, which creates an electric field in the wire and causes current to flow. Let's assume that the resistance of the wire is constant. When the wire is connected to a DC electric source of 7.0 V, the electric field in the wire increases by a factor of 7.0/1.5 = 4.67. Since the drift velocity is directly proportional to the electric field, we can assume that the drift velocity of the charge carriers in the wire will increase by the same factor of 4.67. In other words, the drift velocity will increase by 367% (i.e., 4.67 minus 1 = 3.67, or 367%).

It is worth noting that the actual change in drift velocity depends on various factors, such as the type of conductor, the temperature, and the concentration of charge carriers. Additionally, if the resistance of the wire changes when it is connected to the 7.0 V source, then the change in drift velocity will be different. However, for the purpose of this question, we assume that the resistance of the wire is constant.

To know more about Drift velocity visit:-

https://brainly.com/question/4269562

#SPJ11

Suppose a generator has a peak voltage of 210 V and its 500 turn, 5.5 cm diameter coil rotates in a 0.25 T field.Randomized Variable:ε0=210VB=0.25Td=5.5cm

Answers

The generator's peak voltage is 1.77 V.

We can use Faraday's law of electromagnetic induction to calculate the peak emf generated in the coil:

ε = -NΔΦ/Δt,

where ε is the emf, N is the number of turns in the coil, and ΔΦ/Δt is the rate of change of magnetic flux through the coil.

The magnetic flux through the coil can be calculated as:

Φ = B*A*cos(θ),

where B is the magnetic field strength, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the coil.

Substituting the given values, we have:

A = π*(d/2)² = π*(0.055 m/2)² = 0.00237 m²

cos(θ) = 1 (since the coil is rotating perpendicular to the magnetic field)

N = 500

B = 0.25 T

Using a rotational frequency of 60 Hz, the rate of change of magnetic flux can be calculated as:

ΔΦ/Δt = B*A*(2π*60) = 0.00354 Wb/s

Substituting these values into the first equation, we have:

ε = -NΔΦ/Δt = -500 * 0.00354 = -1.77 V

Since the emf is alternating, its peak value is the absolute value of its amplitude, which is 1.77 V. Therefore, the peak voltage of the generator is 1.77 V.

Learn more about voltage on:

https://brainly.com/question/29867409

#SPJ11

The complete question is:

Suppose a generator has a peak voltage of 210 V and its 500 turn, 5.5 cm diameter coil rotates in a 0.25 T field.

Randomized Variable:

ε₀=210V

B=0.25T

d=5.5cm

Order the following mass wasting processes in terms of velocity from the slowest (1) to the fastest (4). No exra credit for reversed order. Slump Rock fall Solifluction Debris slide

Answers

The order of the mass wasting processes from slowest to fastest velocity is as follows Solifluction Slump  Debris slide Rock fall

Solifluction is the slowest mass wasting process because it involves the gradual movement of soil and sediment due to the freezing and thawing of water in the ground. This movement is usually very slow and can take years to cause any significant damage. Slump is the second-slowest mass wasting process because it involves the gradual movement of soil and sediment down a slope due to the loss of internal support. This movement is usually faster than solifluction, but still relatively slow.

Debris slide is the third-fastest mass wasting process because it involves the sudden movement of soil, rock, and vegetation down a slope due to the failure of a slope or the saturation of the material with water. This movement is much faster than solifluction or slump. Rock fall is the fastest mass wasting process because it involves the sudden and rapid movement of large boulders and rocks down a steep slope due to the force of gravity.

To know more about velocity visit

https://brainly.com/question/17127206

#SPJ11

Design a circuit that can add two 2-digit BCD numbers, A1A0 and B1B0 to produce the three-digit BCD sum S2S1S0. Use two instances of your circuit from part IV to build this two-digit BCD adder. Perform the steps below: 1. Use switches SW15?8 and SW7?0 to represent 2-digit BCD numbers A1A0 and B1B0, respectively. The value of A1A0 should be displayed on the 7-segment displays HEX7 and HEX6, while B1B0 should be on HEX5 and HEX4. Display the BCD sum, S2S1S0, on the 7-segment displays HEX2, HEX1 and HEX0. Note: Part IV asks to do a circuit that adds two BCD digits. I don't have this code yet.

Answers

Design a 2-digit BCD adder circuit using two instances of the BCD digit adder circuit. Use switches to input BCD numbers and display the result on 7-segment displays.

To design a circuit for adding two 2-digit BCD numbers, we can utilize two instances of a BCD digit adder circuit. The circuit should have switches SW15-8 and SW7-0 to represent the BCD numbers A1A0 and B1B0, respectively. The 7-segment displays HEX7 and HEX6 should display the value of A1A0, while HEX5 and HEX4 should display B1B0. The resulting BCD sum, S2S1S0, should be displayed on HEX2, HEX1, and HEX0. It is important to note that the code for the BCD digit adder is not yet available, which is necessary for implementing this two-digit BCD adder circuit.

Learn more about design a circuit here:

https://brainly.com/question/23867172

#SPJ11

Assume that is(t) = 0.01sin(10^4t - 90). Find the currents iR(t), İL(t), ic(t) and the voltage v(t).

Answers

iR(t) = 0.01sin(10^4t - 90), İL(t) = -0.01sin(10^4t), ic(t) = 0.01sin(10^4t + 90), and v(t) = 0. the given current is a sinusoidal function with an amplitude of 0.01 and a frequency of 10^4 Hz. iR(t) represents the current through a resistor and is in phase with the given current.

İL(t) represents the current through an inductor and lags the given current by 90 degrees. ic(t) represents the current through a capacitor and leads the given current by 90 degrees. Since there are no components in the circuit that can create a voltage, v(t) must be 0.

In summary, the currents through the resistor, inductor, and capacitor are in different phases with respect to the given current and there is no voltage in the circuit.

Learn more about circuit here:

https://brainly.com/question/27206933

#SPJ11

monochromatic light is incident on a metal surface, and electrons are ejected. if the intensity of the light increases, what will happen to the ejection rate of the electrons? monochromatic light is incident on a metal surface, and electrons are ejected. if the intensity of the light increases, what will happen to the ejection rate of the electrons?

Answers

increasing the intensity of monochromatic light incident on a metal surface will not affect the ejection rate of electrons, but it will increase the total number of electrons ejected per unit time.

What is Photoelectric effect.?

The photoelectric effect refers to the emission of electrons from a metal surface when light shines on it. When a photon of light with sufficient energy (i.e., frequency) strikes the metal surface, it can transfer its energy to an electron in the metal, causing the electron to be ejected from the metal. This phenomenon was first observed by Heinrich Hertz in 1887 and explained by Albert Einstein in 1905, who proposed that light consists of discrete packets

The ejection rate of electrons from a metal surface is determined by the energy of the photons of light that strike the surface. In the photoelectric effect, electrons are ejected from a metal surface when they absorb photons of sufficient energy. The energy of a photon is directly proportional to its frequency, as given by the equation:

E = hf

where E is the energy of the photon, h is Planck's constant, and f is the frequency of the photon.

Increasing the intensity of monochromatic light does not change the frequency or energy of the photons. Therefore, the ejection rate of electrons from the metal surface will not change with an increase in the intensity of the light. However, the total number of electrons ejected per unit time (i.e., the current) will increase with increasing intensity, since there are more photons striking the surface per unit time.

In summary, increasing the intensity of monochromatic light incident on a metal surface will not affect the ejection rate of electrons, but it will increase the total number of electrons ejected per unit time.

To know more about Photoelectric effect visit:

https://brainly.com/question/1359033

#SPJ4

You use a concave mirror to focus light from a window 1.8 m away. It makes an image 20 cm in front of the mirror.a) Find the focal length of the mirror.b) If the window is 1 m high what is the height of the image? Give your answer as a positive number and then chose whether the image should be upright or inverted.

Answers

The focal length of the concave mirror is -0.2 m and b) the height of the image is 0.111 m and it is inverted.

To find the focal length of the concave mirror, we can use the mirror equation: 1/f = 1/d_o + 1/d_i, where f is the focal length, d_o is the distance of the object from the mirror, and d_i is the distance of the image from the mirror. Plugging in the given values, we get 1/f = 1/1.8 + 1/0.2, which simplifies to f = -0.2 m (since the mirror is concave, the focal length is negative).
To find the height of the image, we can use the magnification equation: M = -d_i/d_o, where M is the magnification (negative for inverted images), d_i is the distance of the image from the mirror, and d_o is the distance of the object from the mirror. Plugging in the given values, we get M = -0.2/1.8 = -0.111. Since the magnification is negative, the image is inverted.
Finally, we can use the equation h_i = M*h_o, where h_i is the height of the image and h_o is the height of the object, to find the height of the image. Plugging in the given values and solving for h_i, we get h_i = -0.111*1 = -0.111 m. However, since the question asks for a positive number, we take the absolute value to get h_i = 0.111 m. Therefore, the height of the image is 0.111 m and it is inverted.
In summary, a) the focal length of the concave mirror is -0.2 m and b) the height of the image is 0.111 m and it is inverted.

To know more about concave mirror visit :

https://brainly.com/question/13101215

#SPJ11

small changes in the orbits of planets caused by the gravitational pull of the other planets in the solar system are called:

Answers

Answer:  Orbital resonance

Explanation: An interesting consequence of such iterations is something called orbital resonance; after long periods of time - and remember that the current estimate for our planet's existence is 4.54 billion years - the ebb and flow of tiny gravitational pulls cause nearby celestial bodies to develop an interlocked behavior.

Solved for niobium, c11 = 242 gn/m2, c12 = 129 gn/m2, and c44 = 28 gn/m2.

Answers

The elastic constants of niobium are C11 = 242 GPa (longitudinal stiffness), C12 = 129 GPa (transverse stiffness), and C44 = 28 GPa (shear stiffness).

Niobium, a metallic element, possesses specific elastic constants that describe its mechanical behavior. These constants indicate how the material responds to different types of stress. For niobium, the elastic constants are as follows: C11 = 242 GPa, representing its longitudinal stiffness or resistance to compression along its crystal structure; C12 = 129 GPa, indicating its transverse stiffness or resistance to deformation perpendicular to the crystal structure; and C44 = 28 GPa, denoting its shear stiffness or resistance to shearing forces. These values provide insights into the material's ability to withstand and transmit stress, aiding in the characterization and engineering of niobium-based structures and devices.

Learn more about Niobium here:

https://brainly.com/question/28814913

#SPJ11

the momentum of a photon is pick those that apply h divided by lambda e divided by c m v h f divided by c

Answers

The momentum of a photon is given by the equation p = h/λ, where p is the momentum, h is Planck's constant, and λ is the wavelength of the photon.

This equation is known as the de Broglie equation and it relates the wavelength of a particle to its momentum. In addition, the momentum of a photon can also be expressed as p = E/c, where E is the energy of the photon and c is the speed of light.

To understand the equation p = h/λ, we need to understand that photons are both particles and waves. As a result, they exhibit properties of both particles and waves, including momentum. When photons are emitted or absorbed, they transfer their momentum to the object they interact with. This momentum transfer can be used in various applications, such as solar sails or photon rockets.

In summary, the main answer to the question is that the momentum of a photon is given by the equation p = h/λ. This equation relates the momentum of the photon to its wavelength and is known as the de Broglie equation. Additionally, the momentum of a photon can also be expressed as p = E/c, where E is the energy of the photon and c is the speed of light.

To know more about momentum refer to

https://brainly.com/question/29113044

#SPJ11

The correct term to use for calculating the momentum of a photon is "h divided by lambda" or "h / λ".

The momentum of a photon can be calculated using the formula p = h/λ, where p is the momentum, h is Planck's constant, and λ is the wavelength of the photon. Another way to express this formula is p = E/c, where E is the energy of the photon and c is the speed of light. Therefore, we can also use the formula p = (hf)/c, where f is the frequency of the photon. It's important to note that photons have zero rest mass, so their momentum is entirely determined by their energy and wavelength or frequency. To summarize, the momentum of a photon can be calculated using one of these three formulas: p = h/λ, p = E/c, or p = (hf)/c.
The momentum of a photon can be calculated using the following equation:
Momentum = h / λ
where h is the Planck's constant and λ is the wavelength of the photon.

To know more about momentum visit :-

https://brainly.com/question/22418297

#SPJ11

a wave whose wavelength is 0.3 m is traveling down a 300 m long wire whose total mass is 1.5 kg. if the wire is under a tension of 1000n, what are the velocity and frquency of the wave?

Answers

The velocity of the wave is 173.2 m/s and its frequency is 577.4 Hz. to calculate the velocity of the wave, we can use the equation v = sqrt(T/μ), where T is the tension in the wire and μ is the linear mass density (mass per unit length) of the wire.

In this case, μ = m/L, where m is the total mass of the wire and L is its length. Plugging in the given values, we get v = sqrt(1000 N / (1.5 kg / 300 m)) = 173.2 m/s.

To calculate the frequency of the wave, we can use the equation v = λf, where λ is the wavelength of the wave and f is its frequency. Solving for f, we get f = v/λ = 173.2 m/s / 0.3 m = 577.4 Hz.

Learn more about velocity here:

https://brainly.com/question/17127206

#SPJ11

A simple pendulum is swinging back and forth through a small angle, its motion repeating every 1.13 s. How much longer should the pendulum be made in order to increase its period by 0.29 s?

Answers

The pendulum should be made approximately 8.7 cm longer in order to increase its period by 0.29 s.

The period of a simple pendulum is given by the formula T=2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. In this case, the original period of the pendulum is given as 1.13 s.

To find out how much longer the pendulum should be made, we can use the following equation:
(T + 0.29) = 2π√((l+x)/g), where x is the additional length that the pendulum needs to be made longer by.

Substituting the given values, we get:
(1.13 + 0.29) = 2π√((l+x)/9.81)

Simplifying the equation, we get:
1.42 = √(l+x)

Squaring both sides, we get:
2 = l/g + x/g

Therefore, x/g = 2 - l/g.

Substituting the values of l and g, we get:
x/9.81 = 2 - (1.13/2π)^2

Solving for x, we get:
x = 0.087 m or 8.7 cm (approx.)

Hence, the pendulum should be made approximately 8.7 cm longer in order to increase its period by 0.29 s.

To know more about gravity refer to

https://brainly.com/question/31321801

#SPJ11

To increase the period by 0.29 s, the pendulum should be made approximately 0.0941 m (or 9.41 cm) longer. To answer your question, we need to use the formula for the period of a simple pendulum: T = 2π√(L/g). where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.



Given that the pendulum's period is 1.13 s, we can solve for its current length as follows: 1.13 s = 2π√(L/g),Squaring both sides, we get: 1.28 s^2 = 4π^2(L/g),Solving for L, we get: L = (g/4π^2) * 1.28 s^2
Now we can find the new length of the pendulum that would increase its period by 0.29 s. Let's call this new length L'.
The new period would be: T' = T + 0.29 s = 1.13 s + 0.29 s = 1.42 s,L' = (g/4π^2) * 2.01 s^2.Finally, to find how much longer the pendulum should be made, we can subtract L from L': L' - L = (g/4π^2) * 0.73 s^2

Since we don't know the value of g, we can't calculate this difference exactly. However, we can use the approximate value of g = 9.81 m/s^2 to estimate the answer. Plugging in this value, we get: L' - L ≈ 0.295 m
Therefore, the pendulum should be made approximately 0.295 m longer to increase its period by 0.29 s.

To know more about pendulum  visit :-

https://brainly.com/question/31880331

#SPJ11

For an observer located on the North Pole, the altitude of the stars in the East will... A) increase. B) increase and decrease. C) stay the same. D) decrease

Answers

For an observer located on the North Pole, the altitude of the stars in the East will (c) stay the same.

This is because the North Pole is located at the Earth's axis, which is perpendicular to the plane of the Earth's orbit. As a result, the North Pole is constantly pointed towards the same region of space, and the stars in the East will always be at the same altitude.
This is different from what would be observed at other latitudes on Earth. For example, an observer at the Equator would see the stars in the East rise and set over the course of a day, as the Earth rotates on its axis. Similarly, an observer at a mid-latitude would see the stars in the East rise at an increasing altitude, reach their highest point in the sky, and then decrease in altitude as they set in the West.
However, at the North Pole, the stars in the East will appear to circle around the observer at a constant altitude, never rising or setting. This can make navigation and timekeeping more challenging, as there are no clear markers for the passage of time or changes in direction. Nevertheless, this unique perspective on the stars can also be a source of wonder and inspiration, as the observer is able to witness the timeless dance of the heavens from a truly unique vantage point.

To know more about altitude visit:

https://brainly.com/question/31017444

#SPJ11

calculate the maximum kinetic energy of the electrons ejected from this tungsten surface by ultraviolet radiation of frequency 1.45×1015hz1.45×1015hz . express the answer in electron volts

Answers

The electrons are emitted by a metal surface when the light of frequency (ν) is incident on it.

The maximum kinetic energy (KEmax) is given by the following equation:

KEmax = hν - Φ

Where h is Planck's constant (6.626 × 10^-34 J s) and Φ is the work function of the metal, which is the minimum amount of energy required to remove an electron from the metal surface.

For tungsten, the work function is Φ = 4.5 eV.

Substituting the given frequency into the equation, we get:

KEmax = (6.626 × 10^-34 J s) × (1.45 × 10^15 Hz) - (4.5 eV)

Converting Joules to electron volts (eV), we get:

KEmax = (4.14 × 10^-15 eV s) × (1.45 × 10^15 Hz) - (4.5 eV)

KEmax = 5.69 eV - 4.5 eV

KEmax = 1.19 eV

Therefore, the maximum kinetic energy of the electrons ejected from the tungsten surface by the ultraviolet radiation of frequency 1.45×1015hz is 1.19 electron volts (eV).

To know more about electrons ejected from this tungsten surface by ultraviolet radiation, refer here

https://brainly.com/question/31790042#

#SPJ11

A 0. 500-kg glider, attached to the end of an ideal spring with force constant k = 450

N/m, undergoes SHM with an amplitude of 0. 040 m. Compute (a) the maximum speed

of the glider; (b) the speed of the glider when it is at x = -0. 015 m; (c) the magnitude of

the maximum acceleration of the glider; (d) the acceleration of the glider at x = -0. 015

m; (e) the total mechanical energy of the glider at any point in its motion

Answers

a. The maximum speed of the glider is 1.26 m/s.

b. The speed of the glider when it is at x = -0.015 m is -0.714 m/s.

c. The magnitude of the maximum acceleration of the glider is 36.0 m/s².

d. The acceleration of the glider at x = -0.015 m is 30.6 m/s².

e. The total mechanical energy of the glider at any point in its motion is 0.36 J.

SHM (Simple Harmonic Motion) can be described as a motion that is periodic and moves back and forth over an equilibrium position. A simple spring-mass oscillator system is a model that is used to understand the principles of SHM. To solve the given problem, we need to use the equations given below,
Maximum Speed: vmax = Aω
Speed at a given displacement: v = -ωA sin(ωt)
Maximum acceleration: amax = ω^2A
Acceleration at a given displacement: a = -ω^2 x
(a) The maximum speed of the glider:
We can use the formula vmax = Aω where A = 0.040 m and ω = √(k/m) to find the maximum speed of the glider.
vmax = Aω
vmax = (0.040 m) x √(450 N/m ÷ 0.500 kg)
vmax = 1.26 m/s
Therefore, the maximum speed of the glider is 1.26 m/s.
(b) The speed of the glider when it is at x = -0.015 m:
We can use the formula v = -ωA sin(ωt) where A = 0.040 m, x = -0.015 m, and ω = √(k/m) to find the speed of the glider when it is at x = -0.015 m.
v = -ωA sin(ωt)
v = -√(k/m)A sin(ωt)
v = -√(450 N/m ÷ 0.500 kg)(0.040 m)sin(ωt)
v = -0.714 m/s
Therefore, the speed of the glider when it is at x = -0.015 m is -0.714 m/s.
(c) The magnitude of the maximum acceleration of the glider:
We can use the formula amax = ω^2A where A = 0.040 m and ω = √(k/m) to find the magnitude of the maximum acceleration of the glider.
amax = ω^2A
amax = (√(k/m))^2A
amax = (450 N/m ÷ 0.500 kg)(0.040 m)
amax = 36.0 m/s²
Therefore, the magnitude of the maximum acceleration of the glider is 36.0 m/s².
(d) The acceleration of the glider at x = -0.015 m:
We can use the formula a = -ω^2 x where x = -0.015 m and ω = √(k/m) to find the acceleration of the glider at x = -0.015 m.
a = -ω^2 x
a = -√(k/m)^2 x
a = -√(450 N/m ÷ 0.500 kg)^2(-0.015 m)
a = 30.6 m/s²
Therefore, the acceleration of the glider at x = -0.015 m is 30.6 m/s².
(e) The total mechanical energy of the glider at any point in its motion:
We can use the formula E = (1/2)kA^2 to find the total mechanical energy of the glider at any point in its motion.
E = (1/2)kA^2
E = (1/2)(450 N/m)(0.040 m)^2
E = 0.36 J
Therefore, the total mechanical energy of the glider at any point in its motion is 0.36 J.

learn more about Simple Harmonic Motion Refer: https://brainly.com/question/30404816

#SPJ11

60 kg acceleration due to gravity in the moon

Answers

Therefore, a 60kg object would weigh approximately 96 Newtons on the moon.

Weight calculation .

The acceleration due gravity on the moon is a measure of how much objects accelerate toward the moon's surface under the influence of its gravitational force. It is denoted by the symbol g and gas a value of approximately 1.6m/s²

To calculate the weight of a 60kg object on the moon, you can use the formula:

Weight = mass × acceleration due to gravity

Weight = 60kg × 1.6m/s²

Weight on the moon = 96N

Therefore, a 60kg object would weigh approximately 96 Newtons on the moon.

Learn more about weight below.

https://brainly.com/question/487218

#SPJ1

Use Newton’s method to find solutions accurate to within 10−4 for the following problems.
a. x 3 − 2x2 − 5 = 0, [1, 4] b. x3 + 3x2 − 1 = 0, [−3,−2]
c. x − cos x = 0, [0, π/2] d. x − 0.8 − 0.2 sin x = 0, [0, π/2]

Answers

The solution for first equation is x ≈ 2.6906,the solution for second  equation is x ≈ -2.2408,The solution for third equation is x ≈ 0.7391,The solution for fourth equation is x ≈ 0.8627.

Sure, here are the simplified solutions for each problem:

a. [tex]x^3 - 2x^2[/tex] - 5 = 0, [1, 4]

- Start with x0 = 2.5 (the midpoint of the interval [1, 4])

- Apply Newton's method: xn+1 = xn - f(xn)/f'(xn)

- f(x) = [tex]x^3 - 2x^2[/tex] - 5

- f'(x) = [tex]3x^2[/tex]- 4x

- After several iterations, the solution is x ≈ 2.6906

b. x^3 + 3x^2 - 1 = 0, [-3, -2]

- Start with x0 = -2.5 (the midpoint of the interval [-3, -2])

- Apply Newton's method: xn+1 = xn - f(xn)/f'(xn)

- f(x) = [tex]x^3 + 3x^2[/tex] - 1

- f'(x) = [tex]3x^2[/tex] + 6x

- After several iterations, the solution is x ≈ -2.2408

c. x - cos(x) = 0, [0, π/2]

- Start with x0 = 0.5 (the midpoint of the interval [0, π/2])

- Apply Newton's method: xn+1 = xn - f(xn)/f'(xn)

- f(x) = x - cos(x)

- f'(x) = 1 + sin(x)

- After several iterations, the solution is x ≈ 0.7391

d. x - 0.8 - 0.2sin(x) = 0, [0, π/2]

- Start with x0 = 0.5 (the midpoint of the interval [0, π/2])

- Apply Newton's method: xn+1 = xn - f(xn)/f'(xn)

- f(x) = x - 0.8 - 0.2sin(x)

- f'(x) = 1 - 0.2cos(x)

- After several iterations, the solution is x ≈ 0.8627

Learn more about Newton's method here:

https://brainly.com/question/14865059

#SPJ11

Final answer:

The process of Newton's method involves approximating the roots of a function by repetitively applying a formula until the result is found within the desired accuracy. This method is applied to each problem given, assuming the corresponding intervals.

Explanation:Newton's method

Newton's method is an iterative procedure used to find successively better approximations for the roots (or zeroes) of a real-valued function.

For example, to solve the problem (a) x^3 - 2x^2 - 5 = 0, we must first choose an initial approximation (x0) in the given interval. Second, find the derivative of the function which in this case is 3x^2 - 4x. Third, use the formula x1 = x0 - (f(x0) / f'(x0)) to find the new approximation. Repeat the third step until the equation f(x1) equals 0 within the desired accuracy.

This same process will be done for the other equations and also maintaining their respective intervals as stated in the question.

Learn more about Newton's Method here:

https://brainly.com/question/31910767

If it takes 526 J of energy to warm 7. 40 gr of water by 17°C, how much energy would be needed to warm 7. 40 gr of water by 55°C?

Answers

The energy required to warm 7.40 grams of water by 17°C is 526 J. Now we need to determine the energy needed to warm the same amount of water by 55°C.

To calculate the energy needed to warm water, we can use the equation [tex]Q = mc\triangle T[/tex], where Q represents the energy, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature. In this case, we are given the mass of water (m = 7.40 g) and the change in temperature (ΔT = 55°C - 17°C = 38°C).

However, we need to know the specific heat capacity of water to proceed with the calculation. The specific heat capacity of water is approximately 4.18 J/g°C. Now we can substitute the values into the equation: Q = (7.40 g) * (4.18 J/g°C) * (38°C). Calculating this gives us Q = 1203.092 J.

Therefore, to warm 7.40 grams of water by 55°C, approximately 1203.092 J of energy would be needed.

Learn more about specific heat capacity here:

https://brainly.com/question/28302909

#SPJ11

Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the following quark combinations:
Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the quark combination uus.
Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the quark combination cs (s bar).
Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the quark combination ddu (bar over all three).
Determine the electric charge, baryon number, strangeness quantum number, and charm quantum number for the quark combination cb (b bar).

Answers

a) Electric charge = +2/3, Baryon number = 1/3, Strangeness quantum number = 0, Charm quantum number = 0

b) Electric charge = 0, Baryon number = 1/3, Strangeness quantum number = 0, Charm quantum number = +1

c) Electric charge = 0, Baryon number = 1/3, Strangeness quantum number = 0, Charm quantum number = 0

d) Electric charge = 0, Baryon number = 1/3, Strangeness quantum number = -1, Charm quantum number = 0

a) The quark combination "uss" consists of two strange quarks and one up quark. Therefore, the electric charge of this combination is:

(2/3) x 2 + (-1/3) x 1 = +1/3

The baryon number of this combination is: (1/3) x 3 = 1/3

Since there are no strange quarks in this combination, the strangeness quantum number is: 0

Similarly, there are no charm quarks in this combination, so the charm quantum number is also: 0

b) The quark combination "cs" consists of one charm quark and one strange quark. Therefore, the electric charge of this combination is:

(2/3) x 1 + (-1/3) x 1 = 1/3 - 1/3 = 0

The baryon number of this combination is: (1/3) x 2 = 2/3

Since there is one strange quark in this combination, the strangeness quantum number is: -1

There is one charm quark in this combination, so the charm quantum number is: +1

c) The quark combination "ddu" consists of two down quarks and one up quark. Therefore, the electric charge of this combination is:

(-1/3) x 2 + (2/3) x 1 = -2/3 + 2/3 = 0

The baryon number of this combination is: (1/3) x 3 = 1/3

Since there are no strange quarks in this combination, the strangeness quantum number is: 0

Similarly, there are no charm quarks in this combination, so the charm quantum number is also: 0

d) The quark combination "cb" consists of one charm quark and one bottom quark. Therefore, the electric charge of this combination is:

(2/3) x 1 + (-1/3) x 1 = 1/3

The baryon number of this combination is: (1/3) x 2 = 2/3

Since there is one strange quark in this combination, the strangeness quantum number is: -1

There is one charm quark in this combination, so the charm quantum number is: 0

For more such questions on Electric charge, click on:

https://brainly.com/question/2373424

#SPJ11

The probable question may be:

follow the image for the question and table

Two particles, A and B, are moving in the directions shown. What should be the angle theta so that vB/A is minimum? 0degree 180 degree 90 degree 270 degree

Answers

The correct option is 90 degree.To minimize vB/A, the angle theta should be 90 degree.

What angle theta minimizes vB/A?

The velocity ratio vB/A is given by the formula vB/A = vB * sin(theta) / vA, theta is the angle between their respective directions, where vB is the velocity of particle B, vA is the velocity of particle A.

To minimize vB/A, we need to find the angle theta that results in the smallest value.

By analyzing the given options, we can see that the angle 90 degrees (option c) is the one that yields the minimum value for sin(theta).

When theta is 90 degrees, sin(theta) reaches its minimum value of 1. This means that vB/A is minimized, resulting in the smallest velocity ratio between particles A and B. therefore the option c is correct ,angle theta should be 90 degrees.

Learn more about angle

brainly.com/question/28451077

#SPJ11

A 0.70-kg air cart is attached to a spring and allowed to oscillate.A) If the displacement of the air cart from equilibrium is x=(10.0cm)cos[(2.00s−1)t+π], find the maximum kinetic energy of the cart.B) Find the maximum force exerted on it by the spring.

Answers

The maximum kinetic energy of the air cart is 4.43 J.

The maximum force exerted by the spring on the air cart is 11.08 N.

A) The maximum kinetic energy of the air cart can be found using the formula:

K_max = (1/2) * m * w² * A²

where m is the mass of the cart, w is the angular frequency (2pif), and A is the amplitude of oscillation (in meters).

Given that m = 0.70 kg, A = 0.10 m, and the frequency f = 2.00 s⁻¹, we can calculate the angular frequency as:

w = 2pif = 2pi2.00 s⁻¹ = 12.57 s⁻¹

Substituting these values in the formula, we get:

K_max = (1/2) * 0.70 kg * (12.57 s⁻¹)² * (0.10 m)²

K_max = 4.43 J

As a result, the air cart's maximum kinetic energy is 4.43 J.

B) The maximum force exerted by the spring can be found using the formula:

F_max = k * A

where k is the spring constant and A is the amplitude of oscillation (in meters).

We are not given the spring constant directly, but we can calculate it using the formula:

w = √(k/m)

where m is the mass of the cart and w is the angular frequency (in radians per second). Solving for k, we get:

k = m * w²

k = 0.70 kg * (12.57 s⁻¹)²

k = 110.78 N/m

Substituting the amplitude A = 0.10 m, we get:

F_max = k * A

F_max = 110.78 N/m * 0.10 m

F_max = 11.08 N

As a result, the spring's maximum force on the air cart is 11.08 N.

To know more about the Kinetic energy, here

https://brainly.com/question/10417121

#SPJ4

An inclined plane rise to aheight of 2m ovr a distanse of 6m find the angle of slope and velocity ratio

Answers

A theoretical force of 1962 Newtons is required to push an object with a mass of 200kg up the slope of the inclined plane that rises to a height of 2m over a distance of 6m.

An inclined plane is a simple machine that is a sloping surface that is used to raise or lower loads. It is a flat surface whose endpoint is at a higher level than its starting point, and it is one of the six classical simple machines.An inclined plane's slope is given by the ratio of its vertical rise to its horizontal run. In the case of the question, an inclined plane rises to a height of 2m over a distance of 6m. To calculate the angle of the slope, use the formula:tanθ = vertical rise/horizontal run= 2/6= 0.3333θ = tan-1 (0.3333)≈ 18.434°

The vr (and so ima) of the inclined plane is given by:Vr = L/h= 6/2= 3IMA = 1/sinθ= 1/sin18.434°= 1/0.3249≈ 3.08

The theoretical force required to push an object with a mass of 200kg up the slope can be determined using the formula:

Force = mass * acceleration

Force = 200 *9.81

Force = 1962 Newtons

learn more about inclined plane Refer: https://brainly.com/question/29360090

#SPJ11

a ferris wheel has a radius of r = 15 m and makes one complete rotation every t = 43 s. there is a rider on the ferris wheel of mass m = 45 kg.

Answers

The rider's weight on the Ferris wheel is mg = 441 N. The rider experiences a centripetal force of mv^2/r = 992 N at the top and 540 N at the bottom.

The rider's weight provides the necessary centripetal force for circular motion, causing the rider to feel lighter at the top of the Ferris wheel and heavier at the bottom. Using the equation for centripetal force, we can calculate the additional force felt by the rider at each point of the wheel's rotation. At the top, the rider experiences a force of mv^2/r, where v is the velocity of the rider at the top of the wheel. At the bottom, the rider experiences a force of mg + mv^2/r. Given the radius and time period of the Ferris wheel, we can find the velocity of the rider at the top and bottom and calculate the additional forces experienced.

Learn more about rotation here:

https://brainly.com/question/1571997

#SPJ11

An object moves in a horizontal circle with a speed of 2.0 m/s. What would be its speed if the radius of its motion doubled? (Assume the centripetal force and mass remain constant.)
ons in
Finance - on
plorer
1.5 m/s
0 2.8 m/s
4.0 m/s
5.2 m/s
8.3 m/s

Answers

Answer: how do do it

Explanation:

ur welcome

Other Questions
In these views of the larynx, what structure does number 4 indicate?A. Tracheal cartilageB. Thyroid cartilageC. Arytenoid cartilageD. Cricoid cartilageE. Corniculate cartilage Why is it possible to set the energy of the ground vibrational and electronic energy level to zero?Answer choices: The energy of the ground state can be set to zero since it is the relative energy of the levels that is important in determination of quantities such as occupation probabilities.The energy of the ground state can be set to zero because the second derivative of the partition function is equal to zero.The energy of the ground state can be set to zero because the partition function cannot be constructed without setting the ground-state energy to zero.The energy of the ground state can be set to zero because the amount of thermal energy available to any system is much greater than the energy of the ground state. Calculate the volume that 38.8 g of CO2 occupies at 725 mmHg and 25.0C. SECTION B: ACTIVITY 2 Answer ALL the questions in this section Write paragraphs on the questions below Marks will only be allocated for responses written in full sentences 2. 1 Explain how a commitment to a decision could assist a school leaver to adapt to the change of entrepreneurship (4 x 2) (8) 22 Discuss FOUR reasons why it is important for a novice entrepreneur to build positive relationships with customers. (4x 2) (8) 23 Discuss TWO social factors (excluding friends and social interaction) that may contribute to unemployment in South Africa amongst the youth (2 x 2) (4) 24 Advise school leavers on FOUR stress management techniques to deal with the psychological impact of unemployment (4x2) (8) Multiple Linear Regression: A) Multiple linear regression allows for the effect of potential confounding variables to be controlled for in the analysis of a relationship between X and Y (T or F)? B) If researchers want to assume that X1 is the explanatory variable in a linear model Y=+1*X1+2*X2+3*X3, and then decide that they want to observe the relationship as though X2 were the explanatory variable, they must re-work the model and compute new beta coefficients (T or F)? C) Deviations away from the diagonal line presented in a normal Q-Q plot output indicate a high R2 value, and thus a proper approximation by the multiple linear regression model (T or F)? a student determines that the value of ka for hf = 9.910-4 . what is the value of pka? a. move the endpoints of the demand (d) and marginal revenue (mr) curves to depict a typical gas station in this short-run situation. You are evaluating the purchase of a high precision end mill. Today's price of this end mill is $300,000. Calculate the inflated interest rate "if" given the real interest rate of 6% and the inflation rate of 3%.Question 10 options:a) 8.82%. b) 9.18%. c) 12.32%. d) 10.56% A eukaryotic cell can use glucose and hexanoic acid as fuels for cellular respiration. On the basis of their structural formulas, which substrate releases more energy per gram on complete combustion to co2 and h2o If it is impossible to raise the landing gear of a jet airplane, to obtain best range, the airspeed must be _____ from that for the clean configurationa) increasedb) decreasedc) not change what is cryptolocker? what are the three ways to protect yourself from ransomware infection? an object is located a distance of d0 = 15 cm in front of a concave mirror whose focal length is f = 11 cm.Write an expression for the image distance di The theoretical probability of winning a prize at the fair is 2/13. You play the game 435 times trying to win. How many times do you expect to win? the relationship between stages of a dynamic programming problem is called electromagnetic write up of the brave little toaster movie in what chamber of the u.s. congress do democrats currently have control by the slimmest of margins? Find the derivative of the function f(x, y) = arctan(y/x) at point (3, 3) in the direction the function increases most rapidly. Select the correct text in the passage. Which sentence in the excerpt the best supports the idea that the government has an obligation to provide certain things to its citizens?Excerpt from message to the Congress in special session July 4, 1861 Select the correct statement.Stack canaries stop all buffer overflow exploits by adding a random value to the stack that helps detect if the return address was modified.Stack canaries make buffer overflow attacks impossible by rearranging the memory inside of a process so that the stack grows away from the return address, rather than towards it.Stack canaries make buffer overflow attacks more difficult by adding a random value to the stack that helps detect if the return address was modified.Stack canaries make buffer overflow attacks more difficult by rearranging the memory inside of a process so that the stack grows away from the return address, rather than towards it. The major impact of product innovation tends to be on the firms' revenues, while that of process innovation tends to be on costs. True or False