We will make the comparison between each of the sizes against the known wavelengths.
In the case of the hydrogen atom, we know that this is equivalent to [tex]10^{-10}[/tex] m on average, which corresponds to the wavelength corresponding to X-rays.
In the case of the Virus we know that it is oscillating in a size of 30nm to 200 nm, so the size of the virus is equivalent to the range of the wavelength of an ultraviolet ray.
In the case of height, it fluctuates in a person around [tex]10 ^ 0[/tex] to [tex]10 ^ 1[/tex] m, which falls to the wavelength of a radio wave.
The region of the spectrum that best corresponds to light with a wavelength equal to the diameter of a hydrogen atom is the X-ray region. The visible light spectrum corresponds to objects around the same size as the wavelength. The size of a virus is much smaller than the wavelength of visible light
Explanation:The region of the spectrum that best corresponds to light with a wavelength equal to the diameter of a hydrogen atom is the X-ray region of the electromagnetic spectrum.
The wavelength of visible light corresponds to the size of objects that are around the same size as the wavelength. For example, if you want to use light to see a human, you would need to use a wavelength at or below 1 meter, since humans are about 1 meter in size.
The size of a virus is much smaller than the wavelength of visible light, so the wavelength is very small compared to the object's size.
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.
The displacement of a wave traveling in the positive x-direction is:
y(x,t) = (3.5cm) cos (2.7x−92t), where x is in m and t is in s.
Part A) What is the frequency of this wave?
Part B) What is the wavelength of this wave?
Part C) What is the speed of this wave?
The frequency, wavelength, and speed of the wave are equal to 14.65 Hz, 0.4299m, and 6.298 Hz.
What are frequency and wavelength?The frequency can be described as the number of oscillations or cycles in 1 second. The SI unit of frequency has per second or hertz.
The wavelength can be defined as the distance between the two adjacent crests or troughs on a wave that is separated by a distance.
The standard equation of wave can be expressed as:
[tex]{\displaystyle y(x,t) = Acos (\frac{2\pi x}{\lambda} \pm 2\pi ft )[/tex]
Given the equation of the wave: y(x,t) = (3.5cm) cos (2.7x−92t)
Therefore, the wavelength can be calculated as:
2π/ λ = 2.7
λ = 2.7/2π
λ = 0.4299 m
The frequency of the given wave can be calculated as:
2πf = 92
f = 92/2π
f = 14.65 Hz
The speed of the wave can determine from the above-mentioned relationship:
V = νλ
V = 14.65 × 0.4299
V = 6.29 m/s
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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.
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]
Which is the most appropriate units for expressing angular velocity in kinematics problems?
Answer:
[tex]\frac{rad}{s}[/tex]
Explanation:
The most appropriate units for expressing the angular velocity are the [tex]\frac{rad}{s}[/tex], since they are the units assigned for this magnitude in the International System of Units. Which is derived from the fact that radians are dimensionless and the second is the unit assigned for time in this unit system.
Final answer:
The most appropriate units for expressing angular velocity in kinematics problems are radians per second (rad/s). This unit arises from the definition of angular velocity as the change in angular position (ΔΘ) over time (Δt).
Explanation:
When discussing angular velocity in kinematics problems, the most appropriate unit to express it is radians per second (rad/s). Angular velocity is the rate of change of the angular position over time, defined as ΔΘ/Δt. For example, if a disc makes one-fourth of a revolution in 0.0150 seconds, its angular velocity would be π/2 rad / 0.0150 s, equaling 104.7 rad/s.
In situations where the rotation rate is given in revolutions per second or cycles per second, we can convert it to angular velocity by multiplying by 2π rad, as one complete revolution is equivalent to 2π radians. It is also important to note that the centripetal acceleration in circular motion is related to the angular velocity, and the units are critical in deriving related kinematics equations.
A gadget of mass 21.85 kg floats in space without motion. Because of some internal malfunction, the gadget violently breaks up into 3 fragments flying away from each other. The first fragment has mass m1 = 6.42 kg and speed v1 = 6.8 m/s while the second fragment has mass m2 = 8.26 kg and speed v2 = 3.54 m/s. The angle between the velocity vectors ~v1 and ~v2 is θ12 = 64 ◦ . What is the speed v3 of the third fragment? Answer in units of m/s.
To solve this problem we will apply the concepts related to the conservation of momentum. For this purpose we will determine the velocities in the three body in the vertical and horizontal components. Once the system of equations is obtained, we will proceed to find the angle and the speed at which the third fragment is directed.
Mass of third part is
[tex]m_3 = m-(m_1+m_2)[/tex]
[tex]m_3= 21.85-6.42-8.26[/tex]
[tex]m_3 =7.17 kg[/tex]
Assume that [tex]m_1[/tex] is along X-axis we have that [tex]m_2[/tex] makes an angle is 64 degrees with x-axis and [tex]m_3[/tex] makes an angle [tex]\theta[/tex] with x-axis.
Using law of conservation of momentum along X-axis
[tex]0 = (6.42*6.8)+(8.26*3.54*cos(64))+(7.71v_3 cos\theta)[/tex]
[tex](7.71v_3 cos\theta) = 56.4741[/tex]
[tex]v_3 cos\theta = 7.3247[/tex] [tex]\rightarrow \text{Equation 1}[/tex]
Now applying the same through the Y-axis.
[tex]0=0+8.26*3.54*sin(64\°) + 7.71*v_3*sin\theta[/tex]
[tex]-8.26*3.54*sin(64\°)=7.71*v_3*sin\theta[/tex]
[tex]v_3*sin\theta = -3.409[/tex] [tex]\rightarrow \text{Equation 2}[/tex]
If we divide the equation 1 with the equation 2 we have that
[tex]\frac{v_3cos\theta}{v_3 sin\theta } = \frac{7.3247}{-3.409}[/tex]
[tex]tan\theta = \frac{7.3247}{-3.409}[/tex]
[tex]\theta = tan^{-1} (\frac{7.3247}{-3.409})[/tex]
[tex]\theta = -65.04\°[/tex]
Using this angle in the second equation we have that velocity 3 is,
[tex]v_3 = \frac{-3.409}{sin(-65.04)}[/tex]
[tex]v_3 = 3.7601m/s[/tex]
Therefore the speed of the third fragment is [tex]3.7601\frac{m}{s} \angle -65.04\°[/tex]
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]
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.
A chair is at rest on the floor. The chair absorbs thermal energy from the floor, and begins moving spontaneously with kinetic energy equal to the thermal energy absorbed. This process violates ___________.
A- Both the 1st and 2nd laws of thermodynamicsB- Only the 1st law of thermodynamicsC- Neither the 1st nor the 2nd law of thermodynamicsD- Only the 2nd law of thermodynamics
Answer:
D- Only the 2nd law of thermodynamics
Explanation:
It violates 2nd law because according to 2nd law of thermodynamics, it is impossible that the sole result of a process is is to absorb energy and do equivalent amount of work. so some heat must lose to surrounding which is not specified here. so it violates 2nd law.
so option D is correct
The process violates the 2nd law of thermodynamics. The chair absorbing thermal energy from the floor and beginning to move spontaneously with kinetic energy equal to the thermal energy absorbed implies a perfect conversion of heat into work, which is against the principle of entropy increase stated by the 2nd law.
Explanation:This process violates D- Only the 2nd law of thermodynamics.
The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. Isolated systems spontaneously evolve towards thermal equilibrium—the state of maximum entropy of the system.
In the scenario described where a chair absorbs thermal energy from the floor and begins moving spontaneously with kinetic energy equal to the thermal energy absorbed, it would mean that 100% of the thermal energy has been converted into kinetic energy. This is a violation of the second law of thermodynamics because it implies a perfect conversion of heat energy into work with no increase in entropy, i.e., the thermal energy is fully converted into kinetic energy without any of it being 'wasted' or dispersed.
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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.
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.
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.
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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A hypodermic syringe contains a medicine with the density of water (see figure below). The barrel of the syringe has a cross-sectional area A = 2.20 10-5 m2, and the needle has a cross-sectional area a = 1.00 10-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force F with arrow of magnitude 2.05 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle's tip. m/s
The speed of the medicine as it leaves the needle's tip is the same as the speed of the medicine inside the syringe, which is 4.0 mm/s.
Explanation:To determine the speed of the medicine as it leaves the needle's tip, we can use Bernoulli's equation.
Bernoulli's equation states that the sum of the pressure energy, kinetic energy, and potential energy per unit volume is constant along a streamline in a fluid flow.
Applying Bernoulli's equation, we have:
P1 + (1/2)ρv1² + ρgh1 = P2 + (1/2)ρv2² + ρgh2
Where P1 and P2 are the pressures, v1 and v2 are the velocities, ρ is the density of the fluid, g is the acceleration due to gravity, and h1 and h2 are the heights.
In this case, the medicine is moving horizontally, so the heights (h1 and h2) are the same. Also, the pressure everywhere is 1.00 atm, so P1 and P2 are equal. Additionally, the density of the medicine is the same as water. Therefore, the equation simplifies to:
(1/2)ρv1² = (1/2)ρv2²
Cancelling out the common terms, we have:
v1² = v2²
Taking the square root of both sides, we find:
v1 = v2
Therefore, the speed of the medicine as it leaves the needle's tip is the same as the speed of the medicine inside the syringe, which is 4.0 mm/s.
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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.
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
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.
. The charge entering the positive terminal of an element is ???? = 10 sin 4???????? m????, while the voltage across the element is ???? = 2 cos 4???????? ????. (i) Find the power delivered to the element at t = 0.3s. (ii) Calculate the energy delivered to the element between 0 and 0.6s.
Answer:
P (t = 0.3) = 164.5 mW
W ( 0 < t < 0.6) = 78.34 mJ
Explanation:
Given:
q (t) = 10*sin(4*pi*t) mC
V (t) = 2 *cos(4*pi*t) V
part a
The current i (t) flowing through the element is obtained as follows:
i (t) = dq / dt
= d (10*sin(4*pi*t)) / dt
= 40 * pi * cos (4*pi*t) mA
Next P(t) delivered to the element is obtained as follows:
P (t) = i (t)*V(t)
= 40 * pi * cos (4*pi*t) * 2 *cos(4*pi*t)
= 80*pi*(cos(4*pi*t))^2 mW
Finally the power delivered to element @ t = 0.3 s
P (t=0.3) = 80*pi*(cos(4*pi*0.3))^2 = 164.50 mW
Answer: P (t = 0.3) = 164.5 mW
part b
Energy delivered to the element time 0 to 0.6 s is obtained as follows:
[tex]W (0 <t<0.6) = \int\limits {P(t)} \, dt\\\\ =\int {80*pi*(cos(4*pi*t))^2} \, dt\\\\= (5 sin (8*pi*t) + 40*pi*t )\limits^0.6_0 \\\\= 78.33715mJ[/tex]
Answer: W ( 0 < t < 0.6) = 78.34 mJ
A single roller-coaster car is moving with speed v0 on the first section of track when it descends a 4.7-m-deep valley, then climbs to the top of a hill that is 5.4 m above the first section of track. Assume any effects of friction or of air resistance are negligible.
(a) What is the minimum speed v0 required if the car is to travel beyond the top of the hill?
(b) Can we affect this speed by changing the depth of the valley to make the coaster pick up more speed at the bottom?
Explanation:
From the curve given in the attachment,
a) minimum speed v0 required if the car is to travel beyond the top of the hill
climb to the top = 5.4 m
Therefore, [tex]V_0=\sqrt{2gh}[/tex]
[tex]V_0=\sqrt{2(9.81)(5.4)}[/tex] = 10.29 m/s
b) No, we cannot affect this speed by changing the depth of the valley to make the coaster pick up more speed at the bottom as this speed does not depend upon depth of the valley.
(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.
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
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.
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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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.
We experience fictitious forces due to: a. Rotation of a reference frame b. Inertial reference frames c. Translational motion d. Universal gravitation.
Answer:
A.
Explanation:
A fictional force (also called force of inertia, pseudo-force, or force of d'Alembert, 5), is a force that appears when describing a movement with respect to a non-inertial reference system, and that therefore it does not correspond to a genuine force in the context of the description of the movement that Newton's laws are enunciated for inertial reference systems.
The forces of inertia are, therefore, corrective terms to the real forces, which ensure that the formalism of Newton's laws can be applied unchanged to phenomena described with respect to a non-inertial reference system. The correct answer is A.
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]
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]
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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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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The metal gold crystallizes in a face centered cubic unit cell with one atom per lattice point. When X-rays with λ = 1.436 Å are used, the second-order Bragg reflection from a set of parallel planes in a(n) gold crystal is observed at an angle θ = 20.62°. If the spacing between these planes corresponds to the unit cell length (d = a), calculate the radius of a(n) gold atom.
Answer:
r = 1.45 Å
Explanation:
given,
λ = 1.436 Å
θ = 20.62°
d = a
n = 2
metal gold crystallizes in a face centered cubic unit cell
Radius of the gold atom = ?
using Bragg's Law
n λ = 2 d sin θ
2 x 1.436 Å = 2 a sin 20.62°
a = 4.077 Å
We know relation of radius for face centered cubic unit cell
[tex]a = \dfrac{4r}{\sqrt{2}}[/tex]
[tex]4.077= \dfrac{4\times r}{\sqrt{2}}[/tex]
r = 1.45 Å
the radius of a(n) gold atom. is equal to 1.45 Å