a. A single electron loses 6.408 × 10⁻¹⁵ J of potential energy.
b. The maximum speed of the electrons is 8.9 × 10⁶ m/s.
a. The potential energy lost by a single electron can be calculated using the equation for electric potential energy:
ΔPE = qΔV, where ΔPE is the change in potential energy, q is the charge of the electron (1.6 × 10⁻¹⁹ C), and ΔV is the change in voltage (40,000 V). Plugging in the values,
we get ΔPE = (1.6 × 10⁻¹⁹ C) × (40,000 V)
= 6.4 × 10⁻¹⁵ J.
b. To determine the maximum speed of the electrons, we can equate the loss in potential energy to the gain in kinetic energy.
The kinetic energy of an electron is given by KE = ½mv²,
where m is the mass of the electron (9.1 × 10⁻³¹ kg) and v is the velocity. Equating ΔPE to KE, we have ΔPE = KE.
Rearranging the equation, we get
(1.6 × 10⁻¹⁹ C) × (40,000 V) = ½ × (9.1 × 10⁻³¹ kg) × v².
Solving for v, we find
v = √((2 × (1.6 × 10⁻¹⁹ C) × (40,000 V)) / (9.1 × 10⁻³¹ kg))
= 8.9 × 10⁶ m/s.
Learn more About electron from the given link
https://brainly.com/question/25674345
#SPJ11
Two balls are side by side initially. At time = 0s, ball A is thrown at an initial angular velocity of pi radians per second and at time = 5s, the second ball is thrown down at the same angular velocity of pi radians per second down identical inclines with negligible friction. Assume the ramp is big enough so that the balls do not reach the bottom in the time values given.
a) Construct the angular velocity vs. time graph of both balls from time = 0 s to 15 seconds. Clearly label which line represent which ball and the time values.
b) The experiment is repeated on the same ramps with the same balls but this time, both balls are thrown down the incline at the same time with the same angular velocity. Ball A has twice the radius of Ball B.
i) Construct the linear velocity vs. time graph of both balls.
ii) Shade in the part of your linear velocity vs. time graph that represent the separation displacement between Ball A and Ball B as time progresses. Does this distance increase, decrease, or remain the same over time? Explain your answer.
a) Ball A: Horizontal line at pi radians per second from 0s to 15s.
Ball B: Horizontal line at pi radians per second from 5s to 15s.
b) i) Ball A: Positive sloped line indicating constant increase in linear velocity.
Ball B: Positive sloped line indicating constant increase in linear velocity.
ii) The separation distance between Ball A and Ball B remains the same over time.
a) The angular velocity vs. time graph for both balls can be represented as follows:
- Ball A: The graph is a horizontal line at the value of pi radians per second starting from time = 0s and continuing until time = 15s.
- Ball B: The graph is also a horizontal line at the value of pi radians per second starting from time = 5s and continuing until time = 15s.
b) i) The linear velocity vs. time graph for both balls can be represented as follows:
- Ball A: The graph is a straight line with a positive slope, indicating a constant increase in linear velocity over time.
- Ball B: The graph is also a straight line with a positive slope, indicating a constant increase in linear velocity over time.
ii) The separation displacement between Ball A and Ball B will remain the same over time. This is because both balls are thrown down the incline at the same time with the same angular velocity, meaning they will have the same linear velocity at any given time. Since they start at the same position, their relative distance or separation will remain constant throughout their motion.
Learn more about angular velocity:
https://brainly.com/question/29342095
#SPJ11
Write a x; in a form that includes the Kronecker delta. Now show that V.r=3.
x; = Σn=1 to ∞ δn,x vn,
where δn,x is the Kronecker delta and vn is a vector in the basis of x.
Kronecker delta is a mathematical symbol that is named after Leopold Kronecker. It is also known as the Kronecker's delta or Kronecker's symbol. It is represented by the symbol δ and is defined as δij = 1 when i = j, and 0 otherwise. Here, i and j can be any two indices in the vector x. The vector x can be expressed as a sum of vectors in the basis of x as follows: x = Σn=1 to ∞ vn, where vn is a vector in the basis of x.
Using the Kronecker delta, we can express this sum in the following form:
x; = Σn=1 to ∞ δn,x vn, where δn,x is the Kronecker delta. Now, if we take the dot product of the vector V and x, we get the following:
V·x = V·(Σn=1 to ∞ vn) = Σn=1 to ∞ (V·vn)
Since V is a 3-dimensional vector, the dot product V·vn will be zero for all but the third term, where it will be equal to 3. So, V·x = Σn=1 to ∞ (V·vn) = 3, which proves that V·x = 3.
Learn more about Kronecker delta here:
https://brainly.com/question/30894460
#SPJ11
A block with a mass m = 2.48 kg is pushed into an ideal spring whose spring constant is k = 5260 N/m. The spring is compressed x = 0.076 m and released. After losing contact with the spring, the block slides a distance of d = 1.72 m across the floor before coming to rest.
Part (a) Write an expression for the coefficient of kinetic friction between the block and the floor using the symbols given in the problem statement and g (the acceleration due to gravity). (Do not neglect the work done by friction while the block is still in contact with the spring.)
Part (b) What is the numerical value of the coefficient of kinetic friction between the block and the floor?
A block with a mass m = 2.48 kg is pushed into an ideal spring whose spring constant is k = 5260 N/m, the numerical value of the coefficient of kinetic friction between the block and the floor is approximately 0.247.
The spring's work when compressed and released is equal to the potential energy contained in the spring.
This potential energy is subsequently transformed into the block's kinetic energy, which is dissipated further by friction as the block slides over the floor.
Work_friction = μ * m * g * d
To calculate the coefficient of kinetic friction (), we must first compare the work done by friction to the initial potential energy stored in the spring:
Work_friction = 0.5 * k * [tex]x^2[/tex]
μ * m * g * d = 0.5 * k * [tex]x^2[/tex]
μ * 2.48 * 9.8 * 1.72 m = 0.5 * 5260 *[tex](0.076)^2[/tex]
Solving for μ:
μ ≈ (0.5 * 5260 * [tex](0.076)^2[/tex]) / (2.48 * 9.8 * 1.72)
μ ≈ 0.247
Therefore, the numerical value of the coefficient of kinetic friction between the block and the floor is approximately 0.247.
For more details regarding kinetic friction, visit:
https://brainly.com/question/30886698
#SPJ4
Part (a) The coefficient of kinetic friction between the block and the floor is f_k = (1/ d) (0.5 k x² - 0.5 m v²)
Part (b) The numerical value of the coefficient of kinetic friction between the block and the floor is 0.218.
Part (a), To derive an expression for the coefficient of kinetic friction between the block and the floor, we need to use the conservation of energy. The block is released from the spring's potential energy and it converts to kinetic energy of the block. Since the block slides on the floor, some amount of kinetic energy is converted to work done by friction on the block. When the block stops, all of its energy has been converted to work done by friction on it. Thus, we can use the conservation of energy as follows, initially the energy stored in the spring = Final energy of the block
0.5 k x² = 0.5 m v² + W_f
Where v is the speed of the block after it leaves the spring, and W_f is the work done by the friction force between the block and the floor. Now, we can solve for the final velocity of the block just after leaving the spring, v as follows,v² = k x²/m2.48 kg = (5260 N/m) (0.076 m)²/ 2.48 kg = 8.1248 m/s
Now, we can calculate the work done by friction W_f as follows: W_f = (f_k) * d * cosθThe angle between friction force and displacement is zero, so θ = 0°
Therefore, W_f = f_k d
and the equation becomes,0.5 k x² = 0.5 m v² + f_k d
We can rearrange it as,f_k = (1/ d) (0.5 k x² - 0.5 m v²)f_k = (1/1.72 m) (0.5 * 5260 N/m * 0.076 m² - 0.5 * 2.48 kg * 8.1248 m/s²)f_k = 0.218
Part (b), The numerical value of the coefficient of kinetic friction between the block and the floor is 0.218 (correct to three significant figures).
Learn more about coefficient of kinetic friction
https://brainly.com/question/19392943
#SPJ11
(a) Find the distance of the image from a thin diverging lens of focal length 30 cm if the object is placed 20 cm to the right of the lens. Include the correct sign. cm (b) Where is the image formed?
The image is formed on the same side of the object.
Focal length, f = -30 cm
Distance of object from the lens, u = -20 cm
Distance of the image from the lens, v = ?
Now, using the lens formula, we have:
1/f = 1/v - 1/u
Or, 1/-30 = 1/v - 1/-20
Or, v = -60 cm (distance of image from the lens)
The negative sign of the image distance indicates that the image formed is virtual, erect, and diminished.
The image is formed on the same side of the object. So, the image is formed 60 cm to the left of the lens.
To learn more about image, refer below:
https://brainly.com/question/30725545
#SPJ11
On a day when the speed of sound is 345 m/s, the fundamental frequency of a particular stopped organ pipe is 220 Hz. The second overtone of this pipe has the same wavelength as the third harmonic of an open pipe. How long is the open pipe? Express your answer in mm
The length of the open pipe can be determined by comparing the wavelength of the third harmonic of the open pipe to the second overtone of the stopped organ pipe.
The fundamental frequency of a stopped organ pipe is determined by the length of the pipe, while the frequency of a harmonic in an open pipe is determined by the length and speed of sound. In this case, the fundamental frequency of the stopped organ pipe is given as 220 Hz.
The second overtone of the stopped organ pipe is the third harmonic, which has a frequency that is three times the fundamental frequency, resulting in 660 Hz (220 Hz × 3). The wavelength of this second overtone can be calculated by dividing the speed of sound by its frequency: wavelength = speed of sound / frequency = 345 m/s / 660 Hz = 0.5227 meters.
Now, we need to find the length of the open pipe that produces the same wavelength as the third harmonic of the stopped organ pipe. Since the open pipe has a fundamental frequency that corresponds to its first harmonic, the wavelength of the third harmonic in the open pipe is four times the length of the pipe. Therefore, the length of the open pipe can be calculated by multiplying the wavelength by a factor of 1/4: length = (0.5227 meters) / 4 = 0.1307 meters.
Finally, to express the length in millimeters, we convert the length from meters to millimeters by multiplying it by 1000: length = 0.1307 meters × 1000 = 130.7 mm. Hence, the length of the open pipe is 130.7 mm.
To learn more about wavelength.
Click here:brainly.com/question/29548846
#SPJ11
The leneth of a steel bear increases by 0.73 mm when its temperature is raised from 22°C to 35°C. what
is the length of the beam at 22°C? What would the leneth be at 15°C?
The steel beam's length at 22°C can be found using the temperature coefficient of linear expansion, and the length at 15°C can be calculated similarly.
To find the length of the steel beam at 22°C, we can use the given information about its temperature coefficient of linear expansion. Let's assume that the coefficient is α (alpha) in units of per degree Celsius.
The change in length of the beam, ΔL, can be calculated using the formula:
ΔL = α * L0 * ΔT,
where L0 is the original length of the beam and ΔT is the change in temperature.
We are given that ΔL = 0.73 mm, ΔT = (35°C - 22°C) = 13°C, and we need to find L0.
Rearranging the formula, we have:
L0 = ΔL / (α * ΔT).
To find the length at 15°C, we can use the same formula with ΔT = (15°C - 22°C) = -7°C.
Please note that we need the value of the coefficient of linear expansion α to calculate the lengths accurately.
To know more about linear expansion, click here:
brainly.com/question/32547144
#SPJ11
A proton (charge +e, mass mp), a deuteron (charge +e, mass 2mp), and an alpha particle (charge +2e, mass 4m) are accelerated from rest through a common potential difference AV. Each of the particles enters a uniform magnetic field B, with its velocity in a direction perpendicular to B. The proton moves in a circular path of radius p (a) In terms of r, determine the radius r of the circular orbit for the deuteron.
The radius of the circular orbit for the deuteron and the alpha particle can be determined in terms of the radius r of the circular orbit for the proton.
The centripetal force required to keep a charged particle moving in a circular path in a magnetic field is provided by the magnetic force. The magnetic force is given by the equation F = qvB, where q is the charge of the particle, v is its velocity, and B is the magnetic field strength.
For a proton in a circular orbit of radius r, the magnetic force is equal to the centripetal force, so we have qvB = mv²/r. Rearranging this equation, we find that v = rB/m.
Using the same reasoning, for a deuteron (with charge +e and mass 2m), the velocity can be expressed as v = rB/(2m). Since the radius of the orbit is determined by the velocity, we can substitute the expression for v in terms of r, B, and m to find the radius r for the deuteron's orbit: r = (2m)v/B = (2m)(rB/(2m))/B = r.
Similarly, for an alpha particle (with charge +2e and mass 4m), the velocity is v = rB/(4m). Substituting this into the expression for v, we get r = (4m)v/B = (4m)(rB/(4m))/B = r.
Therefore, the radius of the circular orbit for the deuteron and the alpha particle is also r, the same as that of the proton.
Learn more about velocity here ;
brainly.com/question/30540135
#SPJ4
In terms of r, the radius of the circular orbit for the deuteron is r.
The magnetic field B that each of the particles enters is uniform. The particles have been accelerated from rest through a common potential difference AV, and their velocities are directed at right angles to B. Given that the proton moves in a circular path of radius p. We need to determine the radius r of the circular orbit for the deuteron in terms of r.
Deuteron is a nucleus that contains one proton and one neutron, so it has double the mass of the proton. Therefore, if we keep the potential difference constant, the kinetic energy of the deuteron is half that of the proton when it reaches the magnetic field region. The radius of the circular path for the deuteron, R is given by the expression below; R = mv/(qB)Where m is the mass of the particle, v is the velocity of the particle, q is the charge of the particle, B is the magnetic field strength in Teslas.
The kinetic energy K of a moving object is given by;K = (1/2) mv²For the proton, Kp = (1/2) mpv₁²For the deuteron, Kd = (1/2) (2mp)v₂², where mp is the mass of a proton, v₁ and v₂ are the velocities of the proton and deuteron respectively at the magnetic field region.
Since AV is common to all particles, we can equate their kinetic energy at the magnetic field region; Kp = Kd(1/2) mpv₁² = (1/2) (2mp)v₂²4v₁² = v₂²From the definition of circular motion, centripetal force, Fc of a charged particle of mass m with charge q moving at velocity v in a magnetic field B is given by;Fc = (mv²)/r
Where r is the radius of the circular path. The centripetal force is provided by the magnetic force experienced by the particle, so we can equate the magnetic force and the centripetal force;qvB = (mv²)/rV = (qrB)/m
Substitute for v₂ and v₁ in terms of B,m, and r;(qrB)/mp = 2(qrB)/md² = 2pThe radius of the deuteron's circular path in terms of the radius of the proton's circular path is;d = 2p(radius of proton's circular path)r = (d/2p)p = r/2pSo, r = 2pd.
Learn more about deuteron
https://brainly.com/question/31978176
#SPJ11
PROBLEM STATEMENT Housewives claims that bulk red label wine is stronger than the Red Label wine found on Supermarket shelves. Plan and design an experiment to prove this claim HYPOTHESIS AM APPARATUS AND MATERIALS DIAGRAM OF APPARATUS (f necessary METHOD On present tense) VARIABLES: manipulated controlled responding EXPECTED RESULTS ASSUMPTION PRECAUTIONS/ POSSIBLE SOURCE OF ERROR
To prove the claim that bulk red label wine is stronger than the Red Label wine found on supermarket shelves, an experiment can be designed to compare the alcohol content of both types of wine.
To investigate the claim, the experiment would involve analyzing the alcohol content of bulk red label wine and the Red Label wine available in supermarkets. The hypothesis assumes that bulk red label wine has a higher alcohol content than the Red Label wine sold in supermarkets.
In order to conduct this experiment, the following apparatus and materials would be required:
1. Samples of bulk red label wine
2. Samples of Red Label wine from a supermarket
3. Alcohol meter or hydrometer
4. Wine glasses or containers for testing
The experiment would proceed as follows:
1. Obtain representative samples of bulk red label wine and Red Label wine from a supermarket.
2. Ensure that the samples are of the same vintage and have been stored under similar conditions.
3. Use the alcohol meter or hydrometer to measure the alcohol content of each wine sample.
4. Pour the wine samples into separate wine glasses or containers.
5. Observe and record any visual differences between the wines, such as color or clarity.
Variables:
- Manipulated variable: Type of wine (bulk red label wine vs. Red Label wine from a supermarket)
- Controlled variables: Vintage of the wine, storage conditions, and volume of wine used for testing
- Responding variable: Alcohol content of the wine
Expected Results:
Based on the hypothesis, it is expected that the bulk red label wine will have a higher alcohol content compared to the Red Label wine from a supermarket.
Assumption:
The assumption is that the bulk red label wine, being purchased in larger quantities, may be sourced from different suppliers or production methods that result in a higher alcohol content compared to the Red Label wine sold in supermarkets.
Precautions/Possible Sources of Error:
1. Ensure that the alcohol meter or hydrometer used for measuring the alcohol content is calibrated properly.
2. Take multiple measurements for each wine sample to ensure accuracy.
3. Avoid cross-contamination between the wine samples during testing.
4. Ensure the wine samples are handled and stored properly to maintain their integrity.
Learn more about alcohol
brainly.com/question/29268872
#SPJ11
Light is travelling from medium A tretractive index 1.4) to medium B (retractive index 1.6. If the incident angle is 32.70 what would be retracted ankle in medium B? Express your answer in degrees
The refractive angle in medium B is 15.22°
The given values are:Medium A has a refractive index of 1.4.Medium B has a refractive index of 1.6.The incident angle is 32.70.The formula for the refractive index is:n1sin θ1 = n2sin θ2Where,n1 is the refractive index of medium A.n2 is the refractive index of medium B.θ1 is the angle of incidence in medium A.θ2 is the angle of refraction in medium B.By substituting the given values in the above formula we get:1.4sin 32.70° = 1.6sin θ2sin θ2 = (1.4sin 32.70°) / 1.6sin θ2 = 0.402 / 1.6θ2 = sin⁻¹(0.402 / 1.6)θ2 = 15.22°The refractive angle in medium B is 15.22°.Hence, the correct option is (D) 15.22°.
Learn more about refractive angle:
https://brainly.com/question/30048990
#SPJ11
A satellite of mass 648.9 kg is moving in a stable circular orbit about the Earth at a height of 7RE, where RE = 6400km = 6.400 x 106 m = 6.400 Mega-meters is Earth’s radius. The gravitational force (in newtons) on the satellite while in orbit is:
To calculate the gravitational force on the satellite while in orbit, we can use Newton's law of universal gravitation. The formula is as follows:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2 / kg^2)
m1 and m2 are the masses of the two objects (in this case, the satellite and Earth)
r is the distance between the centers of the two objects (the radius of the orbit)
In this scenario, the satellite is in a circular orbit around the Earth, so the gravitational force provides the necessary centripetal force to keep the satellite in its orbit. Therefore, the gravitational force is equal to the centripetal force.
The centripetal force can be calculated using the formula:
Fc = (m * v^2) / r
Where:
Fc is the centripetal force
m is the mass of the satellite
v is the velocity of the satellite in the orbit
r is the radius of the orbit
Since the satellite is in a stable circular orbit, the centripetal force is provided by the gravitational force. Therefore, we can equate the two equations:
(G * m1 * m2) / r^2 = (m * v^2) / r
We can solve this equation for the gravitational force F:
F = (G * m1 * m2) / r
Now let's plug in the values given in the problem:
m1 = mass of the satellite = 648.9 kg
m2 = mass of the Earth = 5.972 × 10^24 kg (approximate)
r = radius of the orbit = 7RE = 7 * 6.400 x 10^6 m
Calculating:
F = (6.67430 × 10^-11 N m^2 / kg^2 * 648.9 kg * 5.972 × 10^24 kg) / (7 * 6.400 x 10^6 m)^2
F ≈ 2.686 × 10^9 N
Therefore, the gravitational force on the satellite while in orbit is approximately 2.686 × 10^9 Newtons.
To know more about gravitational force click this link -
brainly.com/question/32609171
#SPJ11
If the period of a 70.0-cm-long simple pendulum is 1.68 s, what
is the value of g at the location of the pendulum?
The value of g at the location of the pendulum is approximately 9.81 m/s², given a period of 1.68 s and a length of 70.0 cm.
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, andg is the acceleration due to gravity.Rearranging the formula, we can solve for g:
g = (4π²L) / T².
Substituting the given values:
L = 70.0 cm = 0.70 m, and
T = 1.68 s,
we can calculate the value of g:
g = (4π² * 0.70 m) / (1.68 s)².
g ≈ 9.81 m/s².
Therefore, the value of g at the location of the pendulum is approximately 9.81 m/s².
To learn more about acceleration due to gravity, Visit:
https://brainly.com/question/88039
#SPJ11
A copper wire has a length of 1.50 m and a cross sectional area of 0.280 mm? If the resistivity of copper is 1.70 x 100 m and a potential difference of 0.100 Vis maintained across as length determine the current in the wire (in A)
The current in the copper wire is approximately 0.01096 A (or 10.96 mA).
To determine the current in the copper wire, we can use Ohm's Law, which states that the current (I) flowing through a conductor is equal to the potential difference (V) across the conductor divided by the resistance (R).
In this case, the resistance (R) of the copper wire can be calculated using the formula:
R = (ρ * L) / A
Where:
ρ is the resistivity of copper (1.70 x 10^-8 Ω·m)
L is the length of the wire (1.50 m)
A is the cross-sectional area of the wire (0.280 mm² = 2.80 x 10^-7 m²)
Substituting the given values into the formula, we have:
R = (1.70 x 10^-8 Ω·m * 1.50 m) / (2.80 x 10^-7 m²)
R ≈ 9.11 Ω
Now, we can calculate the current (I) using Ohm's Law:
I = V / R
Substituting the given potential difference (V = 0.100 V) and the calculated resistance (R = 9.11 Ω), we have:
I = 0.100 V / 9.11 Ω
I ≈ 0.01096 A (or approximately 10.96 mA)
Therefore, the current in the copper wire is approximately 0.01096 A (or 10.96 mA).
Learn more about Ohm's Law from the given link
https://brainly.com/question/14296509
#SPJ11
For a situation when mechanical energy is conserved, when an object loses potential energy, all that energy goes to: Other Forms of Energy Potential Energy Kinetic Energy Nowhere; that energy is lost.
Kinetic Energy this is correct answer.
For a situation when mechanical energy is conserved, when an object loses potential energy, that energy is converted into kinetic energy. According to the principle of conservation of mechanical energy, the total mechanical energy (the sum of potential energy and kinetic energy) remains constant in the absence of external forces such as friction or air resistance.
When an object loses potential energy, it gains an equal amount of kinetic energy. The potential energy is transformed into the energy of motion, causing the object to increase its speed or velocity. This conversion allows for the conservation of mechanical energy, where the total energy of the system remains the same.
to know more about energy visit:
brainly.com/question/1932868
#SPJ11
Four charged spheres, with equal charges of +2.30 C, are
situated in corner positions of a square of 60 cm. Determine the
net electrostatic force on the charge in the top right corner of
the square.
The net electrostatic force on the charge in the top right corner of the square is 8.91 x 10⁶ N at an angle of 14.0° above the horizontal.
The expression for the electrostatic force between two charged spheres is:
F=k(q₁q₂/r²)
Where, k is the Coulomb constant, q₁ and q₂ are the charges of the spheres and r is the distance between their centers.
The magnitude of each force is:
F=k(q₁q₂/r²)
F=k(2.30C x 2.30C/(0.60m)²)
F=8.64 x 10⁶ N3. If F₁, F₂, and F₃ are the magnitudes of the forces acting along the horizontal and vertical directions respectively, then the net force along the horizontal direction is:
Fnet=F₁ - F₂
Since the charges in the top and bottom spheres are equidistant from the charge in the top right corner, their forces along the horizontal direction will be equal in magnitude and opposite in direction, so:
F/k(2.30C x 2.30C/(0.60m)²)
= 8.64 x 10⁶ N4.
The net force along the vertical direction is: F
=F₃
= F/k(2.30C x 2.30C/(1.20m)²)
= 2.16 x 10⁶ N5.
Fnet=√(F₁² + F₃²)
= √((8.64 x 10⁶)² + (2.16 x 10⁶)²)
= 8.91 x 10⁶ N6.
The direction of the net force can be obtained by using the tangent function: Ftan=F₃/F₁= 2.16 x 10⁶ N/8.64 x 10⁶ N= 0.25tan⁻¹ (0.25) = 14.0° above the horizontal
Therefore, the net electrostatic force on the charge in the top right corner of the square is 8.91 x 10⁶ N at an angle of 14.0° above the horizontal.
To know more about electrostatic force please refer:
https://brainly.com/question/20797960
#SPJ11
An electron that is moving through a uniform magnetic held has velocity 7 = 40.0 km/sli+ /33 0km/s) 7 when it experiences
a force h = (421 are + (stor) " due to the maenetic held. If B, = 0, calculate the magnetic held B
The magnetic field B is approximately -1.32 x 10^-3 Tesla in the ar direction.
To calculate the magnetic field B, we can use the formula for the magnetic force experienced by a charged particle:
F = qvB
where F is the magnetic force, q is the charge of the particle, v is its velocity, and B is the magnetic field.
In this case, the force experienced by the electron is given as F = (421 ar + 8°) N.
We know that the charge of an electron is q = -1.6 x 10^-19 C (negative because it's an electron).
The velocity of the electron is given as v = (40.0 km/s)i + (33.0 km/s)j = (40.0 x 10^3 m/s)i + (33.0 x 10^3 m/s)j.
Comparing the components of the force equation, we have:
421 = qvB (in the ar direction)
0 = qvB (in the θ direction)
For the ar component:
421 = (-1.6 x 10^-19 C)(40.0 x 10^3 m/s)B
Solving for B:
B = 421 / [(-1.6 x 10^-19 C)(40.0 x 10^3 m/s)]
Similarly, for the θ component:
0 = (-1.6 x 10^-19 C)(33.0 x 10^3 m/s)B
However, since the θ component is zero, we don't need to solve for B in this direction.
Calculating B for the ar component:
B = 421 / [(-1.6 x 10^-19 C)(40.0 x 10^3 m/s)]
B ≈ -1.32 x 10^-3 T
So, the magnetic field B is approximately -1.32 x 10^-3 Tesla in the ar direction.
Visit here to learn more about magnetic field brainly.com/question/19542022
#SPJ11
billy, a student, sounds two tuning forks that are supposed to be tuned to A 440.0hz. in which one is correct. When sounded with the other tuning ford, he hears a periodic volume change at a rate of 24 times in 6.0s
a) In physics, what is this called?
b) What would be the possible frequencies for the tuning fork that happens to be out of tune?
In physics, the periodic volume change heard when two sound waves with nearly similar frequencies interfere with each other is called beats. The frequency of the out-of-tune tuning fork is 222 Hz.
When two sound waves interfere with each other, the periodic volume change heard when two sound waves with nearly similar frequencies interfere with each other is called beats.
The frequency of the out-of-tune tuning fork can be calculated from the number of beats heard in a given time. Billy hears 24 beats in 6.0 seconds. Therefore, the frequency of the out of tune tuning fork is 24 cycles / 6.0 seconds = 4 cycles per second.
In one cycle, there are two sounds: one of the tuning fork, which is at a frequency of 440.0 Hz, and the other is at the frequency of the out-of-tune tuning fork (f). The frequency of the out-of-tune tuning fork can be calculated by the formula; frequency of the out-of-tune tuning fork (f) = (Beats per second + 440 Hz) / 2.
Substituting the values, we get;
frequency of the out-of-tune tuning fork (f) = (4 Hz + 440 Hz) / 2 = 222 Hz.
Learn more about frequency:
https://brainly.com/question/14567997
#SPJ11
A hollow square steel tube has a height and width dimension of 5 in and a wall thickness of 0.4 in. and an original length of 8 in. The tube is loaded with 44000 lb. in compression and is shortened by 0.0017 in. as a result of the load. Determine the Modulus of Elasticity of the steel with 1-decimal place accuracy.E= _______ x10^6
(to 1 decimal place)
The Modulus of Elasticity of the steel with 1-decimal place accuracy is 0.0017 in / 8 in
To determine the modulus of elasticity (E) of the steel, we can use Hooke's law, which states that the stress (σ) is directly proportional to the strain (ε) within the elastic limit.
The stress (σ) can be calculated using the formula:
σ = F / A
Where:
F is the force applied (44000 lb in this case)
A is the cross-sectional area of the steel tube.
The strain (ε) can be calculated using the formula:
ε = ΔL / L0
Where:
ΔL is the change in length (0.0017 in)
L0 is the original length (8 in)
The modulus of elasticity (E) can be calculated using the formula:
E = σ / ε
Now, let's calculate the cross-sectional area (A) of the steel tube:
The outer dimensions of the tube can be calculated by adding twice the wall thickness to each side of the inner dimensions:
Outer height = 5 in + 2 × 0.4 in = 5.8 in
Outer width = 5 in + 2 × 0.4 in = 5.8 in
The cross-sectional area (A) is the product of the outer height and outer width:
A = Outer height × Outer width
Substituting the values:
A = 5.8 in × 5.8 in
A = 33.64 in²
Now, we can calculate the stress (σ):
σ = 44000 lb / 33.64 in²
Next, let's calculate the strain (ε):
ε = 0.0017 in / 8 in
Finally, we can calculate the modulus of elasticity (E):
E = σ / ε
To know more about elasticity click on below link :
https://brainly.com/question/17250844#
#SPJ11
Question 51 1 pts How much heat, in kilo-joules, is required to convert 29 g of ice at -12°C into steam at 119°C, all at atmospheric pressure? (Lice 333 J/g, Lsteam = 2.26 10³ J/g, Cice = 2.090 J/g, Cwater = 4.186 J/g, Csteam = 2.010 J/g).
The amount of heat required to convert 29 g of ice at -12°C to steam at 119°C, at atmospheric pressure, is approximately 290 kJ.
To calculate the total heat required, we need to consider the heat energy for three stages: (1) heating the ice to 0°C, (2) melting the ice at 0°C, and (3) heating the water to 100°C, converting it to steam at 100°C, and further heating the steam to 119°C.
1. Heating the ice to 0°C:
The heat required can be calculated using the formula Q = m * C * ΔT, where m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
Q₁ = 29 g * 2.090 J/g°C * (0°C - (-12°C))
2. Melting the ice at 0°C:
The heat required for phase change can be calculated using Q = m * L, where L is the latent heat of fusion.
Q₂ = 29 g * 333 J/g
3. Heating the water from 0°C to 100°C, converting it to steam at 100°C, and further heating the steam to 119°C:
Q₃ = Q₄ + Q₅
Q₄ = 29 g * 4.186 J/g°C * (100°C - 0°C)
Q₅ = 29 g * 2.26 × 10³ J/g * (100°C - 100°C) + 29 g * 2.010 J/g°C * (119°C - 100°C)
Finally, the total heat required is the sum of Q₁, Q₂, Q₃:
Total heat = Q₁ + Q₂ + Q₃
By substituting the given values and performing the calculations, we find that the heat required is approximately 290 kJ.
To know more about atmospheric pressure refer here:
https://brainly.com/question/31634228#
#SPJ11
Questions 7.39 Homework. Unanswered ★ A pendulum is fashioned out of a thin bar of length 0.55 m and mass 1.9 kg. The end of the bar is welded to the surface of a sphere of radius 0.11 m and mass 0.86 kg. Find the centre of mass of the composite object as measured in metres from the end of the bar without the sphere. Type your numeric answer and submit
The center of mass of the composite object, consisting of the bar and sphere, is approximately 0.206 meters from the end of the bar. This is calculated by considering the individual centers of mass and their weighted average based on their masses.
To find the center of mass of the composite object, we need to consider the individual center of masses of the bar and the sphere and calculate their weighted average based on their masses.
The center of mass of the bar is located at its midpoint, which is L/2 = 0.55 m / 2 = 0.275 m from the end of the bar.
The center of mass of the sphere is at its geometric center, which is at a distance of R/2 = 0.11 m / 2 = 0.055 m from the end of the bar.
Now we calculate the weighted average:
Center of mass of the composite object = ([tex]m_bar[/tex] * center of mass of the bar + [tex]m_bar[/tex] * center of mass of the sphere) / ([tex]m_bar + m_sphere[/tex])
Center of mass of the composite object = (1.9 kg * 0.275 m + 0.86 kg * 0.055 m) / (1.9 kg + 0.86 kg)
To solve the expression (1.9 kg * 0.275 m + 0.86 kg * 0.055 m) / (1.9 kg + 0.86 kg), we can simplify the numerator and denominator separately and then divide them.
Numerator: (1.9 kg * 0.275 m + 0.86 kg * 0.055 m) = 0.5225 kg⋅m + 0.0473 kg⋅m = 0.5698 kg⋅m
Denominator: (1.9 kg + 0.86 kg) = 2.76 kg
Now we can calculate the expression:
(0.5698 kg⋅m) / (2.76 kg) ≈ 0.206 m
Therefore, the solution to the expression is approximately 0.206 meters.
To know more about the center of mass refer here,
https://brainly.com/question/8662931#
#SPJ11
Why must hospital personnel wear special conducting shoes while working around oxygen in an operating room?What might happen if the personnel wore shoes with rubber soles?
Hospital personnel must wear special conducting shoes in operating rooms to prevent the buildup of static electricity, which could potentially ignite the highly flammable oxygen. Wearing shoes with rubber soles increases the risk of static discharge and should be avoided to ensure the safety of everyone in the operating room.
Hospital personnel must wear special conducting shoes while working around oxygen in an operating room because oxygen is highly flammable and can ignite easily. These special shoes are made of materials that conduct electricity, such as leather, to prevent the buildup of static electricity.
If personnel wore shoes with rubber soles, static electricity could accumulate on their bodies, particularly on their feet, due to the friction between the rubber soles and the floor. This static electricity could then discharge as a spark, potentially igniting the oxygen in the operating room.
By wearing conducting shoes, the static electricity is safely discharged to the ground, minimizing the risk of a spark that could cause a fire or explosion. The conducting materials in these shoes allow any static charges to flow freely and dissipate harmlessly. This precaution is crucial in an environment where oxygen is used, as even a small spark can lead to a catastrophic event.
To know more about friction visit:
https://brainly.com/question/28356847
#SPJ11
A loop of wire carrying current I (moving counterclockwise as seen from above) lies in the xy. plane. The loop is placed in a constant magnetic field of magnitude B that points at 30° from the z-axis. If the loop has a radius of 10 meters, carries a current of 2 amps, and the magnitude of the magnetic field is B Tesla, then the magnitude of the torque on the loop is given by am Newton-meters What is the value of a if B=5 Tesla?
The value of a is 100, as it represents the coefficient π in the equation. Therefore, if B = 5 Tesla, the magnitude of the torque on the loop is 500π N·m, or approximately 1570 N·m.
The torque on a current-carrying loop placed in a magnetic field is given by the equation τ = NIABsinθ, where τ is the torque, N is the number of turns in the loop, I is the current, A is the area of the loop, B is the magnitude of the magnetic field, and θ is the angle between the magnetic field and the normal to the loop.
In this case, the loop has a radius of 10 meters, so the area A is πr² = π(10 m)² = 100π m². The current I is 2 amps, and the magnitude of the magnetic field B is 5 Tesla. The angle θ between the magnetic field and the z-axis is 30°.
Plugging in the values into the torque equation, we have: τ = (2)(1)(100π)(5)(sin 30°)
Using the approximation sin 30° = 0.5, the equation simplifies to: τ = 500π N·m
To know more about torque refer here:
https://brainly.com/question/28220969#
#SPJ11
A thermistor is used in a circuit to control a piece of equipment automatically. What might this circuit be used for? A lighting an electric lamp as it becomes darker B ringing an alarm bell if a locked door is opened C switching on a water heater at a pre-determined time D turning on an air conditioner when the temperature rises
A thermistor is used in a circuit to control a piece of equipment automatically, this circuit be used for D. Turn on an air conditioner when the temperature rises.
A thermistor is a type of resistor whose resistance value varies with temperature. In a circuit, it is used as a sensor to detect temperature changes. The thermistor is used to control a piece of equipment automatically in various applications like thermostats, heating, and cooling systems. A circuit with a thermistor may be used to turn on an air conditioner when the temperature rises. In this case, the thermistor is used to sense the increase in temperature, which causes the resistance of the thermistor to decrease.
This change in resistance is then used to trigger the circuit, which turns on the air conditioner to cool the room. A thermistor circuit may also be used to switch on a water heater at a pre-determined time. In this case, the thermistor is used to detect the temperature of the water, and the circuit is programmed to turn on the heater when the water temperature falls below a certain level. This helps to maintain a consistent temperature in the water tank. So therefore the correct answer is D, turn on an air conditioner when the temperature rises.
Learn more about thermistor at:
https://brainly.com/question/31888503
#SPJ11
A proton is moving north at a velocity of 4.9-10 m/s through an east directed magnetic field. The field has a strength of 9.6-10 T. What is the direction and strength of the magnetic force?
The direction of the magnetic force is towards the west, and its strength is [tex]7.7 * 10^{-28}[/tex] N.
Given data, Velocity of proton, v = 4.9 × 10⁻¹⁰ m/s
Strength of magnetic field, B = 9.6 × 10⁻¹⁰ T
We know that the magnetic force is given by the equation:
F = qvBsinθ
where, q = charge of particle, v = velocity of particle, B = magnetic field strength, and θ = angle between the velocity and magnetic field vectors.
Now, the direction of the magnetic force can be determined using Fleming's left-hand rule. According to this rule, if we point the thumb of our left hand in the direction of the velocity vector, and the fingers in the direction of the magnetic field vector, then the direction in which the palm faces is the direction of the magnetic force.
Therefore, using Fleming's left-hand rule, the direction of the magnetic force is towards the west (perpendicular to the velocity and magnetic field vectors).
Now, substituting the given values, we have:
[tex]F = (1.6 * 10^{-19} C)(4.9 * 10^{-10} m/s)(9.6 *10^{-10} T)sin 90°F = 7.7 * 10^{-28} N[/tex]
Thus, the direction of the magnetic force is towards the west, and its strength is [tex]7.7 * 10^{-28}[/tex] N.
Learn more about " magnetic force " refer to the link : https://brainly.com/question/26257705
#SPJ11
Part A A1 1-cm-tall object is 17 cm in front of a concave mirror that has a 69 em focal length Calculate the position of the image. Express your answer using two significant figures. ΨΗ ΑΣΦ O ? cm Submit Request Answer Part 8 A 1.1-cm-tall object is 17 cm in front of a concave mirror that has a 69 cm focal length Calculate the height of the image Express your answer using two significant figures. Vo] ΑΣΦ XE Cm
The position of the image is approximately -6.81 cm, and the height of the image is approximately 0.4 cm.The position of the image is approximately -6.81 cm, and the height of the image is approximately 0.4 cm.
To calculate the position of the image formed by a concave mirror and the height of the image, we can use the mirror equation and magnification formula.
Given:
- Object height (h_o) = 1 cm
- Object distance (d_o) = -17 cm (negative because the object is in front of the mirror)
- Focal length (f) = 69 cm
Using the mirror equation:
1/f = 1/d_i + 1/d_o
Since the object distance (d_o) is given as -17 cm, we can rearrange the equation to solve for the image distance (d_i):
1/d_i = 1/f - 1/d_o
Substituting the values:
1/d_i = 1/69 - 1/-17
To calculate the height of the image (h_i), we can use the magnification formula:
h_i / h_o = -d_i / d_o
Rearranging the formula to solve for h_i:
h_i = (h_o * d_i) / d_o
Substituting the given values:
h_i = (1 * d_i) / -17
Now, let's calculate the position of the image (d_i) and the height of the image (h_i):
1/d_i = 1/69 - 1/-17
1/d_i = (17 - 69) / (69 * -17)
1/d_i = 52 / (-69 * 17)
d_i = -1 / (52 / (-69 * 17))
d_i ≈ -6.81 cm
h_i = (1 * -6.81) / -17
h_i ≈ 0.4 cm
Therefore, the position of the image is approximately -6.81 cm from the mirror and the height of the image is approximately 0.4 cm.
To know more about concave mirror, click here:
brainly.com/question/31379461
#SPJ11
A charge Q is located some distance L from the center of a wire. A small charge −q with mass m is attached to the wire such that it can move along the wire but not perpendicular to it. The small charge −q is moved some small amount Δx<
The work done on the small charge -q when it is moved a small distance Δx along the wire can be determined by substituting the force equation into the work equation and solving for W
When the small charge -q is moved a small distance Δx along the wire, it experiences a force due to the electric field generated by the charge Q.
The direction of this force depends on the relative positions of the charges and their charges' signs. Since the small charge -q is negative, it will experience a force in the opposite direction of the electric field.
Assuming the small charge -q moves in the same direction as the wire, the work done on the charge can be calculated using the formula:
Work (W) = Force (F) × Displacement (Δx)
The force acting on the charge is given by Coulomb's Law:
Force (F) = k * (|Q| * |q|) / (L + Δx)²
Here, k is the electrostatic constant and |Q| and |q| represent the magnitudes of the charges.
Thus, the work done on the small charge -q when it is moved a small distance Δx along the wire can be determined by substituting the force equation into the work equation and solving for W.
It's important to note that the above explanation assumes the charge Q is stationary, and there are no other external forces acting on the small charge -q.
Learn more about work done from the given link
https://brainly.com/question/25573309
#SPJ11
Singly charged uranium-238 ions are accelerated through a potential difference of 2.00kV and enter a uniform magnetic field of magnitude 1.20 T directed perpendicular to their velocities.(c) What If? How does the ratio of these path radii depend on the accelerating voltage?
The ratio of the path radii for the uranium-238 ions is not affected by the accelerating voltage. The ratio is solely determined by the mass of the ions and the magnitude of the magnetic field.
The ratio of the path radii for singly charged uranium-238 ions depends on the accelerating voltage.
When a charged particle enters a uniform magnetic field perpendicular to its velocity, it experiences a force called the magnetic force. This force acts as a centripetal force, causing the particle to move in a circular path.
The magnitude of the magnetic force is given by the equation:
F = qvB
Where:
F is the magnetic force
q is the charge of the particle
v is the velocity of the particle
B is the magnitude of the magnetic field
In this case, the uranium-238 ions have a charge of +1 (since they are singly charged). The magnetic force acting on the ions is equal to the centripetal force:
qvB = mv²/r
Where:
m is the mass of the uranium-238 ion
v is the velocity of the ion
r is the radius of the circular path
We can rearrange this equation to solve for the radius:
r = mv/qB
The velocity of the ions can be determined using the equation for the kinetic energy of a charged particle:
KE = (1/2)mv²
The kinetic energy can also be expressed in terms of the accelerating voltage (V) and the charge (q) of the ion:
KE = qV
We can equate these two expressions for the kinetic energy:
(1/2)mv² = qV
Solving for v, we get:
v = sqrt(2qV/m)
Substituting this expression for v into the equation for the radius (r), we have:
r = m(sqrt(2qV/m))/qB
Simplifying, we get:
r = sqrt(2mV)/B
From this equation, we can see that the ratio of the path radii is independent of the charge (q) of the ions and the mass (m) of the ions.
Therefore, the ratio of the path radii is independent of the accelerating voltage (V).
Learn more about voltage
https://brainly.com/question/32002804
#SPJ11
Problem 1: his Water (density equal to 1000 kg/m) flows through a system of pipes that goes up a step. The water pressure is 140 kPa at the bottom of the step (point 1), the cross-sectional area of the pipe at the top of the step (point 2) is half that at the bottom of the step and the speed of the water at the bottom of the step is 1.20 m/s. The pressure at the top of the step is 120 kPa. Find the value of the height h? (10 points) y h 0 11
The value of the height h is 5 meters.
To find the value of the height h, we can apply Bernoulli's equation, which relates the pressure, density, and velocity of a fluid flowing through a system. Bernoulli's equation states that the sum of the pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline.
Apply Bernoulli's equation at points 1 and 2:
At point 1 (bottom of the step):
P1 + 1/2 * ρ * v1^2 + ρ * g * h1 = constant
At point 2 (top of the step):
P2 + 1/2 * ρ * v2^2 + ρ * g * h2 = constant
Simplify the equation using the given information:
Since the pressure at point 1 (P1) is 140 kPa and at point 2 (P2) is 120 kPa, and the speed of the water at the bottom (v1) is 1.20 m/s, we can substitute these values into the equation.
140 kPa + 1/2 * 1000 kg/m^3 * (1.20 m/s)^2 + 1000 kg/m^3 * 9.8 m/s^2 * h1 = 120 kPa + 1/2 * 1000 kg/m^3 * v2^2 + 1000 kg/m^3 * 9.8 m/s^2 * h2
Since the cross-sectional area of the pipe at the top (point 2) is half that at the bottom (point 1), the velocity at the top (v2) can be calculated as v2 = 2 * v1.
Solve for the value of h:
Using the given values and the equation from Step 2, we can solve for the value of h.
140 kPa + 1/2 * 1000 kg/m^3 * (1.20 m/s)^2 + 1000 kg/m^3 * 9.8 m/s^2 * h1 = 120 kPa + 1/2 * 1000 kg/m^3 * (2 * 1.20 m/s)^2 + 1000 kg/m^3 * 9.8 m/s^2 * h2
Simplifying the equation and rearranging the terms, we can find that h = 5 meters.
Therefore, the value of the height h is 5 meters.
Learn more about Bernoulli's equation
brainly.com/question/29865910
#SPJ11
50. The angle that a reflected light ray makes with the surface normal A) is smaller B) the same size C) greater than the angle that the incident ray makes with the normal 51. The speed of light in gl
The angle that a reflected light ray makes with the surface normal is smaller.
The law of reflection states that the angle of incidence is equal to the angle of reflection. When light is reflected from a surface, the angle at which it is reflected (angle of reflection) is equal to the angle at which it hits the surface (angle of incidence). The angle that a reflected light ray makes with the surface normal is the angle of reflection. Therefore, the answer is that the angle that a reflected light ray makes with the surface normal is smaller than the angle that the incident ray makes with the normal.
The speed of light in glass is less than the speed of light in a vacuum. This means that the refractive index of glass is greater than 1. When light passes through a medium with a higher refractive index than the medium it was previously in, the light is bent towards the normal. Therefore, the answer is that the speed of light in glass is less than the speed of light in a vacuum, and the refractive index of glass is greater than 1.
The angle that a reflected light ray makes with the surface normal is A) is smaller. The law of reflection states that the angle of incidence is equal to the angle of reflection. When light is reflected from a surface, the angle at which it is reflected (angle of reflection) is equal to the angle at which it hits the surface (angle of incidence). The angle that a reflected light ray makes with the surface normal is the angle of reflection. Therefore, the answer is that the angle that a reflected light ray makes with the surface normal is smaller than the angle that the incident ray makes with the normal.
The speed of light in glass is less than the speed of light in a vacuum. This means that the refractive index of glass is greater than 1. When light passes through a medium with a higher refractive index than the medium it was previously in, the light is bent towards the normal. Therefore, the answer is that the speed of light in glass is less than the speed of light in vacuum, and the refractive index of glass is greater than 1.
When a light wave strikes a surface, it can be either absorbed or reflected. Reflection occurs when light bounces back from a surface. The angle at which the light strikes the surface is known as the angle of incidence, and the angle at which it reflects is known as the angle of reflection. The angle of incidence is always equal to the angle of reflection, as stated by the law of reflection. The angle that a reflected light ray makes with the surface normal is the angle of reflection. It's smaller than the angle of incidence.
When light travels through different mediums, such as air and glass, its speed changes, and it bends. Refraction is the process of bending that occurs when light moves from one medium to another with a different density. The refractive index is a measure of the extent to which a medium slows down light compared to its speed in a vacuum. The refractive index of a vacuum is 1.
When light moves from a medium with a low refractive index to a medium with a high refractive index, it bends toward the normal, which is a line perpendicular to the surface separating the two media.
When light is reflected from a surface, the angle of reflection is always equal to the angle of incidence. The angle of reflection is the angle that a reflected light ray makes with the surface normal, and it is smaller than the angle of incidence. The refractive index of a medium is a measure of how much the medium slows down light compared to its speed in a vacuum. When light moves from a medium with a low refractive index to a medium with a high refractive index, it bends toward the normal.
To know more about refractive index visit
brainly.com/question/30761100
#SPJ11
A 2.00-nF capacitor with an initial charge of 5.32μC is discharged through a 1.22-k Ω resistor. (a) Calculate the magnitude of the current in the resistor 9.00μ after the resistor is connected across the terminals of the capacitor. mA (b) What charge remains on the capacitor after 8.00μs ? μC (c) What is the maximum current in the resistor? A
The maximum current in the resistor is 2.18 A.
Capacitance of capacitor, C = 2.00 n
F = 2.00 × 10⁻⁹ F
Resistance, R = 1.22 kΩ = 1.22 × 10³ Ω
Time, t = 9.00 μs = 9.00 × 10⁻⁶ s
(a) The magnitude of the current in the resistor 9.00 μs after the resistor is connected across the terminals of the capacitor can be determined using the formula for current,
i = (Q₁ - Q₂)/RCQ₁
= 5.32 μCQ₂
= Q₁ - iRC
Time constant, RC = 2.44 μsRC is the time required for the capacitor to discharge to 36.8% of its initial charge. Substitute the known values in the equation to find the current;
i = (Q₁ - Q₂)/RC
=> i
= (5.32 - Q₂)/2.44 × 10⁻⁶
The current in the resistor 9.00 μs after the resistor is connected across the terminals of the capacitor is, i = 2.10 mA
(b) The charge remaining on the capacitor after 8.00 μs can be calculated using the formula,
Q = Q₁ × e⁻ᵗ/RC
Where, Q = charge on capacitor at time t, Q₁ = Initial charge on capacitor, t = time, RC = time constant
Substitute the known values to find the charge on capacitor after 8.00 μs;
Q = Q₁ × e⁻ᵗ/RC
=> Q
= 5.32 × e⁻⁸/2.44 × 10⁻⁶
=> Q
= 1.28 μC
Therefore, the charge that remains on the capacitor after 8.00 μs is,
Q₂ = 1.28 μC
(c) The maximum current in the resistor can be calculated using the formula, i = V/R
Where, V = maximum potential difference across the resistor, R = resistance of resistor
The potential difference across the resistor will be equal to the initial voltage across the capacitor which is given by V = Q₁/C
Substitute the known values to find the maximum current in the resistor;
i = V/R
=> i
= Q₁/RC
=> i = 2.18 mA
Therefore, the maximum current in the resistor is 2.18 A (Answer in Amperes)
A quicker way to find the maximum current in the resistor would be to use the formula,
i = Q₁/(RC)
= V/R,
where V is the initial voltage across the capacitor and is given by V = Q₁/C.
To know more about current visit:
https://brainly.com/question/15141911
#SPJ11
Which graphs could represent CONSTANT VELOCITY MOTION
A constant velocity motion will be represented by a straight line on the position-time graph as in option (c). Therefore, the correct option is C.
An object in constant velocity motion keeps its speed and direction constant throughout. The position-time graph for motion with constant speed is linear. The magnitude and direction of the slope on the line represent the speed and direction of motion, respectively, and the slope itself represents the velocity of the object.
A straight line with a slope greater than zero on a position-time graph indicates that the object is traveling at a constant speed. The velocity of the object is represented by the slope of the line; A steeper slope indicates a higher velocity, while a shallower slope indicates a lower velocity.
Therefore, the correct option is C.
Learn more about Slope, here:
https://brainly.com/question/3605446
#SPJ4
Your question is incomplete, most probably the complete question is:
Which of the following position-time graphs represents a constant velocity motion?