Therefore the maximum current in the circuit is 7.11A.
A series RL circuit includes a resistor and an inductor. The behavior of an RL circuit when a switch is closed can be determined by applying Kirchhoff's voltage law (KVL).
The voltage drops across the resistor and inductor must add up to the voltage source. The maximum current in the circuit can be calculated using Ohm's law and Kirchhoff's voltage law.
Kirchhoff's voltage law can be expressed as follows:
VL = VR + VL
Where VL is the voltage drop across the inductor, VR is the voltage drop across the resistor, and V is the voltage source.
Since the circuit is purely resistive and inductive, the voltage across the inductor and resistor can be calculated as follows:
VR = IRRL where IR is the current flowing through the resistor, and RL is the resistor's resistance.
VL = XL/dt where XL is the inductor's inductance and dt is the time difference between t = 0 and t = 0.3s.
When the switch is first closed, the current through the inductor is zero. At t = 0, the current starts to increase in the inductor until it reaches its maximum value at time t = infinity.
The maximum current in the circuit is found by calculating the steady-state current.
The steady-state current, IS can be calculated as follows:
IS = V/RL
where V is the voltage source.
The voltage source is given as 19.9V.
The resistance of the circuit, RL is given as 2.8 ohms.
Therefore,
IS = V/RL
= 19.9/2.8
= 7.11A
The maximum current in the circuit is 7.11A.
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12. A 2.5 x 10¹8 Hz x-ray photon strikes a metal foil and frees an electron. After the collision a lower energy 2.3 x 10¹8 Hz x-ray photon emerges. What is the speed of the electron? [P4]
The speed of the electron is 5.5 x 10⁶ m/s after the collision.
A photon with a frequency of 2.5 × 10¹⁸ Hz collides with a metal foil, freeing an electron. A lower-energy 2.3 × 10¹⁸ Hz X-ray photon emerges from the collision. We need to find out the electron's velocity after the collision.
hf = E, where h is Planck's constant and f is the frequency.
The energy of the photon can be calculated by multiplying the Planck's constant h by the frequency f.
[tex]E = h * fE_1 = (6.626 * 10^-^3^4 J.s) * (2.5 * 10^1^8 Hz)E_1 = 1.66 * 10^-^1^5 J[/tex].
The frequency of the emitted X-ray photon is calculated in the same way.
[tex]E = h * fE_2 = (6.626 * 10^-^3^4 J.s) * (2.3 * 10^1^8 Hz)E_2 = 1.53 * 10^-^1^5 J[/tex].
The electron's kinetic energy can be calculated by subtracting the energy of the emitted photon from the energy of the incident photon.
[tex]KE = E_1 - E_2[/tex]
[tex]KE = (1.66 * 10^-^1^5 J) - (1.53 * 10^-^1^5 J)[/tex]
[tex]KE = 0.13 * 10^-^1^5 J[/tex].
To find the electron's velocity, we'll first convert the kinetic energy to joules.
[tex]KE = (1/2)mv^2v = \sqrt{(2KE/m)}[/tex] where m is the mass of the electron, which is 9.11 × 10⁻³¹ kg.
[tex]v = \sqrt{ [(2 * 0.13 * 10^-^1^5 J)/9.11 * 10^-^3^1 kg]v}[/tex] [tex]= 5.5 * 10^6 m/s[/tex] (to two significant figures).
Therefore, the speed of the electron is 5.5 x 10⁶ m/s after the collision.
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one, by the band u2, is a song that i find very inspirational. a. add quotation marks around one b. remove the comma after u2 c. the sentence is punctuated correctly. d. add quotation marks around u2
In the given sentence, "one, by the band u2, is a song that I find very inspirational," add quotation marks around one, hence option A is correct.
Punctuation is the use of white space, traditional signals, and specific typographical elements to help readers understand and interpret written material correctly, whether they are reading it quietly or loudly.
In many writing systems, quote marks are punctuation symbols that are used in pairs to demarcate a quotation, direct speech, or a phrase.
Thus, the correct sentence is: "One," by the band u2, is a song that I find very inspirational.
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calculate the amount of heat burned if you eat 300.0 grams of ice at -5 c
The amount of heat burned if you eat 300.0 grams of ice at -5°C is 150,196.5 J. When we eat 300.0 g of ice at -5°C, the amount of heat burned can be calculated using the formula, Q = m × C × ΔT.Q = m × C × ΔTWhere, m = mass of iceC = specific heat capacityΔT = change in temperature
The specific heat capacity of ice (C) is 2.09 J/g°C. As the ice is below the freezing point of water, we have to calculate the heat of fusion first, which is the amount of energy required to melt a certain amount of ice at its melting point.Taking the heat of fusion of ice as 334 J/g, we can calculate the amount of heat required to raise the temperature of 300.0 g of ice from -5°C to 0°C:Q1 = m × C × ΔTQ1 = 300.0 g × 2.09 J/g°C × (0°C - (-5°C))Q1 = 3,142.5 JNext, we calculate the heat of fusion required to melt the ice at 0°C:Q2 = m × LfQ2 = 300.0 g × 334 J/gQ2 = 100,200 JFinally, we calculate the amount of heat required to raise the temperature of 300.0 g of water from 0°C to 37°C (body temperature):Q3 = m × C × ΔTQ3 = 300.0 g × 4.18 J/g°C × (37°C - 0°C)Q3 = 46,854 J . Total amount of heat burned = Q1 + Q2 + Q3= 3,142.5 J + 100,200 J + 46,854 J= 150,196.5 J .
The heat burned when we eat 300.0 g of ice at -5°C can be calculated using the formula, Q = m × C × ΔT. Here, Q represents the amount of heat burned, m represents the mass of ice, C represents the specific heat capacity of ice, and ΔT represents the change in temperature. As the ice is below the freezing point of water, we have to calculate the heat of fusion first, which is the amount of energy required to melt a certain amount of ice at its melting point.The specific heat capacity of ice is 2.09 J/g°C. Finally, we calculate the amount of heat required to raise the temperature of 300.0 g of water from 0°C to 37°C (body temperature). The specific heat capacity of water is 4.18 J/g°C. Therefore, the amount of heat required to raise the temperature of 300.0 g of water from 0°C to 37°C can be calculated as follows:Q3 = m × C × ΔTQ3 = 300.0 g × 4.18 J/g°C × (37°C - 0°C)Q3 = 46,854 JTotal amount of heat burned = Q1 + Q2 + Q3= 3,142.5 J + 100,200 J + 46,854 J= 150,196.5 JTherefore, the amount of heat burned when we eat 300.0 g of ice at -5°C is 150,196.5 J.
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What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 107 km above Earth's surface? (b) What is the period of revolution? (a) Number (b) Number Units Units
The linear speed required for an Earth satellite to be in a circular orbit at an altitude of 107 km above Earth's surface is approximately 7.85 km/s. The period of revolution for this satellite is around 1 hour and 34 minutes.
To explain this further, let's consider the concept of circular motion and gravitational force. When an object is in a circular orbit, it experiences centripetal force directed towards the center of the circle. In the case of a satellite orbiting the Earth, this force is provided by the gravitational pull of the Earth.
The centripetal force (F) can be calculated using the equation F = m * a, where m is the mass of the satellite and a is the acceleration towards the center of the circle. In this case, the acceleration is provided by gravity, which can be represented as g (approximately 9.8 m/s²).
Since the satellite is in a circular orbit, the centripetal force is equal to the gravitational force between the satellite and the Earth, given by the equation F = G * (m * M) / r², where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the satellite and the center of the Earth.
By equating these two equations, we can solve for the speed of the satellite. The centripetal force can be rewritten as m * v² / r, where v is the linear speed of the satellite. Setting these two equal and solving for v, we get v = √(G * M / r).
Plugging in the values for G (6.67430 x 10⁻¹¹ m³ kg⁻¹ s⁻²), M (5.97219 x 10²⁴ kg), and r (107 km + 6371 km, since the altitude is given above Earth's surface), we can calculate the linear speed, which comes out to approximately 7.85 km/s.
To find the period of revolution, we can use the formula T = 2πr / v, where T is the period and π is a mathematical constant. Plugging in the values, we find the period to be approximately 1 hour and 34 minutes.
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A person throws a ball upward into the air with an initial velocity of 15 m/s. Calculate
a) how high it goes?
b) how long the ball is in the air before it comes back ?
c) how much time it takes for the ball to reach the maximum height?
a) The maximum height of the ball is 11.52 m. b) The time ball is in the air before coming back is 3.06 seconds. c) The time ball takes to reach maximum height is 1.53 seconds.
The maximum height achieved by the ball is 11.52 m. To find the maximum height, we use the formula for displacement S = ut + 1/2 gt² = 15t + 1/2 × (-9.8) t² = 15t - 4.9 t². Here, u = 15 m/s, g = -9.8 m/s² and time taken to reach maximum height, t = 1.53 seconds.
The time ball is in the air before it comes back is 3.06 seconds. To find the total time taken by the ball to return to the ground, use the formula for time as t = (v - u) / g = (0 - 15) / (-9.8) = 1.53 seconds. So, the total time taken by the ball to return to the ground = 2t = 2 × 1.53 = 3.06 seconds.
Time taken by the ball to reach the maximum height is the time taken to reach the highest point from the time of throwing the ball upward. Time taken to reach the maximum height, t = 1.53 seconds.
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why was the final mass of the food item less than the original mass
The final mass of the food item less than the original mass se of the loss of water.
When cooking, it is not uncommon to notice a difference in mass between the food item before cooking and after cooking. The final mass of the food item is always less than the original mass because of the loss of water. When food is cooked, the heat applied causes the water content in the food to evaporate, causing the food item to shrink in size and weight. The amount of mass lost depends on the water content in the food item and the cooking method used.
When food is boiled, more water content evaporates due to the high temperatures, which can result in a more significant difference in mass. The final mass of the food item may also be affected by the cooking method used. For instance, frying may result in a lower loss of mass compared to boiling. In summary, the final mass of the food item is less than the original mass because of the loss of water through evaporation.
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The final mass of a food item is typically less than the original mass due to the process of dehydration or water loss that occurs during cooking or other forms of food preparation. This can result in a reduction in the total weight of the food item, even though the actual amount of food present remains the same.
When food is cooked or exposed to heat, the heat causes the moisture present in the food to evaporate, and this leads to a loss of weight. As a result, the final mass of the food item is less than the original mass.
The extent to which the weight is reduced will depend on the method of cooking, the temperature at which the food is cooked, and the length of time it is cooked for. For example, when a piece of chicken is cooked on a grill, it will initially weigh more than the final weight once it is cooked. This is because as the chicken cooks, some of the moisture and fat inside it will be released, and this will evaporate.
Therefore, by the time the chicken is fully cooked, it will have lost some of its original weight due to the loss of moisture and fat. Therefore, the final mass of a food item is often less than the original mass due to the process of dehydration or water loss that occurs during cooking or other forms of food preparation.
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The biggest coal burning power station in the world is in Taiwan with a power output capacity of 5500 MW. (a) Assume the power station operates 24 hours a day and every day throughout the year, what is the approximate annual energy capacity (in TWh) of this power station? (6 marks) (b) A coal power plant typically obtains ~2kWh of electrical energy by burning 1 kg of coal. If the energy density of coal is 24MJ/kg, what is the energy conversion efficiency in this case? (6 marks) (c) How much coal supply (in unit of tons) is needed to operate this power station in one year?
(a) The approximate annual energy capacity of the power station is 48,180 TWh. (b) The energy conversion efficiency is 8.3%. (c) The amount of coal supply needed is 24,090,000,000 tonnes.
For part (a), we used the formula for annual energy capacity which takes into account the power output, hours of operation, and days of operation per year. For part (b), we used the energy obtained from burning 1 kg of coal and the energy density of coal to calculate the energy conversion efficiency. We used the formula for energy conversion efficiency and found that it is 8.3%.
For part (c), we used the amount of energy generated in one year and the energy obtained from burning 1 kg of coal to calculate the amount of coal needed. We used the formula for amount of coal needed and found that it is 24,090,000,000 tonnes.
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Was really struggling to do this question , so decided to ask for help here
A compound microscope has and objective lens focal length of 0.15 cm and eyepiece lens focal length of 1.4cm . The distance between the lenses is 20 cm . It is adjusted for relaxed viewing (i.e. the final image is an infinite distance from the eye).
Part A
Find the lateral magnification produced by just the objective lens.
Part B
Find the angular magnification produced by just the eyepiece lens.
A) The magnification produced by the objective lens is -1/2. B) The angular magnification produced by just the eyepiece lens is approximately -0.107.
Lateral magnification is given by the ratio of the size of the image (I) to the size of the object (O). Since the image is inverted, this ratio is negative. So, the lateral magnification of the objective lens is given by:M = -I/O The objective lens has a focal length of f1 = 0.15 cm and is adjusted for relaxed viewing, meaning that the final image is at an infinite distance from the eye.
As a result, the distance between the objective lens and the eyepiece lens, d = 20 cm, is equal to the focal length of the eyepiece lens. Assume that the distance between the object and the objective lens is equal to the focal length of the objective lens, f1 = 0.15 cm.
Then, the distance between the objective lens and the image produced by the objective lens, d1 = f1(1 + M1), is also equal to 20 cm.Substituting the given values into the formula for the magnification produced by the objective lens:M1 = -d1/f1 = -(f1(1 + M1))/f1M1 = -1/2
Angular magnification is given by the ratio of the angle subtended by the image (θ') to the angle subtended by the object (θ). Since the image is magnified and inverted, this ratio is negative. So, the angular magnification of the eyepiece lens is given by:A = -θ'/θ
The final image produced by the objective lens is a real and inverted image, which is then used as the object for the eyepiece lens. Assume that the distance between the eyepiece lens and the final image is equal to the focal length of the eyepiece lens, f2 = 1.4 cm.
Then, the distance between the object (real and inverted) and the eyepiece lens is given by:d2 = f2Substituting the given values into the formula for the angular magnification produced by the eyepiece lens:A = -f1/f2A = -(0.15 cm)/(1.4 cm)A ≈ -0.107 Therefore, the angular magnification produced by just the eyepiece lens is approximately -0.107.
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A simple pendulum, consisting of a mass m, is attached to the end of a 1.5 m string. If the mass is held out horizontally, and then released from rest, its speed at the bottom is O 4.4 m/s O 5.4 m/s 9
The speed of the mass at the bottom of the pendulum is approximately 4.4 m/s.
The speed of the mass at the bottom of the pendulum can be calculated using the principle of conservation of mechanical energy. At the highest point, all the potential energy is converted into kinetic energy at the bottom, neglecting any energy losses due to friction.
The potential energy at the highest point is given by the equation:
Potential Energy = mass × gravitational acceleration × height
Since the mass is held out horizontally, the height is equal to the length of the string, which is 1.5 m.
The kinetic energy at the bottom is given by the equation:
Kinetic Energy = 0.5 × mass × velocity^2
To find the speed at the bottom, we equate the potential energy to the kinetic energy:
mass × gravitational acceleration × height = 0.5 × mass × velocity^2
Simplifying and solving for velocity, we get:
velocity = sqrt(2 × gravitational acceleration × height)
Substituting the values, we get:
velocity = sqrt(2 × 9.8 m/s^2 × 1.5 m) ≈ 4.4 m/s
The speed of the mass at the bottom of the pendulum is approximately 4.4 m/s. This calculation is based on the conservation of mechanical energy, equating the potential energy at the highest point to the kinetic energy at the bottom. The length of the string is 1.5 m, and the gravitational acceleration is taken as 9.8 m/s^2.
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Abbington Company has a manufacturing facility in Brooklyn that manufactures robotic equipment for the auto industry. For Year 1, Abbington collected the following information from its main production line:
Actual quantity purchased
250 units
Actual quantity used
140 units
Units standard quantity
110 units
Actual price paid
$12 per unit
Standard price
$14 per unit
Abbington isolates price variances at the time of purchase. What is the materials price variance for Year 1?
1. $280 favorable
2. $500 unfavorable
3. $280 unfavorable
4. $500 favorable
The materials price variance for Year 1 is $280 unfavorable .
So, the correct is option 3.
How to calculate Material Price Variance?Material price variance formula = (AQ x AP) - (AQ x SP)
Where,
AQ = Actual Quantity
AP = Actual Price
SP = Standard Price
The calculation of the Material Price Variance for Year 1 is as follows:
(AQ × AP) - (AQ × SP)=(250 units × $12 per unit) - (250 units × $14 per unit) = $3,000 - $3,500 = -$500
The Material Price Variance for Year 1 is -$500.
Since the actual cost is more than the standard cost, it is considered unfavorable or adverse.
Therefore, the answer is $280 unfavorable. Option 3 is correct.
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Abbington isolates price variances at the time of purchase. The materials price variance for Year 1 is 2. $500 unfavorable. Hence, option 2) is the correct answer.
Given, Actual quantity purchased = 250 units. Actual quantity used = 140 units. Units standard quantity = 110 units. Actual price paid = $12 per unit Standard price = $14 per unit. Abbington isolates price variances at the time of purchase.
To calculate the materials price variance we use the following formula: Materials price variance = (Actual price paid - Standard price) x Actual quantity purchased. Substituting the values, Materials price variance = ($12 - $14) x 250= -$2 x 250= -$500.
Therefore, the materials price variance for Year 1 is $500 unfavorable. Thus, the correct option is 2. $500 unfavorable.
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A sample of Helium, stored in a 0.0344 m3 container, has an initial temperature of 145.4 ºF, and a gauge pressure of 2.208 atm.
All answer tolerance ±5 on the third significant digit.
a) Calculate the number of mols of Helium in the container
b) Calculate the new temperature that causes the absolute pressure of this Helium to increases to 5.525 bar, should the volume remain constant (isochoric).
c) Calculate the absolute pressure of this Helium when the volume of the container changes to 34.4 L by means of an isothermic process.
d) If the Helium's temperature decreases to 43 ºC by an isobaric process, determine the new volume of the container.
a) The number of moles of helium in the container is approximately 0.002848 mol.
b) The new temperature that causes the absolute pressure of the helium to increase to 5.525 bar (assuming constant volume) is approximately 925.565 K.
c) The absolute pressure of the helium when the volume of the container changes to 34.4 L (assuming isothermal process) is approximately 0.002208 atm.
d) The new volume of the container when the helium's temperature decreases to 43 ºC by an isobaric process is approximately 34.1285% of the initial volume, or 0.0344 m^3 * 0.341285 ≈ 0.011760 m³.
a) To calculate the number of moles of helium in the container, we can use the ideal gas law:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in m³)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
P = 2.208 atm
V = 0.0344 m³
T = (145.4 - 32) / 1.8 + 273.15 = 369.261 K (converted from ºF to Kelvin)
Rearranging the equation, we have:
n = PV / RT
n = (2.208 atm * 0.0344 m³) / (0.0821 L·atm/mol·K * 369.261 K)
n = 0.002848 moles
Therefore, the number of moles of helium in the container is approximately 0.002848 mol.
b) To calculate the new temperature that causes the absolute pressure of the helium to increase to 5.525 bar (which is 5.525 atm), we can use the ideal gas law again:
P1 / T1 = P2 / T2
Where:
P1 = initial pressure (2.208 atm)
T1 = initial temperature (369.261 K)
P2 = final pressure (5.525 atm)
T2 = final temperature (unknown)
Rearranging the equation, we have:
T2 = T1 * (P2 / P1)
T2 = 369.261 K * (5.525 atm / 2.208 atm)
T2 = 925.565 K
Therefore, the new temperature that causes the absolute pressure of the helium to increase to 5.525 bar (assuming constant volume) is approximately 925.565 K.
c) To calculate the absolute pressure of the helium when the volume changes to 34.4 L (converted from 0.0344 m³) by means of an isothermal process, we can use the ideal gas law:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure (2.208 atm)
V1 = initial volume (0.0344 m^3)
P2 = final pressure (unknown)
V2 = final volume (34.4 L)
Rearranging the equation, we have:
P2 = (P1 * V1) / V2
P2 = (2.208 atm * 0.0344 m³) / 34.4 L
P2 = 0.002208 atm
Therefore, the absolute pressure of the helium when the volume of the container changes to 34.4 L (assuming isothermal process) is approximately 0.002208 atm.
d) If the helium's temperature decreases to 43 ºC (which is 316.15 K) by an isobaric process (constant pressure), we can use the ideal gas law again to calculate the new volume:
V1 / T1 = V2 / T2
Where:
V1 = initial volume (unknown)
T1 = initial temperature (925.565 K)
V2 = final volume (unknown)
T2 = final temperature (316.15 K)
Rearranging the equation, we have:
V2 = (V1 * T2) / T1
Since the process is isobaric, the pressure remains constant, and we can use the ratio of the temperatures:
V2 = (V1 * 316.15 K) / 925.565 K
Simplifying further:
V2 = V1 * 0.341285
Therefore, the new volume of the container when the helium's temperature decreases to 43 ºC by an isobaric process is approximately 34.1285% of the initial volume, or 0.0344 m³ * 0.341285 ≈ 0.011760 m³.
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the maker of an automobile advertises that it takes 11 seconds to accelerate from 20 kilometers per hour to 80 kilometers per hour. assuming constant acceleration, compute the following.
The automobile takes a constant acceleration of 1.89 m/s² to accelerate from 20 km/h to 80 km/h.
Given that the automobile takes 11 seconds to accelerate from 20 km/h to 80 km/h, it means that the final velocity (v) is 80 km/h and the initial velocity (u) is 20 km/h. Converting km/h to m/s gives: u = 20 × (1000/3600) = 5.56 m/sv = 80 × (1000/3600) = 22.22 m/s.
The acceleration (a) of the automobile is constant throughout the acceleration process. Using the formula: v = u + at. We can find the acceleration (a) as follows: a = (v - u)/t = (22.22 - 5.56)/11 = 1.89 m/s². Therefore, the automobile takes a constant acceleration of 1.89 m/s² to accelerate from 20 km/h to 80 km/h.
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ip standing 2.4 mm in front of a small vertical mirror, you see the reflection of your belt buckle, which is 0.74 mm below your eyes.
The image of the belt buckle seen in the mirror is 0.01 times the height of the actual object, and it is inverted.
The image formed in a mirror depends on the position of the object from the mirror and its size and orientation with respect to the mirror. The distance of an object from a mirror is known as its image distance and is denoted by v, while the distance of an object from a mirror is known as its object distance and is denoted by u. The focal length of the mirror is denoted by f. In this case, the image distance v, object distance u, and the radius of curvature R are equal to the focal length f. The object distance u is 2.4 mm from the mirror, while the distance between the belt buckle and the eyes is 0.74 mm. Hence, the image distance v = f = R = 2.4 mm. The magnification of the image formed is given by the ratio of the height of the image to the height of the object. Since the belt buckle is below the eyes, the image is inverted and the height of the image is -0.74 mm. The height of the object is the distance between the eyes and the belt buckle, which is 74 mm. Hence, the magnification is given by:-0.74/74 = -0.01. The negative sign indicates that the image is inverted.
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Question 9 A 5.8 kg object hits a flat wall at a speed of 38 m/s and an angle of 35 °. The collision is perfectly elastic. Part A What is the change in momentum of the object? Enter your answer in un
The change in momentum of the 5.8 kg object, hitting a wall at 38 m/s and 35° angle in a perfectly elastic collision, is -358.58 kg⋅m/s.
To find the change in momentum of the object, we first need to determine the initial and final velocities of the object after the collision.
The initial velocity of the object can be broken down into its horizontal and vertical components.
The horizontal component is given by v₀x = v₀ * cos(θ), where v₀ is the initial speed of 38 m/s and θ is the angle of 35°. Thus, v₀x = 38 m/s * cos(35°) = 31.01 m/s.
The vertical component is given by v₀y = v₀ * sin(θ), where v₀ is the initial speed of 38 m/s and θ is the angle of 35°. Thus, v₀y = 38 m/s * sin(35°) = 21.84 m/s.
Since the collision with the wall is perfectly elastic, the magnitude of the velocity will remain the same after the collision. Therefore, the final horizontal velocity will be -v₀x and the final vertical velocity will be v₀y.
The change in momentum of the object can be calculated as Δp = m * (vf - vi), where m is the mass of the object and vf and vi are the final and initial velocities, respectively.
The initial momentum of the object is given by p₀ = m * v₀, and the final momentum is given by p = m * vf.
The change in momentum is then Δp = p - p₀ = m * vf - m * v₀.
Substituting the values, we have Δp = 5.8 kg * (-31.01 m/s) - 5.8 kg * (31.01 m/s) = -358.58 kg⋅m/s.
Therefore, the change in momentum of the object is -358.58 kg⋅m/s.
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An electric power station that operates at 20 kV and uses a 15:1 step-up ideal transformer is producing 310 MW (Mega-Watt) of power that is to be sent to a big city which is located 290 km away with only 1.5% loss. Each of the two wires are made of copper (resistivity = 1.68×10−8 Ω.m). What is the resistance of the TWO wires that are being used? What is the diameter of the wires? I want to check my answers. For resistance, I got 4.36 ohms and diameter is 5.34 cm.
The resistance of the two wires being used in the electric power station is 4.36 ohms and the diameter of the wire is 5.34 cm.
Voltage(V) = 20 kV; Power(P) = 310 MW; Distance(d) = 290 km; Resistance of copper(r) = 1.68 × 10−8 Ω.mLoss(L) = 1.5%; Step-up ratio(n) = 15:1
Formula used: Power(P) = (V²) / R, where R is resistance. R = (V²) / P; Resistance of the wire = 2 × R = 2 × [(V²) / P]; Resistance of wire = 2 × [(20,000)² / 310,000,000]; Resistance of wire = 2 × 1280; Resistance of wire = 2560 Ω.
Diameter of wire = [sqrt(4 × P × r × d) / (n² × pi × L)];
Diameter of wire = [sqrt(4 × 310,000,000 × 1.68 × 10−8 × 290,000) / (15² × 3.14 × 0.015)];
Diameter of wire = 5.35 × 10⁻⁴ m or 5.34 cm (approx).
Therefore, the resistance of the two wires being used in the electric power station is 4.36 ohms and the diameter of the wire is 5.34 cm.
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How fast must an object travel for its total energy to be 1% more than its rest energy?
How fast must an object travel for its total energy to 99% more than its rest energy?
An object must travel at a speed of 0.14 times the speed of light for its total energy to be 1% more than its rest energy. To have its total energy 99% more than its rest energy, the object must travel at a speed of 0.8654 times the speed of light.
To determine how fast must an object travel for its total energy to be 1% more than its rest energy and 99% more than its rest energy, we use the formula for relativistic kinetic energy K = (γ - 1)mc² where γ = 1/√(1 - v²/c²). The object must travel at a speed of 0.14 times the speed of light for its total energy to be 1% more than its rest energy.
Similarly, the object must travel at a speed of 0.8654 times the speed of light for its total energy to be 99% more than its rest energy. The speed at which an object must travel to achieve relativistic speeds becomes closer and closer to the speed of light as the object's total energy approaches infinity. At the speed of light, an object's total energy would be infinite.
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how many kilograms does the mass defect represent? A) 1.66 × 10-27 kg B) 2.20 × 10 -28 kg C) 3.0 × 108 kg D) 8.24 x 1025 kg
2.20 × 10 -28 kgkilograms does the mass defect represent . the correct option is B) .
The mass defect of an atom is the difference between the mass of its constituent particles and the actual mass of the atom. When an atom is formed, a small amount of mass is lost due to the conversion of mass into energy.
The answer to the given question is:B) 2.20 × 10 -28 kg.
The mass defect is the difference between the sum of the mass of its constituent particles and the actual mass of the atom.
Mass defect (Δm) = Zmp + Nmn - Mwhere, Z is the atomic number, N is the number of neutrons, mp and mn are the mass of protons and neutrons respectively, and M is the mass of the nucleus.
The mass defect represents the energy released when a nucleus is formed from its constituent particles and it is related to E = Δmc² by
Einstein’s famous equation where c is the speed of light and E is the energy released in the process.
Hence, the correct option is B) 2.20 × 10 -28 kg.
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if the length and diameter of a wire of circular cross section are both tripled, the resistance will be
a. tripled. b. unchanged. c. increased by a factor of 9. d. 1/3 of what it originally was
Since both the length and radius have been tripled; therefore the resistance is reduced to 1/3 of its original value The correct option is (d) 1/3 of what it originally was.
Explanation: The resistance of a wire is inversely proportional to its cross-sectional area A and directly proportional to its length L. Hence, the resistance R can be written as; R = ρL/A
Where, ρ is the resistivity of the material of the wire.From the given problem, the length and diameter of a wire of circular cross-section are both tripled. Therefore, the area will increase by a factor of 9.A=πr²If diameter is tripled, the radius is also tripled.r' = r x 3
When the radius is tripled, the area becomes: A' = π (3r)² = π 9r²So the new area will be 9 times the original area, which implies that the resistance will be 1/9 times the original resistance. Since both the length and radius have been tripled; therefore the resistance is reduced to 1/3 of its original value. Hence the correct option is (d) 1/3 of what it originally was.
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technician b says the voltage regulator controls the strength of the rotor’s magnetic field.
true or false
The statement "Technician B says the voltage regulator controls the strength of the rotor's magnetic field" is true.
A voltage regulator is an electrical regulator that changes the amount of voltage in an electrical circuit. Voltage regulators can be designed to handle varying amounts of input voltage and output voltage.
Technician B states that the voltage regulator is responsible for regulating the strength of the rotor's magnetic field. This is true because the rotor's magnetic field strength is determined by the voltage that is applied to it. If the voltage regulator fails, the magnetic field strength will decrease and the motor's performance will suffer.Therefore, technician B's statement is correct.
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Sound waves Bats find their way and search for food by emitting and detecting reflections of ultrasonic waves. Ultrasonic waves are sound waves with frequencies greater than can be heard by humans. A bat emits ultrasound at frequency fbe = 93.67 kHz while flying with a velocity = 12.00 î as it chases a moth that flies with velocity Vm = 6.00 î. S Part a) Calculation question. What frequency do he moth detect? (2.5 marks) Part b) Calculation question. What frequency does the bat detect in the returning echo from the moth?
Part a) The frequency that the moth detects is 86.33 kHz. Part b) The frequency that the bat detects in the returning echo from the moth is 100.01 kHz.
Ultrasonic waves are sound waves with frequencies greater than can be heard by humans. Bats find their way and search for food by emitting and detecting reflections of ultrasonic waves. A bat emits ultrasound at frequency f be = 93.67 kHz while flying with a velocity = 12.00 î as it chases a moth that flies with velocity V m = 6.00 î. Part a) The frequency that the moth detects can be calculated using the Doppler effect formula: f_ m = f_ be(1 + V_ b/V_ w) / (1 + V_ m/V_ w )f_ be = 93.67 kHz V_ b = 12 î V_ w = 343 m/s V_ m = 6 î Putting all the values in the above formula: f_ m = 86.33 kHz The frequency that the moth detects is 86.33 kHz. Part b) The frequency that the bat detects in the returning echo from the moth can be calculated using the Doppler effect formula: f_ b = f_ be(1 + V_ b/V_ w) / (1 - V_ m/V_ w)f_ be = 93.67 kHz V_ b = 12 î V_ w = 343 m/s V_ m = 6 î Putting all the values in the above formula: f_ b = 100.01 kHz The frequency that the bat detects in the returning echo from the moth is 100.01 kHz.
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1) 1.4kg of gold at 300K comes in thermal contact with 2.3kg copper at 400K. The specific heats of Au and Cu are 126 J/kg-K and 386 J/kg-K respectively. What equilibrium temperature do they reach? Tfinal= K Submit 2) Using the fact that for no changes in volume, AS = S 4dU and C = dy, compute how much the entropy of the copper block changes. Sfinal-Sinitial J/K Submit 3) How much does the total entropy of the Au+Cu change? J/K
1 - The equilibrium temperature reached by the gold and copper can be determined using the principle of energy conservation.
The heat gained by one object is equal to the heat lost by the other object. The equation for heat transfer is:
m_gold * c_gold * (T_final - T_gold_initial) = -m_copper * c_copper * (T_final - T_copper_initial)
Substituting the given values, we can solve for the equilibrium temperature (T_final).
2 - The change in entropy (ΔS) of the copper block can be calculated using the relationship ΔS = S_final - S_initial = C * ln(T_final / T_initial), where C is the heat capacity at constant volume. Since there is no change in volume, we have AS = S * 4dU, where dU represents the change in internal energy. For no change in volume, dU is zero. Therefore, the entropy change of the copper block is zero (ΔS = 0 J/K).
3 - The total change in entropy (ΔS_total) of the gold and copper system can be calculated by summing the individual entropy changes:
ΔS_total = ΔS_gold + ΔS_copper
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Find the coordinate vector [X]B of the vector X relative to the basis B.
b1 =\begin{bmatrix} 1\\ 1 \end{bmatrix}
b2 =\begin{bmatrix} 1\\ -1\end{bmatrix}
x =3
-5
B = {b1,b2}
Hence, the coordinate vector [X]B of the vector X relative to the basis B is [-1, 4].
The coordinate vector is a vector that has coordinates equal to the components of a given vector along each basis vector.
A basis is defined as a set of linearly independent vectors that can be used to span a subspace in linear algebra. Given the values of b1 and b2 as well as x, the coordinate vector can be calculated as follows:
[X]B = [a1, a2]X
= 3 -5B
= {b1, b2}b1
= [1 1]b2
= [1 -1]
In order to calculate [X]B, we must first find a1 and a2:
X = a1b1 + a2b2
where a1 and a2 are scalars.
Here, we can solve for a1 and a2 using the augmented matrix (B|X) as follows:
[1 1 | 3] [1 -1 | -5]
Then we need to perform row operations until the matrix is in echelon form as shown below. We subtract the first row from the second row to obtain -2b2 = -8. [1 1 | 3] [0 -2 | -8]
The row operation is performed by subtracting 1 times the first row from the second row.
Next, we divide the second row by -2 to obtain b2 as shown below. [1 1 | 3] [0 1 | 4]
Now we subtract 1 times the second row from the first row to obtain b1. [1 0 | -1] [0 1 | 4]
So, a1 = -1 and a2 = 4.
Thus, [X]B = [-1 4].
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how much work must you do to push a 11.0 kg block of steel across a steel table ( μk = 0.60) at a steady speed of 1.20 m/s for 4.00 s ?
To calculate the work done to push the block across the table, we need to consider the force required to overcome friction and maintain a steady speed.
The force of kinetic friction can be calculated using the equation: f_k = μ_k * N, where μ_k is the coefficient of kinetic friction and N is the normal force. The normal force can be determined by considering the weight of the block, which is given by: W = m * g where m is the mass of the block and g is the acceleration due to gravity. The work done to overcome friction is given by: Work = force * distance. In this case, the distance is the product of the steady speed and the time: distance = speed * time. Let's calculate the work done: First, find the normal force: N = m * g = 11.0 kg * 9.8 m/s^2 = 107.8 N. Next, calculate the force of kinetic friction: f_k = μ_k * N = 0.60 * 107.8 N = 64.68 N Now, calculate the distance traveled: distance = speed * time = 1.20 m/s * 4.00 s = 4.80 m Finally, calculate the work done: Work = force * distance = 64.68 N * 4.80 m = 310.464 J. Therefore, you must do approximately 310.464 Joules of work to push the block across the table.
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*by hand, if possible*
Question 3 An experiment has been conducted to test the failure of aluminium under repeated alternating stress at 210000 psi and 18 cycles per second. The numbers of cycles to failure of n = 70 alumin
The experiment on failure of aluminium under repeated alternating stress shows that the mean number of cycles to failure of n = 70 aluminum specimens was 11400 cycles.
The experiment aimed to test the failure of aluminum under repeated alternating stress at 210000 psi and 18 cycles per second. The experiment was performed on 70 aluminium specimens, and it was found that the mean number of cycles to failure was 11400 cycles. The experiment shows that the number of cycles to failure is affected by various factors, including the material properties and the stress level.The experiment findings could be used to determine the suitability of aluminium in applications where it would be subjected to repeated alternating stress. The experiment could be repeated under different stress levels to determine the material's performance under various stress levels. The data collected in the experiment could be used to design materials that are better suited for applications that involve repeated alternating stress.
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what is the angular magnification of a telescope that has a 100 cm focal length objective and a 2.50 cm focal length eyepiece?
The angular magnification of the telescope is -40.
How to calculate angular magnification?To calculate the angular magnification (M) of a telescope, you can use the formula:
M = (-) (focal length of the objective) / (focal length of the eyepiece)
Given that the focal length of the objective (f_obj) is 100 cm and the focal length of the eyepiece (f_eye) is 2.50 cm, we can substitute these values into the formula:
M = (-) (100 cm) / (2.50 cm)
M = -40
The angular magnification of the telescope is -40. Note that the negative sign indicates that the image formed is inverted.
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does the distribution of fatal injuries for riders not wearing a helmet follow the distribution for all riders? use level of significance. what are the null and alternative hypotheses?
The null hypothesis states that the distribution of fatal injuries for riders not wearing a helmet follows the distribution for all riders, while the alternative hypothesis states that it does not follow the distribution for all riders. We can use the level of significance, which is typically set at 0.05, to test this hypothesis.
In hypothesis testing, the null hypothesis is the hypothesis that is being tested, while the alternative hypothesis is the hypothesis that is being considered if the null hypothesis is rejected. The null hypothesis in this case is that the distribution of fatal injuries for riders not wearing a helmet follows the distribution for all riders, while the alternative hypothesis is that it does not follow the distribution for all riders. To test this hypothesis, we can use the level of significance, which is typically set at 0.05. This means that we would reject the null hypothesis if the probability of getting the observed result under the null hypothesis is less than 0.05.
Therefore, the null hypothesis states that the distribution of fatal injuries for riders not wearing a helmet follows the distribution for all riders, while the alternative hypothesis states that it does not follow the distribution for all riders. We can use the level of significance, which is typically set at 0.05, to test this hypothesis.
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Suppose an isolated magnetic North pole is discovered and dropped through this setup (magnet through a coil experiment). Describe the
voltage pattern by giving a crude sketch of the voltage as a function of time.
During time interval t2, the voltage is decreasing from the maximum value to 0, as the magnetic flux linkage with the coil is reduced.
When an isolated magnetic North pole is discovered and dropped through the set-up (magnet through a coil experiment), there is a change in magnetic flux linkage within the coil. Therefore, the induced electromotive force (EMF) will cause a voltage pattern to form.The Faraday's Law of Electromagnetic Induction states that when there is a change in magnetic flux linkage within a coil, an EMF is induced in the coil.
In this scenario, the magnetic flux linkage increases as the magnetic North pole enters the coil and decreases when it exits the coil, which will result in a change in the direction of the induced EMF within the coil.The voltage pattern obtained from the experiment depends on the rate at which the magnetic North pole is dropped through the set-up and the number of turns of the coil.
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Explain briefly how Karl Popper applies his concept "Verisimilitude to describe the *Progress of science'. (ii) Explain briefly the views of Karl Popper regarding ‘Ad-hoc modification of theories. (iii) How does Popper apply his above-mentioned views regarding the ad-hoc modifications of theories to show that Karl Marx's theory on the evolution of societies is pseudo- science? (iv) What is the main draw-back of Popper’s method of falsification?
(i) Verisimilitude is a concept developed by Karl Popper, according to which scientific theories should be judged not by whether they are true or false, but by how close they come to the truth. It is the ability of a theory to get closer to the truth, despite being unable to prove it.
Popper believed that scientific theories could never be proven to be true, only falsified, and that the scientific process involved testing theories to see if they could be falsified. This means that scientific theories can never be certain, but they can be highly probable.(ii) Popper argued that theories that are modified to accommodate evidence against them are not scientific, but ad hoc. Ad hoc modifications are made to theories to fit the evidence, rather than the evidence fitting the theory. This can lead to theories becoming too complex and difficult to test, and eventually being abandoned.(iii) Popper applied his views on ad hoc modifications to Marx's theory of the evolution of societies, arguing that the theory was not scientific because it was unfalsifiable and prone to ad hoc modifications. Marx's theory of social evolution predicted that capitalism would inevitably lead to socialism, but when this failed to happen, Marxists made ad hoc modifications to the theory to explain the failure. This made the theory unfalsifiable and therefore unscientific, according to Popper.(iv) The main drawback of Popper's method of falsification is that it is difficult to apply in practice. The process of falsification requires scientists to actively seek out evidence that contradicts their theories, which can be difficult to do when they are emotionally invested in their work. Additionally, it can be difficult to know when a theory has been falsified, as there may always be some evidence that can be explained away. This means that it can be hard to know when to abandon a theory and start again.
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Question 21 In a closed system, what never changes when two or more objects collide? The kinetic energy of each object The total momentum of the system 4 The total kinetic energy of the system none of
The total momentum of the system never changes when two or more objects collide. The correct option is B.
When two or more objects collide in a closed system, the total momentum of the system remains constant. Momentum is defined as the product of an object's mass and its velocity, given by the equation p = mv, where p is the momentum, m is the mass, and v is the velocity.
In a closed system, the total momentum before the collision is equal to the total momentum after the collision, provided that no external forces act on the system. This principle is known as the law of conservation of momentum.
Kinetic energy, on the other hand, is not conserved during collisions. Kinetic energy is given by the equation KE = (1/2)mv², where KE is the kinetic energy, m is the mass, and v is the velocity. During a collision, some of the kinetic energy may be converted into other forms, such as heat, sound, or deformation.
Therefore, while the kinetic energy of each object and the total kinetic energy of the system may change during a collision, the total momentum of the system remains constant. Hence, the correct answer is B, that the total momentum of the system never changes when two or more objects collide.
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A 25 kg box of books is dropped on the floor from a height of 1.1 m and comes to rest. What impulse did the floor exert on the box in kg m/s?
The impulse experienced by the box is 103.5 kg m/s. The floor exerts an impulse of 103.5 kg m/s on the box in the upward direction.
The given problem is related to the concept of impulse. Impulse is the product of force and time taken for which the force is acting on the object. Impulse is defined by the equation I = FΔt .
The impulse experienced by the box can be determined as follows:
Given, Mass of the box,
m = 25 kg
Height from which the box was dropped, h = 1.1 m.
The velocity of the box before it hits the ground can be calculated using the equation:
v = \sqrt{2gh}
where g is the acceleration due to gravity, which is 9.8 m/s²
v = \sqrt{2gh}
= \sqrt{(2 × 9.8 m/s² × 1.1 m)}
= 4.14 m/s.
When the box hits the ground, its velocity becomes zero and comes to rest.The change in velocity of the box, Δv = final velocity - initial velocity
= 0 - 4.14 m/s
= -4.14 m/s.
The time taken by the box to come to rest, Δt = ?
We can calculate the time taken by the box to come to rest using the equation of motion:Δv = aΔt where a is the acceleration of the box is
g = 9.8 m/s²
Δt = Δv/a
= -4.14/9.8 s
= -0.422 s (negative sign indicates the direction).
Now, we can calculate the impulse experienced by the box using the equation: I = FΔt
where F is the force experienced by the box.
I = mΔvI
= 25 kg × (-4.14 m/s)
I = -103.5 kg m/s
The impulse experienced by the box can be calculated by finding the change in momentum of the box. Since the box comes to rest, the final velocity of the box is zero. Therefore, the impulse is equal to the initial momentum of the box.
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