The brightness of bulb B is twice as much as the brightness (power)of bulb A.
Three light bulbs are connected in series in a circuit, and they all have the same resistance of 1 W. Let's assume that the current passing through all bulbs is equal. This means that each bulb consumes equal power.
The power formula is
P = I²R, where P is power, I is current, and R is the resistance. We can write the equation as:
P₁ = P₂ = P₃
The brightness of the bulb is determined by the power consumed by it. Therefore, all bulbs will have equal brightness.
Suppose now that the switch is removed, and the circuit is open.
When the switch is open, bulb A and bulb B are in parallel, and the total resistance of the circuit is 0.5 Ω. The brightness of the bulb is determined by the power consumed by it. As the bulbs have equal resistance and voltage, the power consumed by them will be proportional to the square of the current passing through them. We can write the equation as:
P₁ = P₂ = P₃
3 = 2PThus, the brightness of bulb B is twice as much as the brightness of bulb A. Hence, the correct option is
O Twice as much.
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consider a case where the wave speed decreases from c to 0.71 c . by what factor does the wavelength change?
Answer: The wavelength must increase as well to maintain the same frequency.
Explanation: As a wave crosses a boundary into a new medium, its speed, and wavelength change while its frequency remains the same. If the speed increases, then the wavelength must increase as well to maintain the same frequency.
The wavelength will decrease by a factor of 1.4 if the wave speed decreases from c to 0.71c.
We know that the wavelength of a wave is given by the equation λ = v/f where λ is the wavelength, v is the wave speed and f is the frequency of the wave. If the wave speed decreases from c to 0.71 c, we can find the factor by which the wavelength changes by using the formula: λ1/λ2 = v2/v1 where λ1 and v1 are the original wavelength and wave speed respectively, and λ2 and v2 are the new values.
Substituting in the values, we get:λ1/λ2 = (0.71c)/c = 0.71Therefore, the wavelength will decrease by a factor of 1.4 (which is the reciprocal of 0.71) when the wave speed decreases from c to 0.71c.
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If the pressure head in the aquifer is 100 ft., calculate the effective stress (N/m") in the aquifer.
If the aquifer is pumped and the hydraulic head at some point is reduce by 12 ft., what will be the resulting changes in the pressure head (m), the effective stress (N/m*), the fluid pressure (N/m*), and the total stress (N/m? ?
The resulting changes will be:
1. Pressure head: 88 ft (or 26.82 m)
2. Effective stress: No change, assuming no other factors affect it
3. Fluid pressure: No change
4. Total stress: Decreased by the same amount as the effective stress
To calculate the effective stress in the aquifer, we need to subtract the fluid pressure from the total stress.
Given:
Pressure head in the aquifer = 100 ft (or 30.48 m)
The pressure head in the aquifer is directly proportional to the fluid pressure, which can be calculated using the formula:
Fluid pressure (P) = ρ * g * h
Where:
ρ = density of the fluid (water) = approximately 1000 kg/m³
g = acceleration due to gravity = 9.8 m/s²
h = pressure head
Fluid pressure = 1000 kg/m³ * 9.8 m/s² * 30.48 m ≈ 298,440 N/m² (or Pa)
The total stress in the aquifer is the sum of the fluid pressure and the effective stress. Therefore, the effective stress can be calculated by subtracting the fluid pressure from the total stress.
Now, let's consider the changes in the hydraulic head due to pumping:
Change in hydraulic head = -12 ft (or -3.66 m)
The resulting changes in each parameter will be as follows:
1. Pressure head:
The pressure head will be reduced by 12 ft, so the new pressure head will be 100 ft - 12 ft = 88 ft (or 26.82 m).
2. Fluid pressure:
The fluid pressure does not change, as it depends on the density of the fluid and the acceleration due to gravity, which remain constant.
3. Effective stress:
The effective stress can be calculated as the total stress minus the fluid pressure. Since the fluid pressure remains constant, the effective stress will also remain constant unless there are other factors affecting it.
4. Total stress:
The total stress is the sum of the fluid pressure and the effective stress. As mentioned earlier, the fluid pressure remains constant, so the total stress will decrease by the same amount as the effective stress, assuming no other factors affect the total stress.
Therefore, the resulting changes will be:
1. Pressure head: 88 ft (or 26.82 m)
2. Effective stress: No change, assuming no other factors affect it
3. Fluid pressure: No change
4. Total stress: Decreased by the same amount as the effective stress
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would schrödinger's equation be valid if applied to the solar system? would it be useful?
Schrödinger's equation, which describes the behavior of quantum systems, would not be valid if directly applied to the solar system due to the significant differences in scale and complexity.
Schrödinger's equation is a fundamental equation in quantum mechanics that describes the behavior of particles at the atomic and subatomic level. It is based on principles such as wave-particle duality and the quantization of energy levels.
However, when it comes to macroscopic systems like the solar system, the dynamics and interactions involved are governed by classical mechanics rather than quantum mechanics.
In the solar system, the objects such as planets, moons, and asteroids are much larger and have masses that are many orders of magnitude greater than individual particles. Their behavior is better described by classical mechanics, specifically Newton's laws of motion and the law of universal gravitation. These laws account for the gravitational interactions between celestial bodies and provide accurate predictions of their motions.
While Schrödinger's equation is not directly applicable to the solar system, it has proven to be extremely useful in understanding and predicting the behavior of quantum systems, such as atoms, molecules, and subatomic particles. It has applications in fields like quantum chemistry, material science, and electronics, where the behavior of small-scale systems is of primary interest.
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Sam runs a 100 m race in 16 seconds. Calculate how fast he was running in m/s.
Answer:
6.25 m/s
Explanation:
100÷16=6.25
An Object with a mass o 5.13kg placed on top of a spring compresses it by 0.25m (a) what is the force constant of the spring (b) How high will this object go when the spring releases its energy?
The force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m
The spring constant is the force needed to stretch or compress a spring, divided by the compressive or expansive distance. It's used to determine stability or instability in the spring, and therefore the system it's intended for. we know,
F = kx
Therefore,
k = F/x
We also know that the force being exerted on the spring is equal to the mass of the object. Hence, F = mg = 5.13 * 9.8 N = 50.174 N and we know compression due to the mass is 0.25m. Therefore,
K = 50.174/0.25 N/m
K = 200.696 N/m
Therefore, The Spring Constant is 200.696 N/m
On release, the spring potential energy gets converted to kinetic energy. Hence, on release, the height attained by the object is given by:
h = \(1/2 kx^{2}\)
We know that k=200.696 N/m and x=0.25 m. Therefore the height is:
h = \(1/2 (200.696 N/m)(0.25 m)^{2}\)
h = 2.5087 m
Therefore, the force constant of the spring is 200.696 N/m & The height the object achieves when the spring releases its energy is 2.5087 m
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Q3A) Sodium emits photons with a wavelength of 589 nm. What is the wavelength in meters? Q3B) What is the frequency of light with a wavelength of 589 nm ? Q3C) What is the energy (in J) of a single photon with a wavelength of 589 nm ? Q3D) What is the energy of a mole of photons with a wavelength of 589 nm ? Q4) What electron transition (n 6
→n 2
) or (n 4
→n 2
) has the higher energy difference? Q5) What electron transition (n 6
→n 2
) or (n 4
→n 2
) emits the higher energy photon?
The wavelength of sodium emissions is 589 nm (5.89 × 10⁻⁷ meters), with a frequency of approximately 5.09 × 10¹⁴ Hz. A single photon at this wavelength has an energy of 3.37 × 10⁻¹⁹ joules.
The wavelength of light is typically measured in meters. To convert from nanometers (nm) to meters, we divide the value by 10⁹, since there are 10⁹ nanometers in a meter. Therefore, the wavelength of sodium emissions, which is 589 nm, can be expressed as 5.89 × 10⁻⁷ meters. The frequency of light is inversely proportional to its wavelength. The relationship between frequency (f) and wavelength (λ) is given by the equation f = c/λ, where c represents the speed of light. By substituting the known values, we can calculate the frequency. The speed of light is approximately 3 × 10⁸ meters per second. Therefore, the frequency of light with a wavelength of 589 nm is approximately 5.09 × 10¹⁴ Hz. The energy of a photon can be determined using the equation E = hf, where E represents energy, h is Planck's constant (approximately 6.63 × 10⁻³⁴ J·s), and f is the frequency of the light. We have already calculated the frequency in the previous answer as approximately 5.09 × 10¹⁴ Hz. By substituting these values into the equation, we find that the energy of a single photon with a wavelength of 589 nm is about 3.37 × 10⁻¹⁹ joules. To determine the energy of a mole of photons, we need to multiply the energy of a single photon by Avogadro's number (approximately 6.022 × 10²³). By doing this calculation using the energy we obtained in the previous answer (3.37 × 10⁻¹⁹ joules), we find that the energy of a mole of photons with a wavelength of 589 nm is approximately 2.03 × 10⁴ joules. The electron transition from n=4 to n=2 has a higher energy difference. The energy difference between electron energy levels in an atom can be calculated using the equation ΔE = E₂ - E₁, where ΔE represents the energy difference, and E₂ and E₁ are the energies of the final and initial states, respectively. In this case, the transition from n=4 to n=2 will have a higher energy difference compared to the transition from n=6 to n=2 since the energy difference is inversely proportional to the principal quantum number (n). As n decreases, the energy difference increases. The energy of a photon emitted during an electron transition is directly proportional to the energy difference between the initial and final states. In this case, the transition from n=6 to n=2 will result in a higher energy photon emission compared to the transition from n=4 to n=2 since the energy difference is larger for the former transition. Therefore, the electron transition from n=6 to n=2 emits the higher energy photon.
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what is the percent efficiency of the laser in converting electrical power to light?
Additionally, these lasers are incredibly effective at converting electricity into light, with a wall-plug efficiency of 10% at room temp and more than 18% at colder temperatures.
What device transforms electrical energy into light?After transforming the electric power it gets from the socket or socket, a light bulb emits heat and light. A commonplace item that transforms energy types are bulbs.
How is energy converted into light?Photons, which are tiny energy packets, are created by light.Photons are created as a result of the heating of an object's atoms.The heat excites the electrons, which then produce more energy.A photon is the energy's primary type of emission, and as a substance heats up, more photons are produced.
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Which astronomer's laws of motion helped to explain the heliocentric model
Answer:
( Galileo )discovered evidence to support Copernicus' heliocentric theory when he observed four moons in orbit around Jupiter
On one stretch of road, any vehicle travelling faster than 25 m/s is breaking the speed limit. The detectors are placed 1.2 m apart. Calculate the speed of a car that takes 0.050 s to travel this distance. Is it breaking the speed limit?
Answer:
Speed = 24 m/s.
No! It doesn't break the speed limit.
Explanation:
The formula we'll be using to find the car's speed:
\( \boxed{ \mathsf{speed = \frac{distance}{time} }}\)
The detectors are placed 1.2 m apart.
==> Distance the car travels = 1.2 m
The car, it says, takes 0.050 s to travel that distance.
==> Time taken by the car to travel 1.2 m = 0.050 s
Using the formula mentioned above, let's calculate the speed of the car:
\( \sf{speed = \frac{distance}{time} }\)
\( \implies \sf{speed = \frac{1.2}{0.050} }\)
On dividing 12 by 0.050 we obtain 24.
\( \implies \sf{speed = 24 \: m/s }\)
Any car traveling with a speed that is greater than or equal to 25 m/s is breaking the speed limit.
And since the car in our focus is traveling at 24 m/s that is less than 25 m/s, it doesn't break the speed limit.
Un consumator electric conectat la o tensiune de 220V are rezistenta electrica R=100ohmi Ce putere electrica are consumatorul? 1 point 484W 220W 440W
On a dry winter day, if you scuff your feet across a carpet, you build up a charge and get a shock when you touch a metal doorknob. In a dark room you can actually see a spark about 2 cm long. Air breaks down at a field strength of 3 × 10^6 N/C. How much charge have you built up? As- sume that just before the spark occurs, all the charge is in your finger, drawn there by in- duction due to the proximity of the doorknob. Approximate your fingertip as a sphere of di- ameter 1.42 cm, and assume that there is an equal amount of charge on the doorknob 2 cm away. Answer in units of C How many electrons does this correspond to? The elemental charge is 1.60218 × 10-19 C.
The number of electrons that corresponds to the number of charges is 2.71 × 10¹⁰ electrons.
How much charge have you built up?
The breakdown field strength of air is 3 × 10⁶ N/C, and the distance between the fingertip and the doorknob is 2 cm, so the electric field between the two is given by:
E = 3 × 10⁶ N/C
The electric field causes the charge on the fingertip to be drawn towards the doorknob, so we can calculate the charge on the fingertip using the formula:
q = 4π ε_0 x Er²
where;
r is the radius of the fingertip (0.71 cm) and
ε_0 is the permittivity of free space (8.854 × 10^-12 C^2/Nm²).
q = 4 x π x 8.854 × 10⁻¹² x 3 × 10⁶ x 0.71²
q = 2.17 × 10⁻⁸ C
The charge on the doorknob is equal and opposite to the charge on the fingertip, so the total charge on both is calculated as;
Q_total = 2 x 2.17 × 10⁻⁸ C
= 4.34 × 10⁻⁸ C.
The number of electrons is calculated as follows;
number of electrons = q / e
where;
e is the elementary charge (1.60218 × 10⁻¹⁹ C).number of electrons = ( 4.34 × 10⁻⁸ C / 1.60218 × ⁻¹⁹ C )
number of electrons = 2.71 × 10¹⁰ electrons
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If the same force is applied to an object with a large mass it will have a blank acceleration
Answer:
If the same force is applied to an object with a large mass it will have a smaller (lesser) acceleration
Explanation:
force and mass are inversely proportional. force and acceleration are directly proportional. which means greater mass have smaller acceleration and smaller mass has greater acceleration. this is due to newtons second law of motion.
In the case when the same force is applied that contains high mass so it contains less acceleration.
Relationship of force and mass:There should be an inverse relationship between the force and mass. However, there is the direct relationship between the force and acceleration. That means in the case when there is the high force so there should be less acceleration and less mass contains high acceleration by applying the second law of motion of newton.
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A machine launches a tennis ball at an angle of 45° with the horizontal, as
shown. The ball has an initial vertical velocity of 9.0 meters per second and an initial
horizontal velocity of 9.0 meters per second. The ball reaches its maximum height
0.p2 second after its launch. [Neglect air resistance and assume the ball lands at the
same height above the ground from which it was launched.]
Elapsed Time
+0.92 s
Viy = 9.0 m/s
Launcher
V = 9.0 m/s
45
Horizontal
The total horizontal distance traveled by the tennis ball during the entire time it is in the air is
The motion or path of the tennis ball is the path of a projectile, which has
both vertical and horizontal motion.
The total horizontal distance traveled by the tennis ball during the entire
time it is in the air ≈ 16.514 meters.
Reasons:
The given parameters are;
The direction in which the ball is launched = 45°
The initial vertical velocity of the ball, \(v_y\) = 9.0 m/s
The initial horizontal velocity of the ball, vₓ = 9.0 m/s
The time it takes the ball to reach the maximum height, t = 0.92 seconds after its launch
The total horizontal distance traveled, by the tennis ball is given by the formula;
\(\Delta d_x = \dfrac{v_1^2 \cdot \left( 2 \cdot cos(\theta) \sin(\theta)}{y} = \dfrac{2 \times v_x \times v_y}{g}\)
Which gives;
\(\mathrm{The \ total \ distance \ travelled, \ \Delta} d_x = \dfrac{2 \times 9.0\times 9.0}{9.81} \approx 16.514\)
The total horizontal distance traveled by the tennis ≈ 16.514 meters
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Which one of the following is true, according to Newton’s laws of motion? Ignore friction.A. A sports utility vehicle (SUV) hits a stationary motorcycle. Since it is stationary, the motorcycle sustains a greater force than the SUV does.B. A semitrailer truck crashes all the way through a wall. Since the wall collapses, the wall sustains a greater force than the truck does.C. Sam (18 years old) and his sister (9 years old) go ice skating. They push off against each other and fly apart. Sam flies off with the greater acceleration.D. Two astronauts on a space walk are throwing a ball back and forth between each other. In this game of catch the distance between them remains constant.E. None of the above is true, according to the third law.
Option A is a true. An SUV strikes a motorcycle that is standing still. The motorcycle can withstand more force than the SUV since it is stationary.
Every time one object applies force to another, the other object applies an equal and opposing force to the first. His third law argues that there is an equal and opposite reaction to every action (force) in nature. If you push a truck and a vehicle with the same amount of effort, the car will accelerate faster than the truck since it is lighter. Due to the full shopping cart's greater bulk compared to the empty one, it is simpler to push one than the other.
In the early stages of having enough grip, engineers frequently discuss "power to weight ratio" because this impacts acceleration. Since it takes longer (more time) to accelerate a heavier car with the same amount of power to go the same distance, more fuel is consumed.
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The hot and neutral wires supplying DC power to a light-rail commuter train carry 800 A and are separated by 75.0 cm. What is the magnitude and direction of the force between 50.0 m of these wires?
The force between the wires is approximately 0.0533 N.
To calculate the force between the two wires, we'll use Ampère's Law, which states that the magnetic force between two parallel conductors is given by the formula:
F/L = μ₀ * I₁ * I₂ / (2π * d)
Where F is the force, L is the length of the wires, μ₀ is the permeability of free space (4π × 10^-7 T·m/A), I₁ and I₂ are the currents in the wires, and d is the distance between the wires.
In this case, I₁ = I₂ = 800 A, L = 50.0 m, and d = 75.0 cm (0.75 m).
F/L = (4π × 10^-7 T·m/A) * (800 A)² / (2π * 0.75 m)
Now, we'll calculate the force by multiplying both sides by L:
F = L * ((4π × 10^-7 T·m/A) * (800 A)² / (2π * 0.75 m))
F ≈ 0.0533 N
The force between the wires is approximately 0.0533 N. Since the currents are in the same direction, the wires will attract each other, and the direction of the force will be towards the other wire for both wires.
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FILL IN THE BLANK.the rate of vibration of a sound is called its _____. response vibration frequency decibel
The rate of vibration of a sound is called its frequency.
Frequency is measured in hertz (Hz), and it is the number of times a sound wave vibrates per second. The higher the frequency, the higher the pitch of the sound. For example, a piccolo has a higher frequency than a tuba, so it has a higher pitch.
Response, vibration, and decibel are all related to sound, but they are not the same as frequency. Response is how the ear and brain react to sound. Vibration is the movement of air molecules that creates sound waves. Decibel is a unit of measurement for sound intensity.
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3. A man heads up a trail going north to see a lake. The trail is 5 miles long and it takes him
2 hours to get there. What was his velocity?
Answer:
v = 2.5 mi/h
Explanation:
The velocity of an object is defined as the time rate of change of its position. In other words the velocity of an object is just a ration of displacement covered by the object to the time taken by the object, to cover that distance. So, in this case we will use the same formula or equation to calculate the velocity of the man. The formula is as follows:
v = s/t
where,
v = velocity of the man = ?
s = distance of the trail = 5 miles
t = time required to complete the trail = 2 h
Therefore,
v = 5 miles/ 2 h
v = 2.5 mi/h
Q9. Two points P and Q on a progressive wave are separated by distance d. The phase difference between P and Q is rad. What is the wavelength?
Two points P and Q on a progressive wave are separated by distance d. The phase difference between P and Q is rad. The wavelength of the wave would be 8 times the distance between points P and Q.
In a progressive wave, the phase difference between two points is related to the wavelength of the wave. To find the wavelength (λ) given the phase difference (ϕ) and the distance (d) between two points, we can use the formula:
ϕ = 2π(d/λ)
Rearranging the equation to solve for λ, we have:
λ = (2πd) / ϕ
In this case, the phase difference between points P and Q is given as ϕ radians. The distance between these points is denoted by d. By substituting these values into the equation, we can determine the wavelength of the wave.
It's important to note that the phase difference is typically measured in radians, and one complete wave cycle corresponds to 2π radians.
For example, let's say the phase difference between points P and Q is π/4 radians, and the distance between them is d. Using the formula above, the wavelength would be:
λ = (2πd) / (π/4)
λ = (8πd) / π
λ = 8d
This calculation demonstrates how the phase difference and distance between points on a wave are related to the wavelength. By knowing the phase difference and distance, we can determine the wavelength of the wave using the formula derived from the wave's periodic nature.
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Why should a physical quantity be measured?
Answer:
It allows us to understand nature much more deeply than does qualitative description alone.
Explanation:
Without explaining the measurements, a quantity cannot always be measured.
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Chris has a part time job as a cannon ball catcher for the circus. One day he was located an unknown distance away from the cannon. A cannonball was fired from the cannon at 425 m/s. The speed of sound was 345 m/s. Unfortunately the cannonball went past Chris 0.20 s before he heard the sound of the blast. How far away was the cannon from Chris?
show work with answer for brainliest plz
Answer: 366.56 meters.
Explanation:
Velocity of the cannon ball = 425m/s
Velocity of sound = 345 m/s
For the "position" of both, we have the equation:
Pc = 425m/s*t
Ps = 345m/s*t
Where t is time in seconds.
If the position of Chris is X, we have that if the ball reaches the position of Chris in T seconds, then the soundwave reaches the position of Chris in T + 0.20 seconds, we can write this as:
425m/s*T = X
345m/s*(T + 0.20s) = X
Now we can solve this system of equations. First we can replace the first equation in the second equation and get
345m/s*(T - 0.20s) = 425m/s*T
Now we solve this for T.
345*T + 69 = 425*T
69 = (425 - 345)*T = 80*T
T = 69/80 = 0.8625 seconds.
Now we replace this in the first equation and get:
X = 425m/s*T = 425m/s*0.8625s = 366.56 meters.
two objects are initially the same height above the ground. simultaneously, one is released from rest and the other is shot fof horizontally with a n initial speed of 2.5 m/s. the two objects collide after falling 20m. how far apart were the object initially?
We may use the equations of motion to calculate the initial distance between the two objects in this issue. Let's call the starting height of the objects "h." Because the first item is at rest, its initial vertical velocity is 0.
When the second item is launched horizontally at a speed of 2.5 m/s, its initial vertical velocity is also 0. When the items crash after falling 20 meters, we may apply the following equation of motion: h = 1/2gt^2 where g denotes gravity's acceleration and t the time it takes for the objects to collide. The horizontal velocity of the second item may be used to calculate the time t: distance = time x speed 20m = 2.5m/s x t t = 8 seconds Now we can use the equation of motion again to find h: h = 1/2gt^2 = 1/2 x 9.81 m/s^2 x (8 s)^2 = 313.92 m Therefore, the initial distance between the objects was 313.92 meters.
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A 4 coulombs charged particle experiences an electric force of 200 N when placed at point P in an electric field. The magnitude of the electric field at point P is :
a) 5 N/C
b) 800 N/C
c) 0.02 N/C
d) 50 N/C
(d) 50N/C
The magnitude of the electric field at point 'P' is 50N/C.
It is derived from the basic concepts of Electrostatics. Coulomb's Law is the basis of relations in Electrostatics. It resembles Newton's Law of Gravitation.
Using the relation between Electric force, charge, and Electric field:
F = qE
F = 200N; q = 4C200 = (4)E
E = 50N/C
It is widely used in the calculation of Electric Force and Electric Field. The S.I. Unit of the Electric Force is Newton. The S.I. Unit of the Electric Field is N/C. The S.I. Unit of charge is Coulomb.
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What is the equivalent resistance of the circuit?
Answer:
Option D. 5.45 Ω
Explanation:
From the question given above, the following data were obtained:
Resistance 1 (R₁) = 10 Ω
Resistance 2 (R₂) = 20 Ω
Resistance 3 (R₃) = 30 Ω
Voltage (V) = 120 V
Equivalent resistance (R) =?
The equivalent resistance can be obtained as follow:
1/R = 1/R₁ + 1/R₂ + 1/R₃
1/R = 1/10 + 1/20 + 1/30
Find the least common multiple (lcm) of 10, 20 and 30. The result is 60
Divide 60 by each of the denominators and multiply by their numerators respectively. We have:
1/R = (6 + 3 + 2)/60
1/R = 11/60
Invert
R = 60/11
R = 5.45 Ω
Thus, the equivalent resistance in the circuit is 5.45 Ω
Find the center of mass of the region bounded by y=9-x^2 y=5/2x , and the z-axis. Center of Mass = __?
Note: You can earn partial credit on this problem.
The centre of mass of the region is bounded by y=9-x^2 y=5/2x, and the z-axis is (3.5, 33/8). Formulae used to find the centre of mass are as follows:x bar = (1/M)*∫∫∫x*dV, where M is the total mass of the system y bar = (1/M)*∫∫∫y*dVwhere M is the total mass of the system z bar = (1/M)*∫∫∫z*dV, where M is the total mass of the systemThe region bounded by y=9-x^2 and y=5/2x, and the z-axis is shown in the attached figure.
The two curves intersect at (-3, 15/2) and (3, 15/2). Thus, the total mass of the region is given by M = ∫∫ρ*dA, where ρ = density. We can assume ρ = 1 since no density is given.M = ∫[5/2x, 9-x^2]∫[0, x^2+5/2x]dAy bar = (1/M)*∫∫∫y*dVTherefore,y bar = (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]y*dA= (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]ydA...[1].
The limits of integration in the above equation are from 5/2x to 9-x^2 for x and from 0 to x^2+5/2x for y.To evaluate the above integral, we need to swap the order of integration. Therefore,y bar = (1/M)*∫[0, 3]∫[5/2, (9-y)^0.5]y*dxdy...[2].
The limits of integration in the above equation are from 0 to 3 for y and from 5/2 to (9-y)^0.5 for x.Substituting the values and evaluating the integral, we get y bar = (1/M)*[(9-5/2)^2/2 - (9-(15/2))^2/2]= (1/M)*(25/2)...[3].
Also, the x coordinate of the center of mass is given by,x bar = (1/M)*∫∫∫x*dVTherefore,x bar = (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]x*dA= (1/M)*∫[5/2x, 9-x^2]∫[0, x^2+5/2x]xdA...[4].
The limits of integration in the above equation are from 5/2x to 9-x^2 for x and from 0 to x^2+5/2x for y.To evaluate the above integral, we need to swap the order of integration. Therefore, x bar = (1/M)*∫[0, 3]∫[5/2, (9-y)^0.5]xy*dxdy...[5].
The limits of integration in the above equation are from 0 to 3 for y and from 5/2 to (9-y)^0.5 for x.
Substituting the values and evaluating the integral, we get x bar = (1/M)*[63/8]= (1/M)*(63/8)...[6]Thus, the centre of mass of the region is bounded by y=9-x^2 y=5/2x, and the z-axis is (3.5, 33/8).
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A heat engine is given by heat and releases by heat to the environment. What is the amount of work done by the system
The amount of work done by a heat engine can be calculated using the first law of thermodynamics. According to this law, the work done by the system is equal to the difference between the heat input and the heat output.
In a heat engine, heat is supplied to the system from a high-temperature reservoir and some of this heat is converted into work. The remaining heat is released to a low-temperature reservoir, typically the environment.
To determine the amount of work done, subtract the heat released to the environment from the heat input to the system. This can be expressed as:
Work = Heat input - Heat released
It's important to note that the efficiency of a heat engine is determined by the ratio of the work output to the heat input. The efficiency is given by the equation:
Efficiency = (Work output / Heat input) * 100%
In summary, the work done by a heat engine is calculated by subtracting the heat released to the environment from the heat input to the system. The efficiency of a heat engine is determined by the ratio of work output to heat input.
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A car weighing 12000 N is parked on a 36° slope. The car starts to roll down the hill. What is the acceleration of the car??
The acceleration of the car down the 36° slope will be 5.76 m/s²
Recall :
Force, F = mass × acceleration F = maThe force which tends to roll the car down the hill :
Fsinθ 12000 × sin(36) = 7053.42 NMass of the car :
F = mg12000 = m × 9.8
m = 12000 / 9.8
m = 1224.49 kg
The acceleration of the car down slope :
a = F/m ; F = Force which tends to pull the car downa = (7053.42) ÷ 1224.49
a = 5.76 m/s²
Therefore, the acceleration of the car is 5.76 m/s²
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suppose you could not see violet, but you could see infrared light. what would be the middle of your hypothetical visible spectrum?
If a person could not see violet but could see infrared light, the middle of their hypothetical visible spectrum would be green.
The middle of the hypothetical visible spectrum in this scenario would be red, as it is the middle of the traditional visible spectrum (ROYGBIV). Infrared light is not part of the visible spectrum, so it would not factor into the middle of the hypothetical visible spectrum.
The traditional visible spectrum is made up of red, orange, yellow, green, blue, indigo, and violet (ROYGBIV).
The visible spectrum of light is the part of the electromagnetic spectrum that is visible to the human eye. The spectrum ranges from red to violet, with red light having the longest wavelength and violet light having the shortest wavelength. If a person could not see violet, but they could see infrared light, the middle of their hypothetical visible spectrum would be green.Infrared light has a longer wavelength than visible light, which means it has a lower frequency. It is not visible to the human eye. The color green, on the other hand, has a wavelength of about 520-570 nm, which is in the middle of the visible spectrum.
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17) Name two ways you could decrease the potential energy of a bucket full of water sitting on a bench.
Explanation:
The potential energy of an object has the following formula
Potential energy = mgh
where m = mass of the object
g = acceleration due to gravity
h = height of the object
This means that the potential energy of an object depends upon its mass, acceleration due to gravity, and height.
In the given situation we have a bucket full of water. If the mass and acceleration due to gravity are not changed, the only way the potential energy can be decreased is by reducing the height of the bucket full of water.
This can be done by: -
(i) Lifting the bucket full of water in such a way that you
decrease its height as compared to the bench.
(ii) Put the bucket full of water on a stool whose height is
lower than the bench.
Answer:
1.By decreasing it's contents- this decreases the weight of the bucket thus decreasing the potential energy of the bucket.
2.By decreasing the height of the bench we have decreased the amount of potential energy stored in the bucket
You are planning to test the water quality at a reservoir at
different depths.
Task 1: Explain the planning that you will do
before you leave for Dam. What are the important aspects you must
consider?
Be sure to adhere to all safety precautions while performing the test, such as wearing protective gear, being cautious of the surroundings, and working in teams.
Ensure that you have obtained the necessary permits and permissions from relevant authorities to test the water at the reservoir. Be sure to adhere to all safety precautions while performing the test, such as wearing protective gear, being cautious of the surroundings, and working in teams.
Before leaving for the dam, planning is essential. It will allow you to test the water quality in a systematic and thorough way. The following are some important aspects that must be considered:
Test Equipment Selection - Choose suitable test equipment to test the water quality at various depths. This equipment must be calibrated, cleaned and checked for accuracy prior to testing. Also, take spare parts or additional equipment just in case something happens.Time and Duration - The testing time and duration should be planned to take into account all factors that may affect the test. This includes the weather, time of day, depth of the water and other environmental factors.
Depending on the location, the test should be done during the same period to ensure consistency.
Transportation - Make sure that the test equipment is safely transported and can be easily moved around the test site. Consider factors like access points, terrain, and the distance from the test site to the base. Make sure you take enough fuel for transportation.
Test Plan - Develop a test plan that outlines the testing procedure, test objectives, testing schedule, and personnel requirements. This plan will be your guide to ensure that the testing is done properly and within a specific time frame.
Record Keeping - During the test, record the data from all the measurements taken. Record-keeping is crucial for future analysis and comparisons. It is also important to have a detailed map of the site to track the exact location of each measurement taken.
Finally, ensure that you have obtained the necessary permits and permissions from relevant authorities to test the water at the reservoir. Be sure to adhere to all safety precautions while performing the test, such as wearing protective gear, being cautious of the surroundings, and working in teams.
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9. What is the gravitational potential energy of a 61.2 kg person standing on the roof of a 10-storey building? (Each storey is 2.50 m high.)
Answer:
15009
Explanation:
PE = mgh
PE = 61.2(9.81)(10 * 2.50)
PE = 15009.3