The mass flow rate of air exiting the turbine is 128.6 kg/s.
What is mass flow rate?The mass flow rate of a fluid is defined as the mass that passes through a given cross-sectional area per unit of time. It is measured in kg/s
What is ideal gas law?The ideal gas law, which relates pressure, temperature, volume, and the number of moles of a gas. PV = nRT is the equation for ideal gas law.
Equation:To calculate the mass flow rate, we need to first determine the number of moles of air that are exiting the turbine per second.
n = PV/RT
where P = 150 kPa, V = 10,000 L/s, R = 8.314 J/mol-K (the gas constant), and T = 150 + 273 = 423 K (convert from Celsius to Kelvin).
Plugging in these values, we get:
n = (150,000 Pa)(10,000 L/s)/(8.314 J/mol-K)(423 K)
= 4,449 mol/s
Next, we need to convert the number of moles to mass using the molecular weight of air, which is approximately 28.97 g/mol:
mass flow rate = n x molecular weight
= 4,449 mol/s x 28.97 g/mol / 1000 g/kg
= 128.6 kg/s
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1. How did the temperature of the mixture change before and after the ice melted? 2. Calculate the average temperature change per minute of the ice-water mixture prior to the ice melting and the average rate after the ice melted, average rate prior to melting______ average rate after melting______
The temperature of the mixture remained constant at the melting point of ice (0 degrees Celsius) before the ice melted.
The average rate of temperature change per minute was 0 degrees Celsius before the ice melted, and increased to the rate at which heat was being applied after the ice melted.
When ice is in contact with water, it melts at its melting point, which is 0 degrees Celsius. During this phase change, the temperature of the mixture remains constant at 0 degrees Celsius until all the ice has melted.
The average rate of temperature change per minute prior to the ice melting is 0 degrees Celsius, as the temperature remains constant.
After the ice melts, the average rate of temperature change per minute will depend on the rate at which heat is being applied to the mixture, which could vary based on the heat source used and the conditions of the experiment.
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Taylor rides her bicycle 5km north from her house to the park, turns around, and then rides the bicycle 3 km back towards her house
Taylor decides to go for a bike ride to the park. Taylor turns around and rides her bicycle back to her home three kilometres away.
The choice is made by Taylor to ride her bicycle to the park. She travels five kilometres on her bicycle north from her home before arriving at the park. After spending some time at the park, she returns home on her bicycle after travelling three kilometres.
This shows that Taylor has pedalled 8 km in total. Both to and from her home, she commutes by bicycle, covering a different distance in each direction. She completes her ride, and it seems that she enjoyed being outside.
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PLEASE HELP An object takes 5.91 Earth years to orbit the Sun. What is its average distance from the Sun? Make sure to show ur work
a 16.0 μf capacitor is charged to a potential of 50.0 vv and then discharged through a 285 ω resistor.
How long does it take the capacitor to lose half of its charge?
How long does it take the capacitor to lose half of its stored energy?
Express your answer with the appropriate units.
It takes approximately 4.16 milliseconds for the capacitor to lose half of its stored energy.
To determine the time it takes for the capacitor to lose half of its charge, we can use the equation: [tex]Q = Q0 * e^(-t/RC)[/tex]
Where Q is the charge remaining in the capacitor at time t, Q0 is the initial charge, R is the resistance of the circuit, C is the capacitance of the capacitor, and e is the mathematical constant e.
Since we want to find the time it takes for the charge to decrease to half its initial value, we can set Q = 0.5Q0 and solve for t:
0.5Q0 = Q0 * e^(-t/RC)
0.5 = e^(-t/RC)
Taking the natural logarithm of both sides:
ln(0.5) = -t/RC
Solving for t:
t = -ln(0.5) * RC
Plugging in the given values:
t = -ln(0.5) * (285 Ω) * (16.0 μF) = 5.93 ms
Therefore, it takes approximately 5.93 milliseconds for the capacitor to lose half of its charge.
To determine the time it takes for the capacitor to lose half of its stored energy, we can use the equation for the energy stored in a capacitor:
U = 0.5 * C * V^2
Where U is the energy stored in the capacitor, C is the capacitance, and V is the voltage across the capacitor.
Since we want to find the time it takes for the energy stored in the capacitor to decrease to half its initial value, we can set U = 0.5U0 and solve for t: 0.5U0 = 0.5 * C * V0^2
0.5 = (V/V0)^2
Taking the square root of both sides:
V/V0 = 1/sqrt(2)
V0/sqrt(2) = V
Therefore, when the voltage across the capacitor has decreased to V0/sqrt(2), the energy stored in the capacitor has decreased to half its initial value. We can use the same equation for the charge remaining in the capacitor and solve for t:
Q/Q0 = V/V0 = 1/sqrt(2)
Q = Q0/sqrt(2)
Using the equation for the charge on a capacitor in a discharging circuit:
Q = Q0 * e^(-t/RC)
Q0/sqrt(2) = Q0 * e^(-t/RC)
1/sqrt(2) = e^(-t/RC)
Taking the natural logarithm of both sides:
ln(1/sqrt(2)) = -t/RC
Solving for t:
t = -ln(1/sqrt(2)) * RC
Plugging in the given values:
t = -ln(1/sqrt(2)) * (285 Ω) * (16.0 μF) = 4.16 ms
Therefore, it takes approximately 4.16 milliseconds for the capacitor to lose half of its stored energy.
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what spring constant must the bungee cord have for the student's lowest point to be 2.0 m above the water? express your answer with the appropriate units.
The spring constant of the bungee cord must be 343.35 N/m for the student's lowest point to be 2.0 m above the water.
What is spring constant?Spring constant is a measure of the stiffness of a spring, indicating the amount of force required to extend or compress it by a certain distance. To determine the spring constant required for the bungee cord, we need to use the equation for the spring force:
F = -kx
where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position.
In this case, we can assume that the equilibrium position is the point where the bungee cord is unstretched, and the displacement x is the distance between the lowest point of the student and the equilibrium position.
If we want the lowest point of the student to be 2.0 m above the water, then the displacement x is:
x = 2.0 m - 0 m = 2.0 m
To calculate the spring constant k, we need to know the weight of the student. Let's assume the student has a mass of 70 kg, which gives a weight of:
W = mg = (70 kg)(9.81 m/s^2) = 686.7 N
where g is the acceleration due to gravity.
At the lowest point of the student, the spring force must be equal to the weight of the student, so we can write:
F = -kx = 686.7 N
Solving for k, we get:
k = -F/x = -686.7 N / 2.0 m = 343.35 N/m
Therefore, the spring constant of the bungee cord must be 343.35 N/m for the student's lowest point to be 2.0 m above the water.
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a 68.3 kg base runner begins his slide into second base while moving at a speed of 4.9 m/s. the coefficient of friction between his clothes and earth is 0.62. he slides so that his speed is zero just as he reaches the base. the acceleration of gravity is 9.81 m/s 2 . a) how much mechanical energy is lost due to friction acting on the runner? answer in units of j.
The mechanical energy lost due to friction acting on the runner is mechanical energy lost due to friction = initial kinetic energy - final kinetic is 1635.5 J.
The mechanical energy lost due to friction acting on the runner can be found using the work-energy principle, which states that the net work done on an object is equal to its change in kinetic energy. In this case, the net work done on the runner is the work done by the force of friction, which is given by: Wfriction = force of friction x distance
The force of friction can be found using the coefficient of friction and the normal force, which is equal to the weight of the runner: force of friction = coefficient of friction x normal force
= coefficient of friction x weight of runner
= 0.62 x 68.3 kg x 9.81
= 414.3 N
The distance over which the force of friction acts is equal to the distance that the runner slides before coming to a stop, which can be found using the equation of motion:
where v_f is the final velocity (zero in this case), v_i is the initial velocity (4.9 m/s), a is the acceleration (which is negative because it is opposite to the direction of motion), and d is the distance:
= (0 - (4.9 m/s)^2) / (2 x (-g))
= 0.607 m
Therefore, the work done by the force of friction is Wfriction = force of friction x distance
= 414.3 N x 0.607 m
= 251.2 J
Since the net work done on the runner is equal to the change in kinetic energy, and the final kinetic energy is zero, the initial kinetic energy must be equal to the mechanical energy lost due to friction:
initial kinetic energy = mechanical energy lost due to friction
= 1/2 x mass x velocity - 0
= 1/2 x 68.3 kg x (4.9 m/s)^2
= 1635.5 J
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A string is wrapped several times around the rim of a hoop with radius R = 0.25 m and mass M = 0.75 kg. The free end of the string is attached to the ceiling and the hoop is released from rest. The moment of inertia of the hoop about its center is I = MR
The moment of Intertia of the loop about its center is 0.1875.It quantifies how challenging it would be to change an object's current rotational speed.
Thus, It quantifies how challenging it would be to change an object's current rotational speed. An object's moment of inertia involves considering a stiff body that is spinning around a fixed axis.
A same object may have quite varied moment of inertia values depending on the location and orientation of the axis of rotation since that measurement is based on the distribution of mass within the object and the position of the axis.
According to Newton's equations of motion, moment of inertia conceptually represents an object's resistance to change in angular velocity, much like mass represents a resistance to change in velocity in non-rotational motion.
Therefore, The moment of Intertia of the loop about its center is 0.1875.
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T/F: Myoglobin "loading" happens at the same PO2 as hemoglobin "unloading".
False. Myoglobin and hemoglobin are two different proteins that have different oxygen binding characteristics. Myoglobin is a single-subunit protein found in muscle cells that binds oxygen with high affinity, while hemoglobin is a multi-subunit protein found in red blood cells that binds oxygen with lower affinity.
The oxygen dissociation curve for myoglobin is different from that of hemoglobin, and myoglobin is saturated with oxygen at a much lower partial pressure of oxygen (PO2) than hemoglobin. Myoglobin has a higher affinity for oxygen than hemoglobin, which means that it can hold onto oxygen even when the PO2 is low. Hemoglobin, on the other hand, has a lower affinity for oxygen and only releases oxygen to the tissues when the PO2 is low.
Therefore, the "loading" of oxygen by myoglobin occurs at a lower PO2 than the "unloading" of oxygen by hemoglobin.
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In the illustration, two particles carry the same magnitude of charge, one is positive and the other is negative. Which of the dashed lines could be an equipotential line of the two charged particles? A) The circle around one charged particle, with every point on the circle equidistant from the center of the charged particle. B) The vertical line that is located halfway between the charges C) The horizontal line that runs directly through the center of each D) None of the three lines could be an equipotential line for bothcharges.
In the illustration with two charged particles of the same magnitude, one positive and the other negative, the equipotential line of the two charged particles would be B) The vertical line that is located halfway between the charges.
An equipotential line is a line in space where all points on the line have the same electric potential, and in this case, the line halfway between the charges fulfills this condition.
Option B) The vertical line that is located halfway between the charges could be an equipotential line of the two charged particles. An equipotential line is a line in space where all points on the line have the same electric potential. Since the vertical line is equidistant from both charged particles, the electric potential at each point on the line would be the same.
Option A) the circle around one charged particle and Option C) the horizontal line that runs directly through the center of each cannot be equipotential lines for both charges as the distance from each point on the line to the charged particles is not the same. Option D) None of the three lines could be an equipotential line for both charges is not correct as the vertical line satisfies the condition for being an equipotential line.
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n new england, the horizontal component of the earth's magnetic field has a magnitude of . a proton is shot vertically straight down towards the ground with a speed of . what is the magnitude of the magnetic force?
The magnitude of the horizontal component of the earth's magnetic field is. With a speed of, a proton is thrown vertically straight down towards the ground.
To calculate the magnitude of the magnetic force on the proton, we need to use the formula F = qvB, where F is the magnetic force, q is the charge of the proton, v is the speed of the proton, and B is the magnitude of the horizontal component of the earth's magnetic field.
Plugging in the given values, we get:
F = (1.6 x 10⁻¹⁹C) x (speed of proton) x (magnitude of earth's magnetic field)
We're given the magnitude of the earth's magnetic field, which is 0.5 gauss (or 5 x 10⁻⁵ T). However, we're not given the speed of the proton, so we can't calculate the magnetic force without that information.
Once we have the speed of the proton, we can plug it into the formula to find the magnitude of the magnetic force. Remember that the magnetic force acts perpendicular to both the magnetic field and the velocity of the charged particle.
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total magnifying for a compound light microscope is calculated by multiplying the power of the
The total magnification of a compound light microscope is calculated by multiplying the power of the objective lens by the power of the eyepiece.
The objective lens is the lens closest to the object being viewed, while the eyepiece is the lens closest to the eye of the observer. The power of the objective lens is typically marked on the lens itself and ranges from 4x to 100x or more. The power of the eyepiece is also marked on the lens and is typically 10x.
To calculate the total magnification, simply multiply the power of the objective lens by the power of the eyepiece. For example, if the objective lens has a power of 40x and the eyepiece has a power of 10x, the total magnification would be 40 x 10 = 400x.
It is important to note that magnification alone does not determine the quality of an image in a microscope. Other factors such as resolution, contrast, and depth of field also play important roles in producing a clear and detailed image.
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a transformer is intended to decrease the rms value of the alternating voltage from 500 volts to 25 volts. the primary coil contains 200 turns. find the necessary number of turns n2 in the secondary coil.
A transformer is intended to decrease the rms value of the alternating voltage from 500 volts to 25 volts. the primary coil contains 200 turns:
To find the necessary number of turns n2 in the secondary coil of the transformer, we can use the equation:
V1/V2 = N1/N2
Where V1 and V2 are the rms values of the voltage in the primary and secondary coils, respectively, and N1 and N2 are the number of turns in the primary and secondary coils, respectively.
In this case, V1 = 500 volts, V2 = 25 volts, and N1 = 200 turns.
Plugging these values into the equation, we get:
500/25 = 200/N2
Simplifying, we get:
N2 = (200 x 25)/500 = 10 turns
Therefore, the necessary number of turns in the secondary coil is 10.
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what current (in ka) is needed to transmit 160 mw of power at a voltage of 20.0 kv?
The current needed to transmit 160 MW of power at a voltage of 20.0 kV is 8,000 A (amperes) or 8 kA (kiloamperes).
To calculate the current needed to transmit 160 MW (megawatts) of power at a voltage of 20.0 kV (kilovolts), we can use the formula for power:
Power (P) = Voltage (V) × Current (I)
Rearranging the formula to solve for current, we get:
Current (I) = Power (P) / Voltage (V)
Given that the power is 160 MW and the voltage is 20.0 kV, we can plug in these values to calculate the current:
Power (P) = 160 MW = 160 × 10⁶ W (since 1 MW = 10⁶ W)
Voltage (V) = 20.0 kV = 20.0 × 10³ V (since 1 kV = 10³ V)
Substituting these values into the formula, we get:
Current (I) = 160 × 10⁶ W / 20.0 × 10³ V
Simplifying, we get:
Current (I) = 8,000 A
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how far from a 21- cm -focal-length lens should you place an object to get an upright image magnified by a factor of 2.0?
To obtain an upright, magnified image with a factor of 2.0 using a 21-cm focal-length lens, place the object at a distance of 14 cm from the lens.
To get an upright image magnified by a factor of 2.0 using a 21-cm focal length lens, you would need to place the object 42 cm away from the lens. This can be determined using the formula: Magnification = Image distance / Object distance. Since the magnification factor is 2.0, and the image distance is the focal length of the lens (21 cm), we can solve for the object distance: 2.0 = 21 / Object distance. Rearranging the equation, we get Object distance = 21 / 2.0, which equals 10.5 cm. Adding this to the focal length of the lens (21 cm), we get a total distance of 31.5 cm from the lens to the object. However, since we want an upright image, the object distance must be greater than the focal length, so we double the distance and get 42 cm as the final answer.
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the magnetic moment of a rectangular loop with 337.000 turns and has dimensions are 0.027 m × 0.06 m is 2.500 am2. what is the current through the loop?
The current through the loop is approximately 4.57 A when the magnetic moment of a rectangular loop with 337.000 turns and has dimensions are 0.027 m × 0.06 m is 4.583 mA.
To calculate the current through the rectangular loop, you can use the formula for magnetic moment:
Magnetic Moment (μ) = Number of Turns (N) × Current (I) × Area (A)
We are given:
Magnetic Moment (μ) = 2.500 Am²
Number of Turns (N) = 337,000
Dimensions of the loop: 0.027 m × 0.06 m
First, find the area of the rectangular loop (A):
A = length × width = 0.027 m × 0.06 m = 0.00162 m²
Now, rearrange the formula to find the current (I):
I = μ / (N × A)
Plug in the values:
I = 2.500 Am² / (337,000 × 0.00162 m²) = 4.583 × 10⁻³ A
The current through the loop is approximately 4.583 mA.
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If the answer to your calculation has units of kg ∙ m2/s, what type of quantity could it be? (There could be more
than one correct choice).
A) force
B) work
C) angular momentum
D) linear momentum
E) power
F) rotational kinetic energy
G) moment of inertia
H) torque
The answer using kg/m2/s units denotes angular momentum. (option C).
The following are the units for the specified quantities:
A) Newtons of force (N)
B) Joules of Work (J)
C) The kilogram-meter-squared per second (kgm2/s) is unit of angular momentum
D) Linear momentum, expressed in kilograms per second (kg/s).
E) Watts (W) Power
F) Joules (rotational kinetic energy)
(G) Moment of inertia expressed in kilograms per square meter (kg/m2)
H) Newton-meters (Nm) of torque.
The quantity must have been momentum since the response had the units (kgm/s).
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What would likely happen if you placed a freshwater fish into seawater? Choose three answers. The fish would have no reason to try drinking seawater. The fish would need to urinate frequently. Water would osmose out of the fish and into the surrounding seawater. Water would osmose into the fish from the surrounding seawater. The fish might try to drink sewater but would have no way to deal with the salt. The fish would become dehydrated.
Placing a freshwater fish into seawater would result in c)water osmosing out of the fish and into the surrounding seawater, e)the fish becoming dehydrated, and potentially dying.
Freshwater fish have a higher concentration of ions in their bodies than the surrounding water, while seawater has a higher concentration of salt. When a freshwater fish is placed in seawater, water will move out of the fish's body in an attempt to balance the concentration of salt on both sides of the fish's cell membranes.
This can lead to dehydration, electrolyte imbalances, and potentially death. The fish may also try to drink seawater, which would only exacerbate the problem by introducing even more salt into its system. Therefore, it is not recommended to place freshwater fish into seawater.
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the first ionization energy of c is 11.3 ev. the first ionization energy of si should be:
The first ionization will most probably be around 19-20 eV
As we know that, when the atom is in gas phase and if we want to remove the outermost electron from that atom, then the energy required to achieve this is known as first ionization energy
Since, we know that in silicon valence electrons are further from the nucleus than in carbon due to shielding effect of it's inner electrons
Also in it's valence shell silicon has one more electron than carbon, so because of all these reasons, Silicon will have higher first ionization energy than carbon
From the estimation, we can analyze that the first ionization energy of silicon will be around 8-9 eV higher than that of Carbon
Since, the first ionization energy of carbon is given as 11.3 eV
So, the first ionization energy of Silicon will be 11.3 + 8 = 19.3 eV
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For Bdamp = 0.1 : What happens to the total energy of the system? what is the relationship between the kinetic and potential energy of the oscillator and the energy dissipated by damping?
Answer:
Explanation:
When Bdamp = 0.1, the oscillator is underdamped. That means that the damping force is not strong enough to stop the oscillations of the system, but it does cause the amplitude of the oscillations to decrease over time.
As the amplitude of the oscillations decreases, the total energy of the system also decreases. This is because the energy dissipated by the damping force is converted from the kinetic and potential energy of the oscillator into thermal energy, which is then dissipated into the surrounding environment. The rate of energy dissipation is proportional to the velocity of the oscillator, so the damping force is strongest when the oscillator is at its maximum amplitude and moving the fastest.
The relationship between kinetic and potential energy of the oscillator and the energy dissipated by damping can be seen mathematically in the equation:
E = 1/2 * K * A^2 + 1/2 * M * V^2
where E is the total energy of the system, K is the spring constant, A is the amplitude of the oscillator, M is the mass of the oscillator, and V is the velocity of the oscillator.
As the amplitude of the oscillator decreases due to damping, the potential energy term 1/2 * K * A^2 also decreases, while the kinetic energy term 1/2 * M * V^2 remains constant. The energy dissipated by damping is proportional to the velocity of the oscillator, which means that the damping force acts to decrease the kinetic energy of the oscillator over time.
Therefore, the energy dissipated by damping is converted from both the kinetic and potential energy of the oscillator into thermal energy, which causes the total energy of the system to decrease over time as the amplitude of the oscillations decreases.
What is the air density at a height of 2km in an atmosphere of
uniform air temp of 15 degrees C?
The air density at a height of 2km in an atmosphere of uniform air temperature of 15 degrees Celsius is approximately 0.944 kg/m³.
How to calculate the air densityThe air density at a height of 2km in an atmosphere of uniform air temperature of 15 degrees Celsius can be calculated using the ideal gas law.
The ideal gas law states that the pressure, volume, and temperature of a gas are related through the equation
PV = nRT,
where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
To calculate the air density, we need to rearrange the ideal gas law to solve for n/V, which is the number of moles of gas per unit volume.
This can be done by dividing both sides of the equation by V and then rearranging the terms:
n/V = P/(RT)
Now we can use this equation to calculate the air density at a height of 2km, where the pressure is lower than at sea level due to the decrease in atmospheric pressure with height.
Assuming a standard atmosphere, the pressure at 2km is approximately 80% of the sea level pressure, or 80 kPa.
The gas constant for air is approximately 287 J/(kg·K), and the temperature is 15+273 = 288 Kelvin.
Substituting these values into the equation above, we get:
n/V = (80 kPa) / (287 J/(kg·K) × 288 K) = 0.944 kg/m³
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a solenoid with 25 turns per centimeter carries a current of 35 ma. 1) what is the magnetic field in the interior of the coils? (express your answer to two significant figures.)
The magnetic field in the interior of the coils is approximately 0.028 T.
To find the magnetic field in the interior of the coils of a solenoid with 25 turns per centimeter and a current of 35 mA, you can use the formula B = μ₀ * n * I:
1. Convert the given values to standard units:
- Turns per centimeter (n): 25 turns/cm = 2500 turns/m
- Current (I): 35 mA = 0.035 A
2. Use the permeability of free space (μ₀) constant, which is 4π × 10^(-7) T m/A.
3. Plug the values into the formula:
B = (4π × 10^(-7) T m/A) * (2500 turns/m) * (0.035 A)
4. Calculate the magnetic field (B):
B ≈ 0.0275 T
5. Express the answer to two significant figures:
B ≈ 0.028 T
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tesla car (100 kwh battery, 0.17 kwh per km) drives at 100 km/h. what is the power output from the battery at this speed?
To calculate the power output from the battery of a Tesla car with a 100 kWh battery and consuming 0.17 kWh per km while driving at 100 km/h, we can use the following formula:
Power Output = Energy Consumption per Unit Distance x Speed
We need to convert the energy consumption from kWh/km to kWh/h, which can be done by multiplying by the speed:
Energy Consumption per Hour = Energy Consumption per Unit Distance x Speed
Energy Consumption per Hour = 0.17 kWh/km x 100 km/h = 17 kWh/h
Now we can calculate the power output:
Power Output = Energy Consumption per Hour / Battery Size
Power Output = 17 kWh/h / 100 kWh = 0.17 kW or 170 W
Therefore, the power output from the battery of a Tesla car with a 100 kWh battery and consuming 0.17 kWh per km while driving at 100 km/h is 170 W.
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Complete the following statement while ignoring any thermodynamic considerations. A candle may be considered a more efficient producer of light than a flashlight because itO converts chemical energy directly into lightO Maintenance costs are lower off-shoreO p-type seminconductorO The heat of the Sun drives large-scale movements of air
A candle may be considered a more efficient producer of light than a flashlight because it converts chemical energy directly into light. Option a is correct.
The statement "A candle may be considered a more efficient producer of light than a flashlight because it converts chemical energy directly into light" implies that the conversion of chemical energy into light is more efficient in candles than in flashlights. While this statement is technically correct, it ignores the fact that candles are not a practical or sustainable source of light for most applications.
Flashlights are more efficient and practical because they allow for easy control of the light source, can be easily turned on and off, and can be powered by rechargeable batteries. Furthermore, candles are not as bright or long-lasting as flashlights, and they pose a fire hazard. Therefore, the practical considerations of using candles versus flashlights must also be taken into account. Hence, option a is correct.
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A turntable turning at rotational speed 33 rpm stops in 50 s when turned off. The turntable's rotational inertia is 1.0 X 10^-2 kg - m^2. How large is the resistive torque that slows the turntable?
The resistive torque that slows the turntable is 6.92 × 10^−1 Nm.
We can use the equation:
torque = (final angular velocity - initial angular velocity) / time / rotational inertia
Where:
final angular velocity = 0 rad/s (since the turntable stops)
initial angular velocity = (33 rpm) x (2π/60) rad/s = 3.46 rad/s (convert rpm to rad/s)
time = 50 s
rotational inertia = 1.0 × 10^−2 kg m^2
Plugging in the values:
torque = (0 - 3.46) / 50 / 1.0 × 10^−2 = -6.92 × 10^−1 Nm
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determine the horizontal velocity va of a tennis ball at a so that it just clears the net at b. also, find the distance s where the ball strikes the ground.
The horizontal velocity, v_a = sqrt(2gh) and the distance s = d * sqrt(2h/g) / v_a.
To determine the horizontal velocity of the tennis ball at point a, we need to use the principle of conservation of energy. At point a, the ball has potential energy due to its height above the ground, but no kinetic energy. At point b, the ball has no potential energy but has some horizontal velocity, which we want to find.
Let's assume that the height of the net above the ground is h, and the distance from point a to point b is d.
Using the principle of conservation of energy, we can equate the potential energy at point a to the kinetic energy at point b:
mgh = (1/2)mv_a^2
where m is the mass of the tennis ball, g is the acceleration due to gravity, and v_a is the horizontal velocity of the ball at point a.
Simplifying this equation, we get:
v_a = sqrt(2gh)
where sqrt denotes the square root function.
To find the distance s where the ball strikes the ground, we need to use the equations of motion. We can assume that the ball is launched from point a with an initial vertical velocity of zero, and that it lands on the ground at point c with a final vertical velocity of zero.
Using the equation of motion for vertical motion, we can find the time t it takes for the ball to fall from point a to the ground:
h = (1/2)gt^2
Solving for t, we get:
t = sqrt(2h/g)
Using the equation of motion for horizontal motion, we can find the distance s that the ball travels before it strikes the ground:
s = d * v_a * t / (v_a^2 + v_c^2)
where v_c is the vertical velocity of the ball at point c.
Since the ball has zero vertical velocity at point c, v_c = 0, so the equation simplifies to:
s = d * t / v_a
Substituting the expression we derived for t, we get:
s = d * sqrt(2h/g) / v_a
Putting all the values together, we get:
v_a = sqrt(2gh)
s = d * sqrt(2h/g) / v_a
where g is the acceleration due to gravity (approx. 9.81 m/s^2). To get numerical values, we need to know the specific values of h, d, and the mass of the tennis ball.
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on a particular day the temperature monitoring system registered 6.5 cooling degree days. what does this mean?
On a particular day, the temperature monitoring system registered 6.5 cooling degree days. This means that the day's average temperature was 6.5 degrees above a specified base temperature, indicating a need for cooling energy to maintain a comfortable indoor environment.
Cooling degree days are a measure of how much cooling is required to maintain a certain indoor temperature on a particular day, relative to a baseline temperature. In this case, the temperature monitoring system recorded 6.5 cooling degree days, which means that the outdoor temperature was higher than the baseline temperature and required 6.5 units of cooling to maintain the desired indoor temperature. This information can be useful in assessing energy usage and costs for cooling systems.
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5 ptsa car is traveling at 90.0 km/hr the tires have a radius =38.4 cm.(a)what is the angular speed of the tire (in si units)?(b) what is the centripetal accelaration (m/s^2) of a piece of tire on the outer edge?
The angular speed of the tire is approximately 65.1 rad/s, and the centripetal acceleration of a piece of tire on the outer edge is approximately 1622.9[tex]m/s^2[/tex]. To find the angular speed and centripetal acceleration of a car's tire, we need to consider the car's linear speed and the tire's radius.
(a) To find the angular speed (in SI units), first convert the linear speed from km/hr to m/s:
90.0 km/hr * (1000 m/km) * (1 hr/3600 s) = 25 m/s.
Next, convert the tire's radius from cm to meters:
38.4 cm * (1 m/100 cm) = 0.384 m.
Now, use the formula for angular speed (ω):
ω = linear speed/radius
ω = 25 m/s / 0.384 m
ω = 65.1 rad/s (approximately)
(b) To find the centripetal acceleration ([tex]m/s^2[/tex]) of a piece of tire on the outer edge, use the formula:
Centripetal acceleration =[tex]ω^2[/tex]* radius
Centripetal acceleration = [tex](65.1 rad/s)^2[/tex] * 0.384 m
Centripetal acceleration ≈ 1622.9 [tex]m/s^2[/tex]
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if you can just barely see a 10th magnitude star in a 5 cm telescope, what magnitude star can you see in a 2.5 m telescope
A 10th magnitude star, a 2.5 m telescope should be able to see stars as faint as 12.5 magnitude.
Assuming the telescopes have the same optical quality and are observing under the same conditions, we can use the ratio of their aperture sizes to determine the difference in brightness (magnitude) of stars they can see.
The ratio of the aperture sizes is:
2.5 m / 0.05 m = 50
The brightness of a star is logarithmically related to its flux, so the ratio of the brightness is:
(50)^2.5 = 562.34
Therefore, a 2.5 m telescope can see stars that are about 2.5 magnitudes fainter than a 5 cm telescope.
So if a 5 cm telescope can barely see a 10th magnitude star, a 2.5 m telescope should be able to see stars as faint as 12.5 magnitude.
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the primary purpose of thermal mass in a passive solar space heating application is to:
The primary purpose of thermal mass in a passive solar space heating application is to store and release thermal energy in order to maintain a comfortable indoor temperature.
Thermal mass materials, such as concrete, brick, and stone, have high heat capacity, which means they can absorb and store a large amount of heat energy. During the day, when the sun is shining, the thermal mass absorbs the heat and stores it. As the indoor temperature cools down at night, the thermal mass releases the stored heat, keeping the indoor temperature more stable and reducing the need for additional heating. Thermal mass also helps to regulate temperature fluctuations by smoothing out temperature swings, creating a more comfortable and consistent indoor environment.
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A circuit contains a 1.00 × 103-Ω resistor and a 7.00 × 102-mH inductor in series.
Part A
What is the impedance of the circuit when a 3.00-kHz AC source is used?
Express your answer with the appropriate units.
Z= SubmitMy AnswersGive Up
The impedance of the circuit, when a 3.00-kHz AC source is used, is approximately 13,227.92 Ω.
A circuit contains a 1.00 × 10³ Ω resistor and a 7.00 × 10² mH inductor in series. To find the impedance of the circuit when a 3.00-kHz AC source is used, follow these steps:
1: Convert the inductor value to Henries (H) and the frequency to Hertz (Hz).
Inductor = 7.00 × 10² mH
= 7.00 × 10² × 10⁻³ H
= 0.7 H
Frequency = 3.00 kHz
= 3.00 × 10³ Hz
= 3000 Hz
2: Calculate the inductive reactance (XL) using the formula XL = 2πfL, where f is the frequency and L is the inductor value.
XL = 2π(3000 Hz)(0.7 H)
= 2π(2100)
≈ 13194.68 Ω
3: Determine the impedance (Z) using the formula Z = √(R² + XL²), where R is the resistor value.
Z = √((1.00 × 10³ Ω)² + (13194.68 Ω)²)
≈ √(1000000 + 174092029.66)
≈ √175092029.66
≈ 13227.92 Ω
The impedance of the circuit, when a 3.00-kHz AC source is used, is approximately 13,227.92 Ω.
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