Free energy is a thermodynamic potential that can be used to calculate the maximum reversible work that can be performed by a thermodynamic system at a constant temperature and pressure. It is fulfilled that if the energy change is less than zero it will mean that the relationship will proceed towards the product, while if the relationship is greater than zero the reaction will proceed towards the reactant. Therefore the correct option is D.
The free energy change of a reaction can determine the reaction direction
Measure the distance from the drop point in Brazil to the drop point in Angola. Use that number in your calculation. Given that this portion of Pangaea broke apart 200,000,000 years ago, calculate how fast South America and Africa are separating in cm/year? (Hint: Speed= Distance/Time)
To develop this point we will start by finding the approximate coordinates of the points that were connected at the time of the Pangaea between Brazil and Angola. These coordinates are presented below.
1 . Brazil - Latitude: 18 0 07’ 55.56” S Longitude: 39 0 35’ 14.50” W 2.
Angola - Latitude: 9 0 08’ 50.02” S Longitude: 13 0 02’ 32.11” E
Using a tool for calculating distances between these two points we will notice that its distance is 576,155,570.12 cm
Applying the equation given in the statement we will have to,
[tex]v = \frac{x}{t} \rightarrow v = Velocity, x = Distance, t = Time[/tex]
200,000,000 years have passed and the movement was previously found, so the speed of travel is,
[tex]v = \frac{576,155,570.12cm}{200.000.000 years}[/tex]
[tex]v = 2.88 cm/year[/tex]
Therefore the velocity is 2.88 cm per year.
In the deep space between galaxies, the density of atoms is as low as 106 atoms/m3, and the temperature is a frigid 2.7 K. What is the pressure (in Pa)?
Answer: 3.73 × 10^-17 Pa
Explanation:
N/V= 10^6 atom/m^3
T=2.7k
Kb=1.38 ×10^-23 J/K
NA= 6.02 × 10^23 mol^-1
R= 8.31J/mol.K
PV= NaKbT
PV= N/V × KbT
P= 10^6 × 1.38 × 10^-23× 2.7
Pressure= 3.73×10^-17 Pa
The pressure in pascal of the deep space whose density of atoms is as low as 10⁶ atoms/m3 is 3.73 × 10-¹⁷ Pa.
How to calculate pressure?The pressure of a space can be calculated using the following expression:
PV= N/V × KbT
Where;
P = pressureV = volumeKb = temperature constantT = temperatureR = gas law constantN/V = 10⁶ atom/m³T = 2.7KKb = 1.38 ×10^-23 J/KNA= 6.02 × 10²³ mol-¹R= 8.31J/mol.KP = N/V × KbT
P= 10⁶ × 1.38 × 10-²³ × 2.7
Pressure = 3.73 × 10-¹⁷ Pa
Therefore, the pressure in pascal of the deep space whose density of atoms is as low as 10⁶ atoms/m3 is 3.73 × 10-¹⁷ Pa.
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A mosquito of mass 0.15 mg is found to be flying at a speed of 50 cm/s with an uncertainty of 0.5 mm/s. (a) How precisely may its position be known? (b) Does this inherent uncertainty present any hindrance to the application of classical mechanics?
(a) The uncertainty principle reveals that the position of a flying mosquito can be known with an extremely high precision that doesn't affect the application of classical mechanics. (b) The inherent uncertainty calculated is extremely small.
(a) The Heisenberg principle states that the more precisely the position (Δx) of a particle is known, the less precisely its momentum (Δp) can be known, and vice versa. This is quantitatively expressed as ΔxΔp ≥ ħ/2, where ħ is the reduced Planck's constant (approximately 1.055 × 10⁻³⁴ J⋅s).
Given the speed (v) of the mosquito is 50 cm/s with an uncertainty in velocity (Δv) of 0.5 mm/s, and the mass (m) of the mosquito is 0.15 mg, we first convert these to SI units: v = 0.5 m/s, Δv = 5 × 10⁻⁴ m/s, and m = 0.15 × 10⁻⁶ kg. The uncertainty in momentum, Δp, is mΔv = (0.15 × 10⁻⁶ kg)(5 × 10⁻⁴ m/s) = 7.5 × 10⁻¹¹ kg⋅m/s.
Using the uncertainty principle, Δx ≥ ħ / (2Δp), where Δp is the momentum uncertainty calculated above. Plugging in values, Δx ≥ (1.055 × 10⁻³⁴ J⋅s) / (2 × 7.5 × 10⁻¹¹ kg⋅m/s) ≈ 7.033 × 10⁻²⁵ meters. This calculation shows how precisely the mosquito's position can be known.
(b) The inherent uncertainty calculated is extremely small, particularly when dealing with macroscopic objects like a mosquito. Therefore, this uncertainty does not present any hindrance to the application of classical mechanics, which comfortably applies at the scale of everyday objects.
consider a perfectly inelastic head-on collision between a small car and a large truck traveling at the same speed. Which vehicle has a greater change in kinetic energy as a result of the collision
Answer: The truck has a greater kinetic energy
Explanation:
The initial velocities of both the truck and car are the same. Likewise, the final velocity is the same. The change in kinetic energy is dependent only on mass. The truck has a greater mass, therefore, the change in its kinetic energy is greater.
The sound from a trumpet radiates uniformly in all directions in air with a temperature of 20∘C. At a distance of 5.18 m from the trumpet the sound intensity level is 54.0 dB . The frequency is 561 Hz .
What is the pressure amplitude at this distance?
Answer:
[tex]P=1.44*10^{-2}Pa[/tex]
Explanation:
The pressure amplitude is given by:
[tex]P=\sqrt{2I\rho v[/tex]
Here, I is the sound intensity, [tex]\rho[/tex] the density of the air and v the speed of air.
The sound intensity can be calculated from:
[tex]I=10^\beta I_0[/tex]
Where [tex]\beta[/tex] is the sound intensity level in bels and [tex]I_0[/tex] is the reference sound intensity. So, replacing (2) in (1):
[tex]P=\sqrt{2(10^\beta) I_o \rho v}\\P=\sqrt{2(10^{5.4})(10^{-14}\frac{W}{m^2})(1.2\frac{kg}{m^3})(344\frac{m}{s})}\\P=1.44*10^{-2}Pa[/tex]
The pressure amplitude is found using the formulas for pressure amplitude and sound intensity. Once the sound intensity is found, the pressure amplitude can be calculated, given the speed and density of air. The pressure amplitude at the given distance is approximately 0.0143 Pa.
Explanation:The pressure amplitude can be found with the formula p = √(2*ρ*v*I), where p is the pressure amplitude, ρ is the density of the medium (air), v is the speed of sound in the medium, and I is sound intensity. The sound intensity level (dB) can be converted to sound intensity (W/m^2) by using the formula I = I0 * 10^(L/10), where I0 is the reference intensity (10^-12 W/m^2) and L is the sound intensity level in decibels.
So, calculating the sound intensity I = (10^-12 W/m^2) * 10^(54/10) = 0.002 W/m^2. Once we have the sound intensity, we can calculate the pressure amplitude using the speeds of sound in air at 20°C (343 m/s), and the density of air at sea level (1.225 kg/m^3). Substituting these values into our formula results in a pressure amplitude of about 0.0143 Pa.
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What is the wavelength, in nm, of the line in the hydrogen spectrum when one n value is 3 and the other n value is 6?
Answer:
[tex]\lambda=1090nm[/tex]
Explanation:
Rydberg formula is used to calculate the wavelengths of the spectral lines of many chemical elements. For the hydrogen, is defined as:
[tex]\frac{1}{\lambda}=R_H(\frac{1}{n_1^2}-\frac{1}{n_2^2})[/tex]
Where [tex]R_H[/tex] is the Rydberg constant for hydrogen and [tex]n_1[/tex], [tex]n_2[/tex] are the lower energy state and the higher energy state, respectively.
[tex]\frac{1}{\lambda}=1.10*10^{7}m^{-1}(\frac{1}{3^2}-\frac{1}{6^2})\\\frac{1}{\lambda}=9.17*10^{5}m^{-1}\\\lambda=\frac{1}{1.09*10^{6}m^{-1}}\\\lambda=1.09*10^{-6}m*\frac{10^{9}nm}{1m}\\\lambda=1090nm[/tex]
For each of the statements below, decide which of the Maxwell equations (forstaticsituations) tells you that the statement is true. Briefly, justify your answers.
(a) There are no magnetic monopoles.
(b) There must be a scalar potential.
(c) There must be a vector potential.
(d) Charges create electric fields.2.
Answer:
(a)There are no magnetic monopoles. true
(c) There must be a vector potential. true
(d) Charges create electric fields.2. true
Explanation:
a) there are no magnetic monopoles because magnetic field is created by charges (electrons) and these electrons have dipole field so it is not possible to have magnetic dipoles, more ever Gauss's law always explained that there are not magnetic dipoles. furthermore magnetic monopoles aree caused by magnetic charges and we have electric charges.
c)vector potential is a vector field which serves as a potential for magnetic field so, the magnetic field B by Faraday and Gauss's law is also known as vector potential.
d) electric field is solely generated by charges be it static charges or moving charges if there are no charges it is not possible to have an electric field.
Determine the period of a 1.7-m-long pendulum on the Moon, where the free-fall acceleration is 1.624 m/s2. Express your answer with the appropriate units.
Answer:
6.42 s
Explanation:
Period: This can be defined as the time taken for a wave or an oscillating body to complete on oscillation. The S.I unit of period is Second (s).
The period of a simple pendulum is represented as,
T = 2π√(L/g)....................................... Equation 1.
Where T = period, L = length of the pendulum, g = acceleration due to gravity. π = pie.
Given: L = 1.7 m, g = 1.624 m/s² and π = 3.14
T = 2(3.14)√(1.7/1.624)
T = 6.28√(1.047)
T = 6.28×1.023
T = 6.42 s.
Thus, the period of the pendulum = 6.42 s
The period of a 1.7-m-long pendulum on the Moon, where the free-fall acceleration is 1.624 m/s² is 6.425 secs
The formula for calculating the period of a simple pendulum is expressed using the formula:
[tex]T=2 \pi\sqrt{\frac{l}{g} }[/tex]
l is the length of the pendulum
g is the acceleration due to gravity
Given the following parameters
g = 1.624 m/s²
l = 1.7m
Substitute the given values into the formula:
[tex]T=2(3.14)\sqrt{\frac{1.7}{1.624} } \\T=6.28\sqrt{1.0468}\\T=6.28(1.0231)\\T = 6.425secs[/tex]
Hence the period of a 1.7-m-long pendulum on the Moon, where the free-fall acceleration is 1.624 m/s² is 6.425 secs.
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Why is everything spinning? Moons, planets and stars all rotate on their axes, moons orbit planets, planets orbit stars, spiral galaxies rotate around super-massive black holes, etc. What force is causing all this spinning?
Answer:
Conservation of angular momentum
Explanation:
When the objects spread in universe after big bang, because of the tremendous force , they gained angular momentum and started to rotate. Since, then the object continue to rotate on their axis because of conservation of angular momentum. In vacuum of space there no other forces that can stop these rotation, therefore, they continue to rotate.
Two small plastic spheres are given positive electrical charges. When they are 16.0 cm apart, the repulsive force between them has magnitude 0.200 N.
a)What is the charge on each sphere if the two charges are equal?
b)What is the charge on each sphere if one sphere has four times the charge of the other?
The smaller charge is approximately **3.37 x 10⁻⁷ C** and the larger charge is approximately **1.35 x 10⁻⁶ C**.
These are approximate values due to rounding during calculations.
Solving for the Charges on the Spheres:
Case (a): Equal Charges
1. **Apply Coulomb's Law:** The force between two charged objects is given by Coulomb's Law:
[tex]$$F = k \cdot \frac{q_1 \cdot q_2}{r^2}$$[/tex]
where:
* F is the force (0.200 N)
* k is Coulomb's constant (8.99 x 10^9 N m²/C²)
* q₁ and q₂ are the charges on the spheres (which are equal in this case)
* r is the distance between the spheres (0.16 m)
2. **Plug in the values and solve for q₁:**
[tex]$$0.200 = 8.99 \times 10^9 \cdot \frac{q_1^2}{(0.16)^2}$$$$q_1^2 = \frac{0.200 \cdot (0.16)^2}{8.99 \times 10^9}$$$$q_1 = \sqrt{ \frac{0.200 \cdot (0.16)^2}{8.99 \times 10^9}} \approx 7.54 \times 10^{-7} \text{ C}$$[/tex]
Therefore, the charge on each sphere is approximately **7.54 x 10⁻⁷ C**.
Case (b): One Sphere has Four Times the Charge
1. **Let q₁ be the smaller charge and q₂ be the larger charge:** We know q₂ = 4q₁.
2. **Apply Coulomb's Law again:
[tex]$$0.200 = 8.99 \times 10^9 \cdot \frac{q_1 \cdot q_2}{(0.16)^2}$$$$0.200 = 8.99 \times 10^9 \cdot \frac{q_1 \cdot (4q_1)}{(0.16)^2}$$3. **Substitute and solve for q₁:**$$0.200 = 8.99 \times 10^9 \cdot \frac{16q_1^2}{(0.16)^2}$$$$q_1^2 = \frac{0.200 \cdot (0.16)^2}{8.99 \times 10^9 \cdot 16}$$$$q_1 = \sqrt{ \frac{0.200 \cdot (0.16)^2}{8.99 \times 10^9 \cdot 16}} \approx 3.37 \times 10^{-7} \text{ C}$$4. **Find the larger charge (q₂):**$$q_2 = 4q_1 = 4 \cdot (3.37 \times 10^{-7} \text{ C}[/tex]
An electronic package with a surface area of 1 m2 placed in an orbiting space station is exposed to space. The electronics in this package dissipate all 1850 W of its power to space through its exposed surface. The exposed surface has an emissivity of 1.0 and an absorptivity of 0.25. Given: σ = 5.67×10–8 W/m2·K4
Final answer:
The temperature of the patch is approximately 1387 Kelvin, and the rate of heat loss through the patch is approximately 0.07 Watts.
Explanation:
The temperature of the patch can be calculated using the Stefan-Boltzmann law of thermal radiation, which states that the power radiated by an object is proportional to the fourth power of its temperature. The equation to calculate the temperature is:
T = sqrt((P / (A * sigma * e))
Where T is the temperature, P is the power, A is the surface area, sigma is the Stefan-Boltzmann constant, and e is the emissivity. Substituting the given values:
T = sqrt((1850 W / (1 m2 * 5.67×10–8 W/m2·K4 * 1.0)))
T = sqrt((1850 W / 5.67×10–8 W/m2·K4))
Calculating the square root:
T = 1387 K
The temperature of the patch is approximately 1387 Kelvin.
The rate of heat loss through the patch can be calculated using the Stefan-Boltzmann law:
P = A * e * sigma * T4
Substituting the known values:
P = (0.05 m * 0.08 m * 5.67×10–8 W/m2·K4 * 0.300 * (1387 K)4)
Calculating the power:
P = 0.07 W
The rate of heat loss through the patch is approximately 0.07 Watts.
the number of electrons in a copper penny is approximately 10 10^23. How large would the force be on an object if it carried this charge and were repelled by an equal charge one meter away?
Answer:
0.000230144 N
Explanation:
n = Number of electrons = [tex]10\times 10^{23}[/tex]
q = Charge of electron = [tex]1.6\times 10^{-19}\ C[/tex]
k = Coulomb constant = [tex]8.99\times 10^{9}\ Nm^2/C^2[/tex]
r = Distance between obects = 1 m
The force would be
[tex]F=\dfrac{nkq^2}{r^2}\\\Rightarrow F=\dfrac{10\times 10^{23}\times 8.99\times 10^9\times (1.6\times 10^{-19})^2}{1^2}\\\Rightarrow F=0.000230144[/tex]
The force would be 0.000230144 N
7. A neutral aluminum rod is at rest on a foam insulating base. A negatively charged balloon is brought near one end of the rod but not in direct contact with it. In what way, if any, will the charges in the rod be affected?
Answer:
If a negatively charged balloon is brought near one end of the rod but not in direct contact, then the negative charges on the balloon repel the same amount of negative charges on the end of the rod that is close to the balloon, and the positive charges stay at the balloon-side of the rod. The total charge of the rod is still zero, but the distribution of the charges are now non-uniform.
A stretched string is fixed at both ends, 77.7 cm apart. If the density of the string is 0.014 g/cm and its tension is 600 N, what is the wavelength of the first harmonic?
Answer:
The wavelength of the first harmonic is 155.4 cm.
Explanation:
Given that,
The separation between a stretched string that is fixed at both ends, l = 77.7 cm
The density of the string, [tex]d=0.014\ g/cm^3[/tex]
Tension in the string, T = 600 N
We need to find the wavelength of the first harmonic. The wavelength of the nth harmonic on the string that is fixed at both ends is given by :
[tex]\lambda=\dfrac{2l}{n}[/tex]
Here, n = 1
[tex]\lambda=2l[/tex]
[tex]\lambda=2\times 77.7[/tex]
[tex]\lambda=155.4\ cm[/tex]
So, the wavelength of the first harmonic is 155.4 cm. Hence, this is the required solution.
The wavelength of the first harmonic will be "155.4 cm".
Wavelength and DensityAccording to the question,
Separation between stretched string, I = 77.7 cm
String's density, d = 0.014 g/cm³
String's tension, T = 600 N
We know the relation,
Wavelength, λ = [tex]\frac{2l}{n}[/tex]
here, n = 1
then, λ = 2l
By substituting the values,
= 2 × 77.7
= 155.4 cm
Thus the above answer is appropriate.
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What is the energy of light that must be absorbed by a hydrogen atom to transition an electron from n = 3 to n = 5?
The energy absorbed by a hydrogen atom to transition an electron from n = 3 to n = 5 can be calculated using the Rydberg formula. The resulting value, given in Joules, can be converted to electron volts for ease of comparison.
Explanation:The energy of light absorbed by a hydrogen atom to transition an electron from n = 3 to n = 5 can be calculated using the Rydberg formula, which describes the energies of the orbits of electrons in a hydrogen atom. The formula uses Rydberg's constant (RH = 2.18 × 10^-18 J) and the principal quantum numbers of the initial (ni) and final (nf) states:
ΔE = RH . ((1/ni²) - (1/nf²))
In this case, ni = 3 (the initial energy level) and nf = 5 (the final energy level). Therefore, to find the energy involved in this transition, we substitute these values into the formula:
ΔE = 2.18 × 10^-18 . ((1/3²) - (1/5²))
The result you get from this calculation is in Joules, and to convert it to electron volts (eV), divide by 1.6 × 10^-19 (since 1 eV = 1.6 × 10^-19 J).
This numerical calculation will represent the energy absorbed by the atom as the electron transitions from n = 3 to n = 5, mentioned in the question.
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The coefficient of performance of a refrigerator is 5.0.
A. If the compressor uses 10 J of energy, how much heat is exhausted to the hot reservoir?
B. if the hot reservoir temperature is 27 degrees Celsius, what is the lowest possible temperature in degrees Celsius of the cold reservoir?
Answer:
[tex]Q_x=60\ J[/tex]
[tex]T_L=-23\ ^{\circ}C[/tex] is the lowest possible temperature of the cold reservoir.
Explanation:
Given:
Coefficient of performance of refrigerator, [tex]COP=5[/tex]
A)
We know that for a refrigerator:
[tex]\rm COP=\frac{ desired\ effect }{\: energy\ supplied }[/tex]
Given that 10 J of energy is consumed by the compressor:
[tex]5=\frac{desired\ effect}{10}[/tex]
[tex]\rm Desired\ effect=50\ J[/tex]
Now the by the conservation of energy the heat exhausted :
[tex]Q_x=50+10[/tex]
[tex]Q_x=60\ J[/tex]
B)
Also
[tex]COP=\frac{T_L}{T_H-T_L}[/tex]
where:
[tex]T_H\ \&\ T_L[/tex] are the absolute temperatures of high and low temperature reservoirs respectively.
[tex]5=\frac{T_L}{(273+27)-T_L}[/tex]
[tex]1500-5\times T_L=T_L[/tex]
[tex]T_L=250\ K[/tex]
[tex]T_L=-23\ ^{\circ}C[/tex] is the lowest possible temperature of the cold reservoir.
Final answer:
The coefficient of performance (COP) of a refrigerator is the ratio of heat removed from the cold reservoir to the work done by the compressor. Using this definition, we can solve for the amount of heat exhausted to the hot reservoir and the temperature of the cold reservoir.
Explanation:
The coefficient of performance (COP) of a refrigerator is a measure of its efficiency. It is defined as the ratio of heat removed from the cold reservoir to the work done by the compressor:
COP = heat removed / work done
(A) To find the amount of heat exhausted to the hot reservoir, we can use the formula:
heat removed = COP x work done
Substituting the given values, we get:
heat removed = 5.0 x 10 J = 50 J
(B) To find the lowest possible temperature of the cold reservoir, we can use the Carnot efficiency formula:
COP = hot temperature / (hot temperature - cold temperature)
Substituting the given values and rearranging the formula, we get:
cold temperature = hot temperature - (hot temperature / COP)
cold temperature = 27°C - (27°C / 5.0) = 21.6°C
Which is true about inelastic collisions: a. An inelastic collision does not obey conservation of energy. b. An inelastic collision conserves kinetic energy. c. Objects will stick together upon collision. d. Momentum is not conserved in inelastic collisions..
Answer:
Option c is correct
Explanation:
There are two types of collisions-elastic collision and inelastic collision.
In elastic collision, both kinetic energy and total momentum are conserved. On the other hand, in inelastic collision, total momentum is conserved but kinetic energy is not conserved. Thus, option b and d are incorrect.
Total energy is always conserved in both types. Thus, option a is incorrect.
In a perfectly inelastic collision, objects stick together. This happens because maximum kinetic energy is dissipated and used in bonding of the two objects. Thus, correct option is c.
Answer:
i believe its a?
Explanation:
In an inelastic collision, momentum is conserved
I’m not accelerating, so the net (vertical) force on me, while I’m sitting here doing this lab is _________
Answer:
Net force is zero
Explanation:
According to the Newton's second law, the net force on the body is equal to the product of mas of body and the acceleration.
here acceleration is equal to zero so net force is also zero because mass of an object can never be zero.
What is the speed v of a wave traveling down such a wire if the wire is stretched to its breaking point?
Answer:
v = 620.17 m/s
Explanation:
There are different formulas for calculating the speed of a wave. Based on the given parameters, the speed of the wave can be estimated as:
v = sqrt(breaking tensile strength/density)
Where:
The breaking tensile strength = 3*10^9 N/m^2
Density = 7800 kg/m^3
Therefore, we can estimate the speed of the wave as shown below:
v = sqrt(3*10^9/7800) = sqrt(384615.3846) = 620.17 m/s
The speed of a wave in a wire at its breaking point depends on the maximum tension the wire can sustain and its linear mass density, calculated with the formula v = (T/μ)¹⁄².
Explanation:The speed v of a wave traveling down a wire at its breaking point would be determined by the tension in the wire just before breaking and the wire's linear mass density. The formula for the speed of a wave on a stretched string is v = (T/μ)¹⁄², where T is the tension in the wire and μ is the linear mass density. For a wire stretched to its breaking point, the tension T would be at its maximum value that the wire can sustain without breaking.
If Earth were twice as massive but it revolved at the same distance from the Sun, its orbital period would be
A) 1 year.
B) 3 years.
C) 2 years.
D) 4 years.
E) 6 months.
A) 1 Year, if the Earth is larger in mass, but still the same distance from the sun, it will orbit at the same rate.
The Earth will continue to orbit at the same rate even if its mass increases but its distance from the sun stays the same, or 1 year. Hence, option A is correct.
What are planets?A huge, spherical celestial object that is not a star nor a remnant is called a planet. The emission nebula hypothesis, which holds that a cosmic cloud collapses out of a supernova to produce a young primitive orbited by a planetary system, is the best theory currently available for explaining planet formation. The slow accumulation of matter propelled by gravity—a process known as accretion—leads to the formation of planets in this disk.
The planetary systems Mercury, Venus, Earth, and Mars, as well as the giant planets Jupiter, Saturn, Uranus, and Neptune, make up the Solar System's minimum number of eight planets. Each of these planets revolves around an axis that is inclined with regard to its orbit pole.
Hence, option A is correct.
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Why isn't Coulomb's law valid for large conducting objects, even if they are spherically symmetrical?
Answer:
The Coulomb’s Law is as follows
[tex] \vec{F} = \frac{1}{4\pi \epsilon_0}\frac{q_1q_2}{r^2}\^r[/tex]
According to this law, the force between two charged objects can be calculated using the distance between the objects. If the objects are large, then it is not possible to determine the distance, r, between that object and the other object. Because, the edge of the object contain charges as well as the center of the object.
In that case, you need to separate the object into infinitesimal points, apply the formula to those points, then integrate over the large object to find the force between objects.
If a rope loaded with a force of 100 lbf had a spring constant of 500 lbf/inch, how far would the rope stretch or elongate?
To solve this problem we will apply the concepts related to Hooke's law for which the force exerted on a spring is described as the product between the spring constant and its displacement, that is
[tex]F = kx[/tex]
Where k is the spring's constant and x is the elongation,
Rearranging to find the elongation we have
[tex]x = \frac{F}{k}[/tex]
Replacing,
[tex]x = \frac{100}{500}[/tex]
[tex]x = 0.2in[/tex]
[tex]x = 5.08mm[/tex]
Therefore the elongation produced in the rope from its original length is 0.2in or 5.08mm
(a) A runner starts from rest and in 3 s reaches a speed of 8 m/s. If we assume that the speed changed at a constant rate (constant net force), what was the average speed during this 3 s interval?
Answer:
During the 3 s interval, the average velocity was 4 m/s.
Explanation:
Hi there!
The average velocity (AV) is calculated as follows:
AV = Δx / Δt
Where:
Δx = traveled distance.
Δt = elapsed time.
The traveled distance (x) is calculated as follows:
x = x0 + v0 · t + 1/2 · a · t²
Where:
x0 = initial position.
v0 = initial velocity.
t = time.
a = acceleration.
Since x0 and v0 are equal to zero, the equation gets reduced to:
x = 1/2 · a · t²
Since the acceleration is constant, it can be calculated with this equation:
a = v/t
a = 8 m/s / 3 s
a = 8/3 m/s²
Then, the traveled distance will be:
x = 1/2 · a · t²
x = 1/2 · 8/3 m/s² · (3 s)²
x = 12 m
And the average velocity will be:
AV = Δx / Δt
AV = 12 m / 3 s = 4 m/s
During the 3 s interval, the average velocity was 4 m/s.
A certain lightning bolt moves 78.3 C of charge. How many fundamental units of charge is this?
Answer:
There are [tex]4.89\times 10^{20}\ electrons[/tex] flowing in the lighting bolt.
Explanation:
Given that,
Charge on certain lighting bolt, q = 78.3 C
We need to find the number of charge flowing in that bolt. Let there are n number of electrons. It is a case of quantization of electric charge. It is given by :
q = ne
[tex]n=\dfrac{q}{e}[/tex]
e is the charge on an electron
[tex]n=\dfrac{78.3\ C}{1.6\times 10^{-19}\ C}[/tex]
[tex]n=4.89\times 10^{20}\ electrons[/tex]
So, there are [tex]4.89\times 10^{20}\ electrons[/tex] flowing in the lighting bolt.
The end of Hubbard Glacier in Alaska advances by an average of 105 feet per year.
What is the speed of advance of the glacier in
m/s
?
Answer:
Speed of the glacier, [tex]v=1.0148\times 10^{-6}\ m/s[/tex]
Explanation:
Given that,
The average speed of Hubbard Glacier, [tex]v=105\ feet/year[/tex]
We need to find speed of advance of the glacier in m/s. As we know that,
1 meter = 3.28 feet
And
[tex]1\ year=3.154\times 10^7\ second[/tex]
Using the above conversions, we can write the value of average speed is :
[tex]v=1.0148\times 10^{-6}\ m/s[/tex]
So, the speed of advance of the glacier is [tex]1.0148\times 10^{-6}\ m/s[/tex]. Hence, this is the required solution.
An astronaut in an orbiting space craft attaches a mass m to a string and whirls it around in uniform circular motion. The radius of the circle is R, the speed of the mass is v, and the tension in the string is F. If the mass, radius, and speed were all to double the tension required to maintain uniform circular motion would be
Answer:
[tex]F'=4F[/tex]
Explanation:
According to Newton's second law, the tension in the string is equal to the centripetal force, since the mass is under an uniform circular motion:
[tex]F=F_c\\F=ma_c[/tex]
Here [tex]a_c[/tex] is the centripetal acceleration, which is defined as:
[tex]a_c=\frac{v^2}{r}[/tex]
So, replacing:
[tex]F=m\frac{v^2}{r}[/tex]
In this case we have [tex]m'=2m[/tex], [tex]v'=2v[/tex] and [tex]r'=2r[/tex]. Thus, the tension required to mantain uniform circular motion is:
[tex]F'=m'\frac{v'^2}{r'}\\F'=2m\frac{(2v)^2}{2r}\\F'=4m\frac{v^2}{r}\\F'=4F[/tex]
Jack and Jill exercise in a 25.0 m long swimming pool. Jack swims 9 lengths of the pool in 156.9 s ( 2 min and 36.9 s ) , whereas Jill, the faster swimmer, covers 10 lengths in the same time interval. Find the average velocity and average speed of each swimmer.
Answer:
Jill average velocity is 0
Jack average velocity is 0.159337
Jill average speed = 1.593372
Jack average speed = 1.434034
Explanation:
given data
long swimming pool = 25.0 m
9 lengths of the pool = 156.9 s ( 2 min and 36.9 s )
10 lengths = same time interval
to find out
average velocity and average speed
solution
we know that average velocity that is express as
average velocity = [tex]\frac{displacement}{time}[/tex] .....................1
Jill come back where she start
so here velocity will be = 0
and
Jack ends up on the other end of pool
so average velocity = [tex]\frac{25}{156.9}[/tex]
average velocity = 0.159337
now we get here average speed that is express as
average speed = [tex]\frac{distance}{time}[/tex] .............2
jack speed = 9 × [tex]\frac{25}{156.9}[/tex]
jack speed = 1.434034
and
Jill speed = 10 × [tex]\frac{25}{156.9}[/tex]
Jill speed = 1.593372
Ask Your Teacher In the air over a particular region at an altitude of 500 m above the ground, the electric field is 120 N/C directed downward. At 600 m above the ground, the electric field is 110 N/C downward. What is the average volume charge density in the layer of air between these two elevations?
Answer:
[tex]1.475\times 10^{-13}\ C/m^3[/tex]
Explanation:
[tex]\epsilon_0[/tex] = Permittivity of free space = [tex]8.85\times 10^{-12}\ F/m[/tex]
A = Area
h = Altitude = 600 m
Electric flux through the top would be
[tex]-110A[/tex] (negative as the electric field is going into the volume)
At the bottom
[tex]120A[/tex]
Total flux through the volume
[tex]\phi=120-110\\\Rightarrow \phi=10A[/tex]
Electric flux is given by
[tex]\phi=\dfrac{q}{\epsilon_0}\\\Rightarrow q=\phi\epsilon_0\\\Rightarrow q=10A\epsilon_0[/tex]
Charge per volume is given by
[tex]\rho=\dfrac{q}{v}\\\Rightarrow \rho=\dfrac{10A\epsilon_0}{Ah}\\\Rightarrow \rho=dfrac{10\epsilon_0}{h}\\\Rightarrow \rho=\dfrac{10\times 8.85\times 10^{-12}}{600}\\\Rightarrow \rho=1.475\times 10^{-13}\ C/m^3[/tex]
The volume charge density is [tex]1.475\times 10^{-13}\ C/m^3[/tex]
A copper cylinder is initially at 21.1 ∘C . At what temperature will its volume be 0.163 % larger than it is at 21.1 ∘C?
Final answer:
The question from the student involves the concept of thermal expansion in physics, where the goal is to determine at what temperature a copper cylinder's volume becomes 0.163% larger than its original volume at 21.1°C.
Explanation:
The student's question is about thermal expansion, which is a concept in physics specifically relating to how the volume of a solid changes with temperature. This falls under the broader subject of thermodynamics. The student is given the initial volume and temperature of the copper cylinder and is asked to find the temperature at which its volume is 0.163% larger. To solve this, we need to use the linear expansion formula for solids.
The formula for the volume expansion of solids is
V = V₀(1 + βΔT), where V is the final volume, V₀ is the initial volume, β is the coefficient of volume expansion for copper, and ΔT is the change in temperature. To find the new temperature, we first need to express the 0.163% increase in volume as a decimal, which gives us 0.00163. We can then rearrange the formula to solve for ΔT. After finding ΔT, we add it to the initial temperature of 21.1°C to find the final temperature.
Plugging in the numbers:
0.00163 = 3(16.5 x 10⁻⁶)ΔT
ΔT = 21.3 °C
Therefore, T2 = T1 + ΔT = 21.1 °C + 21.3 °C = 42.4 °C
The temperature at which the copper cylinder's volume will be 0.163% larger than at 21.1 °C is 42.4 °C.
An insulated beaker with negligible mass contains liquid water with a mass of 0.270 kg and a temperature of 82.5 ∘C . How much ice at a temperature of -22.3 C must be dropped into the water so that the final temperature of the system will be 34.0 C?
Answer:
Explanation:
Given
mass of water [tex]m_1=0.27\ kg[/tex]
Temperature of water [tex]T_{wi}=82.5^{\circ}C[/tex]
Initial Temperature of ice[tex]=-22.3^{\circ}C[/tex]
Final temperature of system [tex]T=34^{\circ}C[/tex]
specific heat of water [tex]c=4.18\ kJ/kg-K[/tex]
specific heat of ice [tex]c_i=2.108\ kJ/kg-K[/tex]
Latent heat of ice [tex]L=336\ kJ/kg[/tex]
Heat loss by Water is equal to heat gained by ice
Heat loss by water [tex]Q_1=m_w\times c\times \Delta T[/tex]
[tex]Q_1=0.27\times 4.18\times (82.5-34)=54.7371\ kJ[/tex]
Heat gained by ice [tex]Q_1=x\times c_i(0-(-22.3))+x\times L+x\times c\times (T-0)[/tex]
[tex]Q_2=x\times 2.108\times (22.3)+x\times 336+x\times 4.18\times 34[/tex]
[tex]Q_2=525.1284x\ kJ[/tex]
[tex]Q_1=Q_2[/tex]
[tex]x=\frac{54.73}{525.1284}[/tex]
[tex]x=0.104\ kg[/tex]