a. The effective resistance of a pocket calculator through which 0.200 mA flows isd 6.75 x 10^3 ohms or 6.75 kohms.
b. The power dissipated is 2.7 x 10^-6 W or 2.7 μW
c. The total energy spent is 7.29 μJ or 7.29 x 10^-6 J.
How to find the effective resistance?a) Let's assume that the pocket calculator has a constant resistance, R. Using Ohm's law, we can calculate the effective resistance:
V = IR
where V is the voltage across the pocket calculator and I is the current flowing through it.
We know that the current flowing through the pocket calculator is 0.200 mA, which is equivalent to 0.200 x 10^-3 A. We also know that the voltage across the pocket calculator is equal to the voltage of the battery, which is 1.35 V.
Therefore, the effective resistance is:
R = V / I = 1.35 V / 0.200 x 10^-3 A = 6.75 x 10^3 ohms or 6.75 kohms
b) To calculate the power dissipated, we can use the formula:
P = VI = I^2R = V^2 / R
where P is the power dissipated, V is the voltage across the pocket calculator, I is the current flowing through it, and R is the effective resistance.
We know that the current flowing through the pocket calculator is 0.200 mA and the effective resistance is 6.75 kohms. Using the formula, we get:
P = (0.200 x 10^-3 A)^2 x 6.75 x 10^3 ohms = 2.7 x 10^-6 W or 2.7 μW
c) To calculate the total energy spent, we need to use the formula:
E = Pt
where E is the energy spent, P is the power dissipated, and t is the time.
We know that the power dissipated is 2.7 μW, and we need to calculate the time in seconds, so we convert 45 minutes to seconds:
t = 45 minutes x 60 seconds/minute = 2700 seconds
Using the formula, we get:
E = 2.7 μW x 2700 seconds = 7.29 μJ or 7.29 x 10^-6 J
Therefore, the total energy spent by the pocket calculator in 45 minutes is 7.29 μJ or 7.29 x 10^-6 J.
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What magnitude point charge creates a 80,000 n/c electric field at a distance of 0.285 m?
The magnitude of the point charge that creates an electric field of 80,000 N/C at a distance of 0.285 m is approximately 2.057 x 10⁻⁶ C.
To determine the magnitude of the point charge that creates an electric field of 80,000 N/C at a distance of 0.285 m, we can use the formula for the electric field strength due to a point charge.
The formula is given by: E = k x (q / r²)
where:
- E is the electric field strength,
- k is the electrostatic constant (k = 8.99 x 10⁹ N m²/C²),
- q is the magnitude of the point charge, and
- r is the distance from the point charge.
In this case, we are given that the electric field strength is 80,000 N/C and the distance is 0.285 m.
Plugging these values into the formula, we can solve for the magnitude of the point charge (q):
80,000 N/C = (8.99 x 10⁹ N m²/C²) x (q / (0.285 m)²)
To isolate q, we can multiply both sides of the equation by (0.285 m)² and divide by 8.99 x 10⁹ N m²/C²:
q = (80,000 N/C) x (0.285 m)² / (8.99 x 10⁹ N m²/C²)
Simplifying this expression, we find:
q ≈ 2.057 x 10⁻⁶ C
So, the magnitude of the point charge that creates an electric field of 80,000 N/C at a distance of 0.285 m is approximately 2.057 x 10⁻⁶ C.
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A truck pulls a trailer on a flat stretch of road. The forces acting on the trailer are
the force due to gravity (250 000 N downward), the force exerted by the road
(250 000 N upward), and the force exerted by the cable connecting the wailer to
the truck (20 000 N to the right). The forces acting on the truck are the force due to
gravity (80 000 N downward), the force exerted by the road (80 000 N upward), the
force exerted by the cable (20 000 N to the left), and the force causing the truck to
move forward (26 400 N to the right).
The net vertical force on the trailer is 0, while the net horizontal force on the trailer is 20,000 N to the right.
The net vertical force on the truck is 0, while the net horizontal force on the truck is 6,400 N to the right.
The given parameters;
the trailer:
force on the trailer due to gravity, Fg = 250,000normal force on the trailer due to the road, N = 250,000 Nhorizontal force on the trailer, Fx = 20,000 N to the rightthe truck:
force on the truck due to gravity, Fg = 80,000 Nnormal force on the truck due to the road, N = 80,000 Nleft horizontal force on the truck, Fx = 20,000 Nright horizontal force on the truck, Fx = 26,400 NThe net force on each vehicle is calculated as follows;
for the trailer:
Net vertical force is calculated as;
\(\Sigma F_y = 250, 000 \ N - 250,000 \ N = 0\)
Net horizontal force is calculated as;
\(\Sigma F_x = 20,000 \ N\)
for the truck;
Net vertical force is calculated as;
\(\Sigma F_y =80,000 \ N - \ 80,000 \ N = 0\)
Net horizontal force is calculated as;
\(\Sigma F_x = 26,400 \ N - \ 20,000 \ N = 6,400 \ N \ to \ the \ right\)
"Your question is not complete, it seems to be missing the following information;"
find the net force on each vehicle.
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a force of 8 n is applied for 4 m to a 12 kg box at an angle of 150 degrees with respect to the displacement.
According to the given question, a force of 8 N is applied at an angle of 150 degrees with respect to the displacement of a 12 kg box. This means that the force is not being applied in the same direction as the displacement of the box.
In order to calculate the work done, we need to first determine the component of the force in the direction of the displacement. To do this, we can use trigonometry to find the cosine of the angle between the force vector and the displacement vector.
Once we have this value, we can multiply it by the magnitude of the force and the distance traveled to get the work done. It is important to note that work is a scalar quantity and is measured in joules.
Therefore, the final answer will be in joules. In this case, the work done will be less than if the force was applied in the same direction as the displacement.
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A forward force acting on the axle accelerates a rolling wheel on a horizontal surface. if the wheel does not slide the frictional force of the surface on the wheel is:______.
If the wheel is rolling without sliding on a horizontal surface, the frictional force between the surface and the wheel is static friction.
The static frictional force opposes the tendency of the wheel to slide. In this case, the forward force acting on the axle provides the torque necessary to accelerate the wheel. As the wheel accelerates, the static frictional force adjusts to match the force needed to prevent sliding.
The magnitude of the static frictional force can be calculated using the equation:
Frictional force = μs * Normal force,
where μs is the coefficient of static friction and Normal force is the perpendicular force exerted by the surface on the wheel.
Since the wheel is not sliding, the static frictional force is equal to the force exerted on the wheel. Therefore, the frictional force of the surface on the wheel is equal to the forward force acting on the axle.
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Which mathematically describes the wave properties of electrons?.
Answer:
On Waves. Quantum mechanically, an electron can be described by a wave function oscillating in space and time that has mean values equal to the expectation values of observables corresponding to given operators. ... Electrons are fermions. They are charged particles. in short the quantum theory
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A metal sphere has a charge of +5.0 C. What is the net charge after 1.00 1014 electrons have been placed on it?
The net charge on the metal sphere after adding 1.00 × 10¹⁴ electrons is 3.596 × 10⁻⁵ C. This is calculated by adding the initial charge of +5.0 C to the charge added by the electrons (-1.602 × 10⁻¹⁹ C per electron).
The net charge on the sphere is the sum of the initial charge and the charge added by the electrons. The charge added by the electrons is equal to the number of electrons multiplied by the charge on each electron (which is -1.602 × 10⁻¹⁹ C).
So, the net charge Qf is:
Qf = Qi + Ne * (-e)
where Qi is the initial charge (+5.0 C), Ne is the number of electrons added (1.00 × 10¹⁴), and -e is the charge on each electron (-1.602 × 10⁻¹⁹ C).
Substituting the values, we get:
Qf = 5.0 C + 1.00 × 10¹⁴ * (-1.602 × 10⁻¹⁹ C) = 3.596 × 10⁻⁵ C
Therefore, the net charge on the sphere after 1.00 × 10¹⁴ electrons have been placed on it is 3.596 × 10⁻⁵ C.
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I need answer ASAP, Will mark brainliest
Q. A car travels along a circular racing track at a constant speed of 100km/hr. Does it have uniform motion?
Answer:
Yes. If a car travels in a circular path with constant speed, its motion is called uniform circular motion
Explanation:
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Answer:
:)
Explanation:
A two-resistor series circuit has an applied voltage of 100 V. The voltage across one of the resistors is 40 V. The voltage across the other resistor is _____.
Given that you have a two-resistor series circuit with an applied voltage of 100 V, we can use the principle of voltage distribution in a series circuit to determine the voltage across the second resistor.
In a series circuit, the total applied voltage is distributed across all the resistors. The voltage across each resistor is directly proportional to its resistance. In this case, we know the voltage across one resistor is 40 V.
Using the principle of voltage distribution, we can calculate the voltage across the other resistor as follows:
Total applied voltage = Voltage across resistor 1 + Voltage across resistor 2
100 V = 40 V + Voltage across resistor 2
Now, we can solve for the voltage across resistor 2:
Voltage across resistor 2 = Total applied voltage - Voltage across resistor 1
Voltage across resistor 2 = 100 V - 40 V
Voltage across resistor 2 = 60 V
So, the voltage across the other resistor in the series circuit is 60 V.
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300 watts of power is produced over 15 seconds. How much work was done transferring the power?
Answer:
4500
Explanation:
Formula: power x time
300 x 15 = 4500
what would have to be the mass of this asteroid for the day to become 20.0% longer than it presently is as a result of the collision? assume that the asteroid is very small compared to the earth and that the earth is uniform throughout. express your answer in terms of the earth's mass m .
The mass of the asteroid for the day to become 20% longer than it presently is as a result of the collision is three times the mass of the Earth.
When an asteroid collides with Earth, the day may become longer or shorter. The asteroid can cause Earth's rotation to slow down, leading to longer days or it may increase Earth's rotation speed, leading to shorter days. To find the mass of the asteroid for the day to become 20% longer than it presently is as a result of the collision, we can use the law of conservation of angular momentum. Angular momentum is the product of mass, velocity, and radius of the rotating object.
According to the law of conservation of angular momentum, the angular momentum of an object is conserved if there is no net external torque acting on it before and after a collision or any other event.
Mathematically, angular momentum is given as:
L = mvr
Where L = angular momentum, m = mass, v = velocity, r = radius of rotation. As the asteroid is very small compared to the Earth, we can assume that the Earth's mass remains constant before and after the collision. Therefore, the angular momentum of the Earth before and after the collision must be the same. Hence, we have:
L initial = L final
m asteroid x v asteroid x r asteroid = (m earth ) x (v earth ) x (r earth )
The speed of rotation of the Earth and the radius of rotation remains constant. Thus, we can substitute
v earth x r earth = constant in the above equation.
m asteroid x v asteroid = (m earth ) x constant x 1.2 {20% increase in length of day = 1.2}
m asteroid/m earth = 1.2/0.4
m asteroid/m earth = 3
The mass of the asteroid for the day to become 20% longer than it presently is as a result of the collision is three times the mass of the Earth.
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A number line goes from 0 to 30. Closed circles are at 6 and 25. A line is drawn from point 6 to point 25. Ari is swimming a 25-meter race. After swimming 6 meters, she catches up to Amanda in a ratio of 7:3 from the 6-meter mark. At what meter mark does Ari catch up to Amanda? Round to the nearest tenth, if necessary. Ari catches up to Amanda at meters.
The position on the meter mark where Ari catches up with Amanda is 19.3 m.
The given parameters:
Range of the number line, = 0 to 30Position of the closed circles, = 6 and 25The ratio between the initial position and final position of Ari = 7:3The distance between 6 m mark and 25 m mark is calculated as follows;
\(d = 25 \ m - \ 6 \ m\\\\\d = 19 \ m\)
The distance traveled by Ari before catching up with Amanda is calculated as follows;
total ratio = 7 + 3 = 10
\(distance = \frac{7}{10} \times 19 \ m\\\\distance = 13.3 \ m\)
The position of Ari from the 6 m mark is calculated as follows;
\(position = 6 \ m \ + \ 13.3 \ m\\\\position = 19.3 \ m\)
Thus, the position on the meter mark where Ari catches up with Amanda is 19.3 m.
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Answer:
The above answer is correct! The answer is 19.3 meters :)
Explanation:
adding a ss for proof!
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One scientist suggests that out of the different possible locations, they should design the model and build it at the equator recieves the most intense solar radiation. Which if the following is the most appropriate critique for the scientist's suggestion?
A. Earth's equator is not hot enough to simulate the Martian daytime.
B. The high mountain top gets the same amount of radiation as the equator, but with atmospheric conditions that are more similar to Mars.
C. The equator has deserts that are actually too dry compared to Mars.
D. The Antarctica has the same nighttime temperature as Mars, but with a similar amount of ice compared to the equator.
Answer:
B.
I think.
Explanation:
Mars doesn't have that much of an atmosphere!
Have a great day!
1) longer storms should print in the correct order, with 200ms between each event in the array and 400ms between each flash! and boom!
For accurate printing of longer storms, it is important to ensure that the events in the array are arranged in the correct order, with a 200ms delay between each event and a 400ms delay between each flash and boom.
When printing longer storms, it is crucial to maintain the correct order of events in the array. By arranging the events in the correct sequence, the storm will be printed accurately, providing a realistic representation. To achieve this, a delay of 200ms should be implemented between each event in the array. This delay ensures that each event is printed with the appropriate timing, creating a smooth and coherent storm simulation.
Additionally, it is necessary to introduce a 400ms delay between each "flash" and "boom" in the storm. This delay creates a distinct gap between these two elements, mimicking the natural occurrence of a lightning flash followed by the accompanying thunder. By allowing sufficient time between the flash and boom, the printed storm will convey a more realistic and immersive experience.
In summary, to accurately print longer storms, it is essential to maintain the correct order of events in the array and introduce appropriate delays. A 200ms delay between each event ensures accurate timing, while a 400ms delay between each flash and boom replicates the natural occurrence of lightning and thunder. Following these guidelines will result in a more realistic representation of storms when printing them.
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How does the motion of gas particles help determine the other properties of gases, like temperature, pressure, and volume?
A body of mass 12kg traveling at 4.2m/s collides with a second body of mass 18kg at rest. Calculate their common velocity if the bodies coalesce after collision
Answer:
.
The common velocity of the two bodies after the collision is 2.7 m/s.
This can be calculated using the equation of conservation of momentum:
m1v1 + m2v2 = (m1 + m2)v
where m1 is the mass of the first body (12 kg), v1 is the velocity of the first body (4.2 m/s), m2 is the mass of the second body (18 kg), v2 is the velocity of the second body (0 m/s), and v is the common velocity of the two bodies after the collision.
Substituting the given values into the equation, we get:
12(4.2) + 18(0) = (12 + 18)v
Solving for v, we get:
v = 2.7 m/s
Your supervisors at A&L Engineering have tasked you with evaluating the durability of three common materials used in the design of cell phone cases
A&L Engineering, as an engineer, you've been tasked with evaluating the durability of three common materials used in the design of cell phone cases.
These materials include:Carbon FiberPolycarbonateTPUExplanation:Carbon fiber is a lightweight, durable, and corrosion-resistant composite material. It is often used in the aerospace, automotive, and sporting goods industries.Polycarbonate is a thermoplastic polymer that is strong, shatter-resistant, and lightweight. It is often used in the production of CDs, DVDs, and eyeglass lenses.
TPU (thermoplastic polyurethane) is a flexible, soft material that is abrasion-resistant and provides excellent impact protection. It is often used in the production of phone cases, as well as sporting equipment and medical devices.To evaluate the durability of these materials, you can conduct a series of tests to measure their resistance to impacts, scratches, and bending.
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A ferry boat is 2.0 m wide and 4.0 m long. When a truck pulls onto it, the boat sinks 2.00 cm in the water. What is the weight of the truck?DENSITY OF WATER IS 1000 Kg/m^3
Answer:
156,800 N
Explanation:
Given: Width = 2.0 m Length = 4.0 m Depth = 2.00 cm. Density of water = 1000 Kg/m³
To find: What is the weight of the truck?
Formula: \(F = m\) × \(9.8 m/s^2\)
Solution: Weight is a measure of the force of gravity pulling down on an object. It depends on the object's mass and the acceleration due to gravity, which is 9.8 m/s² on Earth. F is the object's weight in Newtons (N) and m is the object's mass in kilograms.
Firstly, multiply the length, width, and depth.
\(2.0\) × \(4.0\) × \(2.00\) \(= 16\)
Next, the weight of the truck is found by multiplying the density of water, the result found by multiplying the length, width, and depth, and the formula;
\(1000 kg/m^3\) × \(16\) × \(9.8m/s^2\)\(= 156,800\)
Therefore, the weight of the truck is 156,800 N
Suppose you sketch a model of an atom using the ones here as a guide. how would you build a model that is ionized? how would you build a model that is radioactive? (site 1)
To build a model of an ionized atom, you would need to represent the presence of an ion, which is an atom that has gained or lost electrons. Here's how you can do it:
1. Start with a base representing the nucleus of the atom, which consists of protons and neutrons.
2. Choose an element for your model and determine its atomic number (number of protons) and atomic mass (number of protons plus neutrons).
3. For an ionized atom, you need to indicate the gain or loss of electrons. If the ion has gained electrons, add extra negatively charged particles (representing the extra electrons) around the nucleus. If the ion has lost electrons, remove some of the negatively charged particles.
4. Make sure the total number of protons remains the same, as this determines the element.
5. Consider using different colors or symbols to represent the electrons and protons, which will make it easier to distinguish them.
To build a model of a radioactive atom, you would need to represent the presence of unstable atomic nuclei that undergo radioactive decay. Here's how you can do it:
1. Start with a base representing the nucleus of the atom, which consists of protons and neutrons.
2. Choose an element for your model and determine its atomic number (number of protons) and atomic mass (number of protons plus neutrons).
3. Radioactive atoms have unstable nuclei, so you can represent this by showing some of the particles in the nucleus as being "emitting" or "escaping" from the nucleus. This can be done by drawing or attaching small arrows or lines coming out of the nucleus.
4. Additionally, you can represent the emitted particles such as alpha particles, beta particles, or gamma rays by drawing or attaching symbols or labels to these particles.
5. Keep in mind that the total number of protons should remain the same to maintain the identity of the element.
Remember to label and indicate the different parts of your atom model clearly.
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To build an ionized atom model, add or remove electrons to create a net positive or negative charge. To build a radioactive atom model, attach a symbol representing the radioactive decay process.
Explanation:To build a model of an atom that is ionized, you would need to add or remove electrons from the atom. Ionization occurs when an atom gains or loses electrons, resulting in a net positive or negative charge. For example, if you want to model an ionized sodium atom, you would remove one electron from the outermost energy level. This would leave you with a sodium ion (Na+) that has a net positive charge.
To build a model of an atom that is radioactive, you would need to add a separate component to represent the radioactive decay process. Radioactive decay occurs when the nucleus of an atom spontaneously breaks down, emitting radiation in the process. You can represent this by attaching a small particle or symbol to the atom model to show the emission of radiation. For example, if you want to model a radioactive carbon atom, you can attach a small symbol representing the decay process to the carbon atom.
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The number of protons plus the number of neutrons in an atom is equal to its
Answer:
Atomic Mass
Explanation:
10. A moving car has an internal energy of 900 J. Pressing the accelerator adds 150 J of energy to the car,
and some energy is lost. The system now has an internall energy of 975 J. What is the AQ?
The heat loss (AQ) is 75 J.
What is the heat lost?
The change in internal energy of the car is:
ΔU = 975 J - 900 J = 75 J
The energy added by pressing the accelerator is:
Q = 150 J
According to the first law of thermodynamics, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:
ΔU = Q - W
Assuming no work is done on the system, the heat loss can be calculated as:
Q - ΔU = 150 J - 75 J = 75 J
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Question 16 During a rocket launch, the action force is considered the force of explosion from the burning fuel and expanding gases. Which of the following would be considered the reaction force?
The reaction force to the action force during a rocket launch would be C. the force exerted by the ground or launch pad on the rocket.
How to illustrate the force?The force that the ground or launch pad applies to the rocket during a rocket launch will act as a reaction force to the action force. The rocket is propelled upward by the force of explosion caused by the burning fuel and expanding gases. The force that keeps the rocket grounded and keeps it from moving is known as the reaction force, and it is the force that the launch pad or ground exerts in response to this action force.
Equal in magnitude but directed in the opposite direction, the action and reaction forces act on various objects. The reaction force affects the ground or launch pad, whereas the action force affects the rocket.
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Complete question
During a rocket launch, the action force is considered the force of explosion from the burning fuel and expanding gases. Which of the following would be considered the reaction force?
A. The starting force
B. The force of the explosion
C. The force exerted by the ground or launch pad on the rocket.
A circular area with a radius of 7.00 cm lies in the xy-plane. What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field with For related problem-solving tips and strategies, you a magnitude of 0.270 T in the +z-direction? may want to view a Video Tutor Solution of Magnetic flux calculations. \& Incorrect; Try Again; 4 attempts remaining Part B What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magnitude of 0.270 T ), now at an angle of 51.9°from the +z-direction? What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magntiude of 0.270 T ), now in the +y-direction?
The magnitude of the magnetic flux through the circular area is approximately:
Part A: 0.0124 Wb
Part B: 0.0087 Wb
Part C: 0 Wb
To calculate the magnetic flux through the circular area, we can use the formula:
Φ = B * A * cos(θ)
where Φ is the magnetic flux, B is the magnetic field, A is the area, and θ is the angle between the magnetic field and the normal to the area.
Part A:
Given:
B = 0.270 T,
A = π * (0.07 m)²,
and θ = 0° (since the magnetic field is in the +z-direction).
Putting in the values:
Φ = (0.270 T) * (π * (0.07 m)²) * cos(0°)
Φ = 0.270 T * 0.0154 m² * 1
Φ ≈ 0.0124 Wb (webers)
Part B:
Given: B = 0.270 T, A = π * (0.07 m)², and θ = 51.9° (angle from the +z-direction).
Putting in the values:
Φ = (0.270 T) * (π * (0.07 m)²) * cos(51.9°)
Φ = 0.270 T * 0.0154 m² * cos(51.9°)
Φ ≈ 0.0087 Wb (webers)
Part C:
Given:
B = 0.270 T,
A = π * (0.07 m)², and
θ = 90° (since the magnetic field is in the +y-direction).
Plugging in the values:
Φ = (0.270 T) * (π * (0.07 m)²) * cos(90°)
Φ = 0.270 T * 0.0154 m² * 0
Φ = 0 Wb (webers)
Therefore, the magnitude of the magnetic flux through the circular area is approximately:
Part A: 0.0124 Wb
Part B: 0.0087 Wb
Part C: 0 Wb
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Which scenario would provide the least biased results?
Responses
surveying people at a concert about their favorite bands
surveying people at a concert about their favorite bands
surveying every 10th person who enters a mall about their favorite type of cookie
surveying every 10, th, person who enters a mall about their favorite type of cookie
surveying people at a sporting event about their favorite team
surveying people at a sporting event about their favorite team
surveying 6th grade students about the location of the 8th grade dance
Surveying every 10th person who enters a mall about their favorite type of cookie.
where was the pompeii worm was discovered near
Answer: A Hydrothermal vent
Explanation:
What is the impulse experienced by a 24kg dog as he speeds up from 2m/s to 6m/s
Given
m = 24kg
vi = 2 m/s
vf = 6 m/s
Procedure
Impulse = Change in momentum
\(\begin{gathered} I=m\Delta v \\ I=m(v_f-v_i) \\ I=24\cdot(6-2) \\ I=96\operatorname{kg}m/s \end{gathered}\)The answer would be I = 96 kg*m/s
A piece of warm concrete is placed in a cold-water tank, and energy flows between the concrete and the water. Which way does the energy flow in this system?
Answer:
Heat flows from hot to cold objects. When a hot and a cold body are in thermal contact, they exchange heat energy until they reach thermal equilibrium, with the hot body cooling down and the cold body warming up. This is a natural phenomenon we experience all the time.
Explanation:
identify a source of microwaves
Explanation:
Microwave sources include artificial devices such as circuits, transmission towers, radar, masers, and microwave ovens, as well as natural sources such as the Sun and the Cosmic Microwave Background. Microwaves can also be produced by atoms and molecules.
Answer:
Stars, including the Sun, are natural microwave sources.
Explanation: Under the right conditions, atoms and molecules can emit microwaves. Man-made sources of microwaves include microwave ovens, masers, circuits, communication transmission towers, and radar. Either solid state devices or special vacuum tubes may be used to produce microwaves.
Charge is distributed within a solid sphere of radius r_0 in such a way that the charge density is a function of the radial position within the sphere of the form: rho_E(r)=rho_0(r/r_0).a) If the total charge within the sphere is Q (and positive), what is the magnitude of the electric field everywhere within the sphere in terms of Q, r_0, and the radial position r ?Express your answer in terms of the variables Q, r_0, r, and appropriate constants.b) What is the direction of the electric field everywhere within the sphere?Choose betweeni) radially inwardORii) radially outward
(a) The electric field inside the sphere is given by:
E = ρ_E(r) / 3ε₀r
E = (3Q/(4πr₀³)) * (r/r₀) / 3ε₀r
E = Q/4πε₀r₀0³
(b)The electric field at every point inside the sphere is directed radially inwards.
How to calculate the charge density?(a)The electric field generated by a charge is given by:
E=kQ/r²
Here,k is Coulomb's constant = 9 × 10⁹ Nm²/C²
From Gauss’s law,
Qenc = ε₀E×4πr²
Where ε₀ is the permittivity of free space=8.85×10⁻¹² C²/Nm².
For a uniform spherical charge distribution of radius R, Charge density can be given as :
ρ = Q/V = Q/(4/3πr³)
Q = ρ×4/3πr³
Electric Field at a distance r from the center will be given by:
E = 1/4πε₀ x Q/r²
E = 1/4πε₀ x (ρ×4/3πr³)/r²
E = ρ/3ε₀r
The charge density is given by:
ρE(r) = ρ_0(r/r_0)
ρ₀ = Q/V = Q/(4/3πr³)
ρE(r) = (Q/(4/3πr³)) x (r/r_0)
ρE(r) = (3Q/(4πr_0³)) * (r/r_0)
(a) E = Q/4πε₀r₀³ x r/r₀ x 1/3ε₀r(b) The direction of the electric field inside the sphere is radially inward.
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A microphone is attached to a spring that is suspended from the ceiling, as the drawing indicates. Directly below on the floor is a stationary 375-Hz source of sound. The microphone vibrates up and down in simple harmonic motion with a period of 1.80 s. The difference between the maximum and minimum sound frequencies detected by the microphone is 2.75 Hz. Ignoring any reflections of sound in the room and using 343 m/s for the speed of sound, determine the amplitude (in m) of the simple harmonic motion.
Answer:
\(0.361\ \text{m}\)
Explanation:
\(f_s\) = Frequency of source = 375 Hz
\(\Delta f\) = Difference between the maximum and minimum sound frequencies = 2.75 Hz
v = Speed of sound in air = 343 m/s
T = Time period = 1.8 s
\(v_m\) = Maximum speed of the microphone
We have the relation
\(\Delta f=2f_s\dfrac{v_m}{v}\\\Rightarrow v_m=\dfrac{\Delta fv}{2f_s}\\\Rightarrow v_m=\dfrac{2.75\times 343}{2\times 375}\\\Rightarrow v_m=1.26\ \text{m/s}\)
Amplitude is given by
\(A=\dfrac{v_mT}{2\pi}\\\Rightarrow A=\dfrac{1.26\times 1.8}{2\pi}\\\Rightarrow A=0.361\ \text{m}\)
The amplitude of the simple harmonic motion is \(0.361\ \text{m}\).
Explain how the mass of a planet affects the motion of the planet around the sun? Justify your response in two or more
complete sentences in the essay box below.
The mass of a planet affects the motion of the planet around the sun through the force of gravity.
How does mass affect motion of planets?According to Newton's law of universal gravitation, every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
The greater the mass of a planet, the stronger its gravitational pull and the more it affects the motion of other celestial objects in its vicinity, including its own orbit around the sun.
In summary, the mass of a planet is a crucial factor that determines its motion around the sun, as it affects the strength of the gravitational forces acting on the planet and its orbit.
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