To find the electric field components E(x) and E(y) at any point, we need to take the negative gradient of the potential function V.
Let's first find the partial derivative of potential function V with respect to x:
∂V/∂x = a(3x² - y²)/(x² + y²)^(5/2) - b x/(x² + y²)^(3/2)
Similarly, the partial derivative of V with respect to y is:
∂V/∂y = -2a xy/(x² + y²)^(5/2) - b y/(x² + y²)^(3/2)
Now, we can find the components of the electric field:
Ex = -∂V/∂x = -a(3x² - y²)/(x² + y²)^(5/2) + b x/(x² + y²)^(3/2)
Ey = -∂V/∂y = 2a xy/(x² + y²)^(5/2) + b y/(x² + y²)^(3/2)
Therefore, the components of the electric field at any point (x,y) are:
Ex = -a(3x² - y²)/(x² + y²)^(5/2) + b x/(x² + y²)^(3/2)
Ey = 2a xy/(x² + y²)^(5/2) + b y/(x² + y²)^(3/2)
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The diagram below shows snapshots of an
oscillator at different times. What is the amplitude
of the oscillation?
C
A
B
D
t=0.0 s t=0.30 s t=0.45 s t=0.90 s
+0.10 m.
www.
0
-0.10 m
(Unit = m)
E
t=1.35 s
www
F
t=1.80 s
0
The amplitude of the oscillation is +0.10 m, as shown in snapshots A and E.
Oscillation refers to a repetitive back-and-forth or up-and-down motion of an object or system about an equilibrium position. This motion can be periodic or non-periodic.
The amplitude of an oscillation is the maximum displacement of the object or system from its equilibrium position during one cycle of motion. It is the distance between the equilibrium position and either the crest or trough of the wave. The amplitude determines the energy of the oscillation, with larger amplitudes corresponding to greater energy. In the context of waves, amplitude can also refer to the maximum displacement of the medium from its rest position.
Therefore, The amplitude of the oscillation is +0.10 m, as shown in snapshots A and E.
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1. A body of mass 200 g rotates from rest to 3 rads/s in 1.5 s on a path whose radius of gyration is 50 cm. The torque is .... A. 0.05 B. 1.50 C. 0.075 D. 0.10
lodine trichloride, IC13, is made by reacting iodine with chlorine.
12(s) + Cl2(g) → 2IC(s); AH = +14kJ mol¹
ICl(s) + Cl2(g) → IC¹(s); AH = −88 kJ mol-¹
By using the data above, what is the enthalpy change of the formation for solid iodine trichloride?
The enthalpy change of the formation for solid iodine trichloride is -74 kJ/mol. This indicates that the formation of solid iodine trichloride is exothermic
The enthalpy change of the formation for solid iodine trichloride (ICl3) can be calculated using Hess's law, which states that the total enthalpy change of a chemical reaction is independent of the route by which the reaction occurs.
First, we need to write the balanced chemical equation for the formation of solid ICl3 from its elements:
I2(s) + 3Cl2(g) → 2ICl3(s)
According to Hess's law, the enthalpy change of this reaction is equal to the sum of the enthalpy changes of the following two reactions:
I2(s) + Cl2(g) → 2ICl(g) ΔH1
ICl(g) + Cl2(g) → ICl3(s) ΔH2
where ΔH1 is the enthalpy change for the reaction between iodine and chlorine to form gaseous iodine trichloride, and ΔH2 is the enthalpy change for the condensation of gaseous iodine trichloride to form solid iodine trichloride.
The enthalpy change for the first reaction is given as ΔH1 = +14 kJ/mol, and the enthalpy change for the second reaction is given as ΔH2 = -88 kJ/mol. Therefore, the enthalpy change of the formation for solid iodine trichloride can be calculated as:
ΔHf°(ICl3,s) = ΔH1 + ΔH2
= (+14 kJ/mol) + (-88 kJ/mol)
= -74 kJ/mol
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Define one standard kilogram
The standard kilogram is a physical object which weighs exactly 1 kilogram and is used as the primary reference for the kilogram unit of mass.
What is standard kilogram?The standard kilogram, also known as the international prototype of the kilogram (IPK), is a physical artifact. It is kept at the international bureau of weights and measures and is used as the primary standard for the kilogram unit of mass.
The international prototype of the kilogram (IPK), is a cylindrical shape with a height of 39 mm and a diameter of 39 mm, and it has a mass of exactly 1 kilogram (1000 grams).
Thus, the standard kilogram is a physical object which weighs exactly 1 kilogram and is used as the primary reference for the kilogram unit of mass.
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ver-P = W
(Remember these are metric units!)
Work-W = Fd
I. Solve and show your work
a. If a man carries a 44 pound box of books up a flight of stairs and he has a mass of 100
kg himself. How much work is done if the distance up is 10 meters?
*(remember he must lift himself and the box up the stairs)
b. How much power is necessary to do this in only I minute?
A. The work done, given that the distance is 10 meters is 11756.08 Joules
B. The power necessary to do the work is 195.93 W
A. How do i determine the work done?First, we shall convert 44 pound to Kg. Details below:
1 pound = 0.4536 Kg
Therefore,
44 pound = 44 × 0.4536
44 pound = 19.96 Kg
Finally, we shall determine the work done. Details below:
Mass of book = 19.96 KgMass of man = 100 KgTotal mass (m) = 19.96 + 100 = 119.96 KgAcceleration due to gravity (g) = 9.8 m/s² Force (F) = mg = 119.96 × 9.8 = 1175.608 NDistance (d) = 10 metersWorkdone (Wd) =?Work done (Wd) = force (F) × distance (d)
Work done (Wd) = 1175.608 × 10
Work done (Wd) = 11756.08 Joules
B. How do i determine the power?The power necessary to do the work can be obtain as follow:
Work done (Wd) = 11756.08 JTime (t) = 1 minute = 1 × 60 = 60 secondsPower (P) = ?Power is defined according to the following formula:
Power = Work done / time
P = Wd / t
P = 11756.08 / 60
Power = 195.93 W
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The unit of power is the
a. Joules
b. m/s
C. Watts
d. Newtons
Answer:
It could be both Joules or Watts, Watts for electrical measurements and Joules for power measuremnets.
Hope this helps :)
Pls brainliest...
1. Multiple light bulbs are connected in series across a 120.0 V
source of emf. The current in the circuit is 1.25 A. If each light
bulb has a resistance of 3.00 £2, how many light bulbs are in
the circuit?
2. If the resistance of bulb A is 6 2, the resistance of bulb B is
18 02, and the equivalence resistance of the circuit is 1202,
what is the resistance of bulb C?
1) Since each bulb has a resistance of 3.00 Ω, we can calculate the number of bulbs: n = R/R_bulb = 96 Ω/3.00 Ω = 32 bulbs. There are 32 light bulbs in the circuit.
2) The total resistance is equal to the sum of individual resistances: R_C = 120 Ω - 6 Ω - 18 Ω = 96 Ω. The resistance of bulb C is 96 Ω.
In a series circuit, the total resistance is equal to the sum of individual resistances. Using Ohm's Law, we can find the total resistance:
R = V/I = 120.0 V/1.25 A = 96 Ω
Since each bulb has a resistance of 3.00 Ω, we can calculate the number of bulbs:
n = R/R_bulb = 96 Ω/3.00 Ω = 32 bulbs
Therefore, there are 32 light bulbs in the circuit.
In a series circuit, the total resistance is equal to the sum of individual resistances:
R_eq = R_A + R_B + R_C
Substituting the given values:
120 Ω = 6 Ω + 18 Ω + R_C
Solving for R_C:
R_C = 120 Ω - 6 Ω - 18 Ω = 96 Ω
Therefore, the resistance of bulb C is 96 Ω.
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A car manufacturer wants to change its car's design to increase the car's acceleration. Which changes should the
engineers consider making to the design?
O increase the force that the engine provides
O decrease the force that the engine provides
O increase the mass of the car
O decrease the mass of the car
O increase the top velocity the car can travel
decrease the top velocity the car can travel
To increase a car's acceleration, the engineers should consider decreasing the car's mass and/or increasing the force that the engine provides. Therefore, options A and D are the correct answers.
Acceleration is directly proportional to the net force acting on an object and inversely proportional to its mass. This means that a smaller mass or a larger force will result in a greater acceleration. Therefore, reducing the mass of the car will require less force to achieve the same acceleration, or the same force will result in a greater acceleration.
To decrease the mass of the car, the engineers could consider using lighter materials for the car's body and frame or removing unnecessary components. On the other hand, to increase the force that the engine provides, the engineers could consider upgrading the engine or increasing the fuel intake.
Option B, which suggests decreasing the force that the engine provides, would have the opposite effect and result in a slower acceleration. Option C, which suggests increasing the mass of the car, would also have the opposite effect and require more force to achieve the same acceleration.
Option E, which suggests increasing the top velocity the car can travel, is not directly related to acceleration. Top velocity refers to the maximum speed that a car can reach, whereas acceleration refers to the rate of change of velocity. While increasing the car's top velocity may indirectly affect acceleration, it is not a direct solution to increasing acceleration.
Option A and D.
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Question 4 of 20
Planets A and B have the same size, mass, and direction of travel, but planet
A is traveling through space at half the speed of planet B. Which statement
correctly explains the weight you would experience on each planet?
OA. You would weigh the same on both planets because their masses
and the distance to their centers of gravity are the same.
B. You would weigh the same on both planets because your mass
would adjust depending on the planet's speed.
OC. You would weigh more on planet B because it is traveling twice as
fast as planet A.
OD. You would weigh less on planet B because it is traveling twice as
fast as planet A.
SUBMIT
On two planets with the same size, mass, and direction of travel, your weight will be the same on both planets. Option A.
Weight of objects on different planetsThe weight of an object depends on its mass and the strength of the gravitational force acting on it.
Since planets A and B have the same size and mass, their gravitational forces will be the same. Therefore, an object placed on either planet will experience the same gravitational force and hence the same weight.
The speed of the planets has no effect on the weight of an object on them. Therefore, options (B), (C), and (D) are incorrect.
In other words, you would weigh the same on both planets because their masses and the distance to their centers of gravity are the same.
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which type of electromagnetic wave has more energy than ultraviolet waves?
A Visible light
B Infrared
C Microwaves
D X-rays
Answer:
D. X-rays have more energy than ultraviolet waves.
Calculate the height (in m) of a cliff if it takes 2.37 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.03 m/s. (Enter a number.)
(b)
How long (in s) would it take to reach the ground if it is thrown straight down with the same speed? (Enter a number.)
A) The height of the cliff is approximately 18.93 meters if it takes 2.37 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.03 m/s.
B) It would take approximately 1.63 seconds for the rock to hit the ground if it is thrown straight down with the same speed.
A) To calculate the height of the cliff, we can use the kinematic equation:
h = vi*t + (1/2)at^2
where h is the height of the cliff, vi is the initial velocity, t is the time taken, and a is the acceleration due to gravity (-9.8 m/s^2).
Substituting the given values, we get:
h = 8.032.37 + (1/2)(-9.8)*(2.37)^2
h = 18.93 meters
Therefore, the height of the cliff is approximately 18.93 meters.
B) To determine how long it would take for the rock to reach the ground if it is thrown straight down with the same speed, we can use the same kinematic equation, but with a negative initial velocity:
h = vi*t + (1/2)at^2
where vi is now -8.03 m/s.
Substituting the values, we get:
0 = -8.03t + (1/2)(-9.8)*t^2
Solving for t, we get:
t = 1.63 seconds
Therefore, it would take approximately 1.63 seconds for the rock to hit the ground if it is thrown straight down with the same speed.
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Mr. Bateman creates a standing wave in the front of the classroom with the spring. S nodes form. The distance from Mr. Bateman to the cabinet is 6m. If a student times the spring moving back and forth and gets 0.2s for one cycle of the spring, how fast are the
waves moving?
Answer:
The speed of a wave is equal to the wavelength divided by the period. The wavelength is the distance between two consecutive nodes, and the period is the time it takes for one complete cycle of the wave.
In this case, the wavelength is 6 m and the period is 0.2 s. Therefore, the speed of the wave is 30 m/s.
The answer is 30 m/s.
Explanation:
Two tuning forks with frequencies of 256 Hz and 512 Hz are struck. Which of the sounds will move faster through the air?
Answer:
Two tuning forks with frequencies of 256 Hz and 512 Hz are struck. Which of the sounds will move faster through the air? Neither, the speed of sound is constant in air.
A person standing on the roof of a building drops a 0.125 Kg ball on the ground. A
child on eight floor saw the ball passing with a speed of 33.1 m/s. The first floor of the building
is 12.0 m high and each successive floor is 8.00 m high. Determine the total numbers of floors
in the building. How fast was the ball falling just before it hit the ground? What was its kinetic
energy just before it hit the ground?
Answer:
V = a t velocity after time t
t = 33.1 / 9.80 = 3.38 sec (time ball had been falling)
S = 1/2 a t^2 = 55.9 m
So the ball had been falling for 7 * 8 = 56 m
The child was 7 floors from the top
Since he was on the eight floor the floors below him were
7 * 8 + 12 = 68 m total floors below child
68 + 56 = 124 m total height of building
Total floors in building = 7 + 7 + 1 = 15 floors
PE at top = KE at bottom
KE = m g h = .125 * 9.80 * 124 = 152 Joules
Pretest: Unit 2
Question 17 of 25
Which of the following best defines displacement?
OA. The total length of a path traveled, regardless of th
travel
B. How far something moves in a given direction in a
The displacement is defined as the shortest distance between the starting and ending point along with the direction. Thus, option D is correct.
The displacement is defined as the shortest distance between the starting and ending point. The displacement is the vector quantity. It is also defined as the distance traveled by the object along with a particular direction. The distance is the scalar quantity and the displacement is the vector quantity. The SI unit of distance is a meter. The rate of change of displacement gives rise to velocity and the rate of distance gives rise to distance.
From, the given displacement is defined as the shortest length and direction from a starting and ending point. Thus, the correct option is D.
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The greater the power of an electrical appliance, the more quickly it takes energy from the mains.
True or false give reason for falsee
After analysing the given data we conclude that the given statement is considered true.
The greater the power rating in the electrical appliance, the larger energy is applied every second. And hence longer the usage time, the more electrical energy is consumed.
A process through which measures the maximum amount of power that can be applied with a specific tool or device is known as power rating . It is placed in a series to keep the user safe and apply prevention of the tool or device from becoming damaged.
The power rating generally results from a combination of the maximum power requirements of the electrical load on the consumption side during discharging and the most frequently appearing excess power on the input power during charging.
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what is the similaries between parallel and series circuits
Answer:
same power source
can have more than 1 light bulb in a circuit
requires a source of energy
Explanation:
The diagram shows two circuits.
Which statement correctly describes each circuit?
A. The bulbs in both circuits are connected in series.
B. The bulbs in Circuit 1 are connected in parallel, and the bulbs in Circuit 2 are connected in series.
C. The bulbs in both circuits are connected in parallel.
D. The bulbs in Circuit 1 are connected in series, and the bulbs in Circuit 2 are connected in parallel.
Answer:
(D is correct
the temperature rise a motor when operating for 25 minutes on full load is 25 degrees Celsius and becomes 40degree when the motor operates for another 25 minutes on same load determine heating time constant and steady state temperature.
The heating time constant is 13 seconds and the steady state temperature is 38°C.
How to determine time and temperatures?To find the heating time constant and steady state temperature, use the formula:
ΔT = P × R × (1 - e^(-t/τ))
where ΔT = temperature rise, P = power, R = thermal resistance, t = time, τ = heating time constant, and e = natural logarithmic constant.
Let's use the given information to solve for τ:
ΔT1 = 25°C (for the first 25 minutes)
ΔT2 = 40°C (for the second 25 minutes)
t = 25 + 25 = 50 minutes
The temperature rise over the entire 50 minutes is:
ΔT = ΔT1 + ΔT2 = 25°C + 40°C = 65°C
The average power can be calculated as:
P = ΔT / (t × R)
Assume that the power output is the rated power of the motor. Let's assume that the rated power is 100 W.
Then, solve for R:
R = ΔT / (t × P) = 65°C / (50 min × 100 W) = 0.13 °C/W
Now, solve for the heating time constant:
τ = R × C
where C = thermal capacitance. Value of C is unknown, but make an assumption that the thermal time constant is on the order of minutes to hours. Let's assume that C = 100 J/°C.
Then, τ = 0.13 °C/W × 100 J/°C = 13 seconds
Finally, solve for the steady state temperature:
ΔT = P × R
T_ss = T_amb + ΔT = 25°C + 100 W × 0.13°C/W = 38°C
Therefore, the heating time constant is 13 seconds and the steady state temperature is 38°C.
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Using atleast 4 sentences. Please share three facts you have learned this year in Physical Education and how you will adapt what you have learned to your everyday life.
Three facts I have learned this year in Physical Education are:
a) The importance of stretching before and after exercising.
b) The benefits of cardiovascular exercise.
c) The importance of staying hydrated during exercise.
Firstly, I have learned the importance of stretching before and after exercising. Stretching helps prevent injury and improves flexibility. I will make sure to incorporate stretching into my daily routine, whether it's through a short stretching session in the morning or by taking a few minutes to stretch before and after a workout.
Secondly, I have learned the benefits of cardiovascular exercise. Cardiovascular exercise, such as running or cycling, helps improve heart health and endurance. I will try to incorporate more cardiovascular exercise into my daily routine, such as going for a run or bike ride after work.
Lastly, I have learned the importance of staying hydrated during exercise. Dehydration can lead to fatigue and muscle cramps, so it's important to drink plenty of water before, during, and after exercise. I will make sure to carry a water bottle with me throughout the day and refill it regularly to ensure that I am staying hydrated.
In summary, by incorporating stretching, cardiovascular exercise, and staying hydrated into my daily routine, I hope to improve my overall physical health and well-being.
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is a thermopoteota unicellular or multicellur
Answer:
unicellular
Explanation:
it's a archea so its unicellular
What is the greatest average speed of blood flow at 37∘C in an artery of radius 2.25 mm if the flow is to remain laminar? Take the density of blood to be 1025 kg/m3,
and the viscosity to be 2.084×10^−3 Pa·s.
The Hagen-Poiseuille equation may be used to determine the blood flow rate that is maximum on average at 37°C in an artery with a radius of 2.25 mm. According to this equation, the volumetric flow rate of a laminar flow is equal to the fourth-power product of the vessel's radius (r) and the pressure difference (P) divided by the fluid's viscosity ().
It also takes into account the length (L) of the vessel. The highest average blood flow rate in an artery with a radius of 2.25 mm may be computed using the information provided as follows: Q = (2.25^4 * ΔP) / (2.084*10^-3 * L) Q = (2.25^4 * ΔP) / (2.084*10^-3 * L) Q = (2.25^4 * ΔP) / (2.084*10^-3 * L) Q = (2.25^4 * ΔP) / (2.084*10^-3 * L)
Consequently, the highest average blood flow rate at Therefore, the greatest average speed of blood flow at 37∘C in an artery of radius 2.25 mm is equal to (2.25^4 * ΔP) / (2.084*10^-3 * L).
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Find the equivalent capacitance of the
following combination as shown in figure. C₁
In which C₁ = C₂2 = C3 = C4 = C5 = 100 μF
=C4
C3
C₂
The effective capacitance of the following combination with capacitors C₁, C₂, C₃, C₄, C₅ = 100μF is 350 μF.
Capacitors are the energy storage device in the form of electrical energy. The amount of charge (Q) stored in the capacitors is linearly proportional to the applied Voltage (V). Capacitance equals the ratio of charge and voltage. The unit of capacitance is Farad (F). Capacitors are connected in series and parallel connections. In series connections, the capacitance is 1/C(eff) = 1/C₁ + 1/C₂. In parallel connections, the effective capacitance C(eff) = C₁ + C₂.
From the figure,
The capacitances, C₁, C₄, C₂ are parallelly connected whereas C₃ and C₅ are in series connections.
C(eff) = C₁ + C₂ + C₄ = 100 + 100 + 100 = 300 μF
The capacitance C₅ and C₃ are in series connections, then
1/C(eff) = 1/C₅ + 1/C₃ = 1/100 + 1/100 = 2/100 = 1/50
C(eff) = 50 μF
The effective capacitance = 300 + 50 = 350 μF.
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A pendulum takes 43.6 seconds to complete 10 full swings. What is the length of the pendulum?
4.72 m
5.51 m
6.80 m
9.44 m
The length of the pendulum can be calculated using the formula:
T = 2π√(L/g)
Where T is the period of the pendulum, L is the length of the pendulum, and g is the acceleration due to gravity.
We can rearrange this formula to solve for L:
L = gT^2 / (4π^2)
Given that the pendulum takes 43.6 seconds to complete 10 full swings, the period of the pendulum is:
T = (43.6 seconds) / (10 swings) = 4.36 seconds/swing
The acceleration due to gravity is approximately 9.8 m/s^2.
Substituting these values into the formula, we get:
L = (9.8 m/s^2) × (4.36 s/swing)^2 / (4π^2) = 5.51 m
Therefore, the length of the pendulum is 5.51 m.
Answer: L = 4.72 m
Explanation:
t=43.6 seconds, n=10
T= t/n = time period
= 43.6s/10 = 4.36s
t = 2pie square root of L/g
L= length
L = t^2/4pie^2g
4.36^2 x 9.8/4(22/7)^2
L = 4.791 m
L = 4.72 m
of
30. A person with a low prejudice profile is likely to reject negative stereotypes
a. Ignore and avoid the conversation.
●b. But also list qualifiers about the ethnic group.
●c. But also list negatives about the ethnic group.
●d. And also list positives about the ethnic group.
A person with a low prejudice profile is likely to reject negative stereotypes. Option A.
Low prejudice profileA person with a low prejudice profile is likely to reject negative stereotypes and not make assumptions about individuals based on their group membership.
This is because a person with a low prejudice profile is more likely to have a positive attitude toward diverse groups and recognize that individuals within a group can vary widely in their abilities, attitudes, and behaviors.
By listing positives about the ethnic group, this person can acknowledge the group's strengths and challenge any negative stereotypes that may exist.
Options (a), (b), and (c) do not reflect a low prejudice profile and may perpetuate negative stereotypes or avoid the conversation altogether.
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Weston's friends and family cheered him on during his road bike race, which
kept Weston going even when he felt he couldn't go any farther. This is an
example of which of the following?
A. Physiological states
B. Verbal persuasion
C. Performance accomplishments
OD. Vicarious experience
SUBMIT
The given example is a kind of verbal persuasion. So, option B.
Verbal persuasion is defined as inspiring and motivating others through positive words. When athletes are undertaking competitions, it is done by the people those who are not now participating and are being supportive, motivating, and energizing one another.
The verbal persuasion factor highlights the beneficial effects that words may have on someone's sense of self-efficacy.
In order to overcome self-doubt and concentrate on achieving the goal at hand their best effort, people need verbal persuasion from others.
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an athlete runs some distance before taking a long jump, why?
Answer:
To gain momentum before the jump is made
The winter sport of curling involves sliding a large granite stone on ice with the objective of placing it closest to the center of the ring. The curler causes the path of the stone to curve by giving it an initial circular rotation. Sweepers use brooms to sweep the path in front of the stone. How does the motion of the sweepers relate to the conservation of angular momentum?
The sweepers minimize friction between the stone and ice which helps maintain the angular momentum.
The sweepers motion creates circular air motion which adds to the angular momentum.
The sweepers motion adds torque to the stone's angular momentum.
The sweepers create circular patterns in the ice to increase the angular momentum.
Answer:
The sweepers motion adds torque to the stone's angular momentum.
Explanation:
This is due to angular momentum law.
Figure below shows the total acceleration and velocity of a particle moving clockwise in a circle of radius 2.5 m at a given instant of time. At this instant, find (a) the radial acceleration (b) the speed of the particle (c) its tangential acceleration.
At the given instant, the radial acceleration of the particle moving clockwise in a circle of radius 2.5 m is 21.650 m/s², its speed is 11.625 m/s, and its tangential acceleration is 12.5 m/s².
In circular motion, there are three important quantities: radial acceleration, tangential acceleration, and speed.
At the given instant, the radial acceleration (ar) can be calculated as:
ar = a cosθ
ar = 25 m/s² × cos30°
ar = 25 × 2/3
ar = 21.650 m/s²
The speed of the particle (V) can be calculated as:
V = r ×θ'
θ' = sqrt(rar/r)
θ' = sqrt(2.5×21.650/2.5)
θ' = sqrt(21.65)
θ' = 4.65 rad/s
V = r × θ'
V = 2.5 × 4.65
V = 11.625 m/s
The tangential acceleration (aθ) can be calculated as:
aθ = a sinθ
aθ = 25 m/s² ×sin30°
aθ = 25 × 1/2
aθ = 12.5 m/s²
Therefore, The particle is traveling clockwise in a circle with a radius of 2.5 m, its tangential acceleration is 12.5 m/s², its speed is 11.625 m/s, and its radial acceleration is 21.650 m/s².
I think the actual question is,
The figure shows( find at the bottom of this answer) the total acceleration and velocity of a particle moving clockwise in a circle of radius 2.5 m at a given instant of time. At this instant, find:
(a) the radial acceleration,
(b) the speed of the particle and
(c) its tangential acceleration.
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A 10 KVA, 380 V, 50 Hz, 3-phas, star-connected salient pole alternator has direct axis and quadrature axis reactances of 12 ohms and 8 ohms respectively. The armature has resistance of 1 ohin per phase, The generator delivers rated load at 0.8 p,f lagging with the terminal voltage being maintained at rated value. If the load angle is 16.15, determine (i) the direct axis and quadrature axis components of armature current, (b) excitation voltage of the generator.
Direct axis and quadrature axis components of armature current are 30.28 A and 46.92 A respectively, and the excitation voltage of the generator is 765.36 V.
Given:
Apparent power (S) = 10 KVA = 10,000 VA
Line voltage (V) = 380 V
Frequency (f) = 50 Hz
Xd = 12 ohms
Xq = 8 ohms
Ra = 1 ohm
Power factor (pf) = 0.8 lagging
Load angle (δ) = 16.15 degrees
(i) Armature current's direct axis and quadrature axis components
We know that the apparent power is given by S = 3VLILcos(φ), where VL is the line voltage, IL is the line current, and φ is the angle between them. For a star-connected alternator, line voltage is equal to phase voltage, so we can write:
S = 3Vphase Iphase cos(φ)
Iphase = S / (3Vphase cos(φ))
For a lagging power factor, cos(φ) = 0.8, so
Iphase = 10,000 / (3 x 380 x 0.8) = 10.46 A
The direct axis component (Id) and the quadrature axis component (Iq) make up the armature current. Using the given values of Xd, Xq, and Ra, we can calculate these components as follows:
Id = (VL - IaRa) / Xd
Iq = (VL - IaRa) / Xq
where Ia is the magnitude of the armature current, which is equal to the magnitude of the line current divided by √3. Thus,
Ia = Iphase / √3 = 10.46 / √3 = 6.03 A
Substituting the given values:
Id = (380 - 6.03 x 1) / 12 = 30.28 A
Iq = (380 - 6.03 x 1) / 8 = 46.92 A
(ii) Excitation voltage of the generator:
The excitation voltage (E) of the generator is given by:
E = Vphase + IqXq
Substituting the given values:
E = 380 + 46.92 x 8 = 765.36 V
Therefore, the direct axis and quadrature axis components of armature current are 30.28 A and 46.92 A respectively, and the excitation voltage of the generator is 765.36 V.
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