The magnitude of the force is 1.8 x 10-16 N. The magnetic force on the electron is 1.2 x 10-14 N. The magnitude of the force acting on the charge is 0.04 N. The magnetic flux will be 0.
1. The direction of the magnetic force on an electron traveling to the north with a speed of 3.5 x 106 m/s in a magnetic field of strength 0.030 T directed to the left can be determined using the right-hand rule.
When the thumb of the right hand points in the direction of the velocity vector, and the fingers point in the direction of the magnetic field vector, the direction of the magnetic force is perpendicular to both and can be found by the direction of the palm.
In this case, the force will be directed downward, and its magnitude can be calculated using the formula \(F = qvBsin\theta\) , where q is the charge of the electron, v is its velocity, B is the magnetic field strength, and θ is the angle between the velocity and magnetic field vectors. The magnitude of the force in this case is 1.8 x 10-16 N.
2. The magnetic force on an electron traveling perpendicular to the Earth's magnetic field can also be calculated using the formula F = qvB. In this case, the force is directed perpendicular to both the velocity and magnetic field vectors and is given by
\(F = (1.6 \times 10-19 C) \times (2.0 \times 105\; m/s) \times (5.9 \times 10-5 T)\)
F = 1.2 x 10-14 N.
3. In this problem, a charged particle with charge \(q = 4\mu C\) is moving with a velocity of 2 x 103 m/s at an angle of 30o to a uniform magnetic field of strength B = 100 F.
The force on the charged particle can be calculated using the formula \(F = qvBsin\theta\), where θ is the angle between the velocity and magnetic field vectors. Substituting the values, we get
\(F = (4 \times 10-6 C) \times (2 \times 103\;m/s) \times (100 T) \times sin 30^{\circ}\)
F = 0.04 N.
4. The magnetic flux through a circular loop of area 5 x 10-2m2 rotating about its diameter perpendicular to a uniform magnetic field of strength 0.2 T can be calculated using the formula \(\phi = BAcos\theta\), where A is the area of the loop, B is the magnetic field strength, and θ is the angle between the magnetic field vector and the normal to the plane of the loop.
Since the loop is rotating about its diameter perpendicular to the magnetic field, the angle between the two vectors is 90, and the flux is given by \(\phi = (0.2 T) \times (5 \times 10-2\; m2) \times cos 90^{\circ} = 0\).
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is sliding or static friction greater in magnitude?
Answer: static friction
Explanation:
During sliding, contact points do not get enough time to get interlocked properly. Therefore, less friction. But, when the object is at rest, the surfaces interlock well, therefore friction is more. This explains why sliding friction is less than static friction.
A car leaves a city with a speed of 90 mph. Three hours later and out of the same city another car in pursuit of the first leaves with a speed of 120 mph. Find the time it takes for the second car to reach the first.
Answer:
9 hours
Explanation:
When the 2nd car catches up to the first, both cars will have gone the same distance.
Distance = rate x time
Distance car 1 traveled when car 2 catches up = 90 mph(3 hr + t)
Distance car 2 traveled when it catches up to car 1 = 120t
90(3 + t) = 120t
270 + 90t = 120t
30t = 270
t = 270/30 = 9 hrs
Therefore, 12 hours after car 1 leaves the city and 9 hours after car 2 leaves the same city, they meet up.
To prove it:
90(12) = 120(9) = 1080 Car 2 catches up to Car 1 1080 miles from the city
if the length of the centrifuge arm is 15.0 m m , at what speed is the rider moving when she experiences 10 g's?
The rider is moving at a speed of 12.2 meters per second when she experiences 10 g's.
The speed at which a rider experiences 10 g's (10 times the acceleration due to gravity) on a centrifuge can be calculated using the formula:
speed = (g * r)
Where g is the acceleration due to gravity (9.8 m/s^2) and r is the radius of the centrifuge arm (in this case, 15.0 m).
Plugging in the numbers, we get:
speed = (9.8 * 15.0) = (146) = 12.2 m/s
It's important to note that high g-forces can have serious health effects, and centrifuges are often used to simulate conditions experienced by pilots, astronauts, and other people who are subjected to high g-forces.
The g-forces experienced on a centrifuge can be used to determine the limits of human tolerance and to develop measures to protect people from the harmful effects of high g-forces.
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let: ua and uo are the electric potential energies at point a and the origin, respectively. at which point is the potential energy larger?
If you have two points in an electric field, one at point "ua" and one at the origin (or "uo"), the potential energy at point "ua" will be larger than the potential energy at the origin.
The electric potential energy at a point in an electric field is defined as the amount of work required to move a point charge from the origin to that point. The electric potential energy increases as you move away from the origin in the direction of the electric field.
Therefore, if you have two points in an electric field, one at point "ua" and one at the origin (or "uo"), the potential energy at point "ua" will be larger than the potential energy at the origin. This is because it takes more work to move a point charge from the origin to point "ua" than it does to move it from the origin to the origin.
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What are two safety devices used in circuits and how do they work?
Two essential safety devices used in electrical circuits are circuit breakers and fuses. These devices protect circuits and electrical equipment from damage caused by excessive current flow.
Which could result from overloads or short circuits. Circuit breakers are electro mechanical switches designed to automatically interrupt the flow of current when it exceeds a predetermined limit. They consist of a bimetallic strip or an electro magnetic coil that is sensitive to the amount of current passing through it. When the current exceeds the specified threshold, the strip bends or the coil activates a mechanism that trips the breaker, opening the circuit and stopping the flow of electricity. Circuit breakers can be reset manually after the issue is resolved, making them reusable and convenient.
Fuses, on the other hand, are one-time use safety devices that consist of a thin wire or metal strip enclosed in a protective casing. When the current in the circuit exceeds the fuse's rating, the excessive heat generated causes the wire or strip to melt, breaking the circuit and preventing further damage. Once a fuse has blown, it must be replaced with a new one of the appropriate rating.
The ability of a physical system to carry out work is known as energy. Electrical energy is the capacity of the charged particles in an atom to start an action or move an object. The movement of electrons between atoms results in the production of electrical energy. In order to create electricity or other grid services when needed, an electro-chemical device known as a battery energy storage system first charges energy from the grid or a power plant. In an electric circuit, the battery converts chemical energy into electrical energy while also supplying power to the other components of the circuit.
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Mr. Krabs created a secret ingredient for breath mint that he thinks will "cure" the bad breath people
get from eating crabby patties at the Krusty Krab. He asked 100 customers with a history of bad breath
to try his new breath mint. He had fifty customers (Group A) eat a breath mint after they finished
eating a crabby patty. The other fifty (Group B) also received a breath mint after they finished the
sandwich, however, it was just a regular breath mint and did not have the secret ingredient. Both
breath mint that would cure their bad breath. Two hours
groups were told that they were getting the
after eating the crabby patties, thirty customers in Group A and ten customers in Group B reported
having better breath than they normally had after eating crabby patties.
2. What is the independent variable?
3. What is the dependent variable?
4. What should Mr. Krabs' conclusion be?
5. Why do you think 10 people in group B reported fresher breath?
The answers to the following questions are 1. Group B, 2. secret ingredient, 3. bad breath, 4. not effective cent percent, 5. the placebo effect.
1. The group of people who received the normal mint which does not contain Mr. krab's secret ingredient for breath mint is the control group. So, Group B of people are in the control group.
2. Independent variable in the one for which the research is being conducted. So in this case the secret ingredient in the breath mint is the independent variable.
3. Dependent variable is the one that affects the result of the research. So, the bad breath, in this case, is the dependernt variable.
4. The Group A of fifty people received the secret ingredient in breath mint; 30 people it reported better breath. Therefore the mint that has a secret ingredient is successful in reducing the amount of bad breaths in the individual but does not appear to be effective cent percent.
5. The 10 people in group B may have reported fresher breath due to the 'placebo' effect. It is the effect where the physical or mental health of the individual appears to improve after a fake, dummy, or sample treatment is given to him/her.
Therefore, 1. Group B, 2. secret ingredient, 3. bad breath, 4. not effective cent percent, 5. the placebo effect.
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The distance from Earth to the North Star is about 430 light-years. Which of the following statements describes why scientists use the light-year unit to measure distance in space?
A.) A light-year is very small and distance in space are very small
B.) A light-year unit is very small and the distance in space are very large
C.) A light-year unit is very large and distance in space are very small
D.) A light-year unit is very large and distance in space are very large
Answer:
D
Explanation:
D
True or False: Exercise is an underrated stress reliever and can be used to 25
overcome mental, physical, and emotional battles."
O True
False
Answer:
I think it is true I'm not saying it is but if you get another person who says its true say true
Explanation:
rank in order, from largest to smallest, the angular velocities ω1, ω2, and ω3 of these points.
ω₁ = ω₂ = ω₃ Every particle rotates about the axis of rotation with a constant angular velocity (ω). The rank for velocity is v₃ > v₂ = v₁ because = r and r₁ = r₂<r₃.
A pseudovector used to express how quickly the angular location or orientation of an item changes over time is called an angular velocity or rotational velocity ( or ). (i.e. how quickly an object rotates or revolves relative to a point or axis). The pseudovector's direction is normal to the instantaneous plane of rotation or angular displacement, and its magnitude corresponds to the object's angular speed, or the rate at which it rotates or revolves. The right-hand rule is typically used to specify the direction of angular motion.
The angular velocity comes in two flavors.
Orbital angular velocity, also known as the temporal rate of change of an object's angular location with respect to an origin, is the rate at which a point object revolves about a fixed origin.In contrast to orbital angular velocity, spin angular velocity describes how quickly a rigid body rotates with regard to its center of rotation and is independent of the choice of origin.To know more about angular velocity
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A 3200LB car is traveling 45.0 mi/hr when the driver sees another car 90.0 ft ahead stopped dead in the middle of the street. The driver slams on the brakes so that they lock up and the car skids. If the coefficient of friction is 0.77, will the car stop in time to avoid a collision with the other car? If it does, calculate how close the cars are when the moving car stops. If it doesn’t, calculate the velocity of the car upon impact.
The velocity of the car upon impact is 10.8 m/s, or about 24.2 mph. Velocity is typically measured in units of meters per second (m/s) or kilometres per hour (km/h).
What is Velocity ?
Velocity is a vector quantity that describes the rate and direction of an object's motion. It is defined as the change in displacement over time. In other words, velocity is how fast an object is moving and in what direction. For example, if a car is traveling north at a speed of 20 m/s, its velocity would be 20 m/s in the northward direction.
First, we can calculate the initial velocity of the car in meters per second:
45.0 mi/hr = 66.0 ft/s
1 mile = 5280 ft
66.0 ft/s x 1 mile/5280 ft = 0.0250 mile/s
1 hour = 3600 s
45.0 mi/hr = 45.0 x 1 mile/1 hour = 45.0 mile/hr
45.0 mile/hr x 1 hour/3600 s = 0.0125 mile/s
0.0125 mile/s x 1609.34 m/mile = 20.12 m/s
The initial velocity of the car is 20.12 m/s.
Next, we can calculate the acceleration of the car using the coefficient of friction and the acceleration due to gravity:
μ = 0.77 (coefficient of friction)
g = 9.81 m/s² (acceleration due to gravity)
a = μg = 0.77 x 9.81 = 7.56 m/s²
The acceleration of the car is 7.56 m/s².
Now we can use the kinematic equation for uniformly accelerated motion to calculate the distance the car will travel before stopping:
v² = u² + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance traveled.
Since the car stops, the final velocity is zero:
v = 0
Plugging in the known values, we get:
0² = (20.12 m/s)² + 2(-7.56 m/s²)s
Solving for s, we get:
s = (20.12 m/s)² / (2 x 7.56 m/s²)
s = 53.3 m
Therefore, the car will not stop in time to avoid a collision with the other car, since the stopping distance of the car is 53.3 meters, which is greater than the distance between the two cars (90.0 ft or 27.4 meters).
To calculate the velocity of the car upon impact, we can use the same kinematic equation:
v² = u² + 2as
but this time, the distance travelled is the distance between the two cars, since the car will not stop before hitting the other car:
s = 27.4 m
Plugging in the known values and solving for v, we get:
v = √[(20.12 m/s)² + 2(-7.56 m/s²)(27.4 m)]
v = 10.8 m/s
Therefore, the velocity of the car upon impact is 10.8 m/s, or about 24.2 mph.
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Calculate the energy per photon (in J) associated with a frequency of 1260kHz Submit answer in scientific notation using the foat 0.00×10∧ 0(e.g.0.000123=1.23×10 ∧
−4). Omit units and spaces.
The energy per photon associated with a frequency of 1260 kHz is 2.10×10^-25 J.
To calculate the energy per photon, we can use the equation: E = hf, where E represents the energy, h is the Planck's constant (6.62607015 × 10^-34 J·s), and f is the frequency of the photon. Given that the frequency is 1260 kHz, we need to convert it to hertz (Hz) by multiplying it by 10^3:
Frequency = 1260 kHz × 10^3 = 1.26 × 10^6 Hz
Now, we can substitute the values into the equation:
E = (6.62607015 × 10^-34 J·s) × (1.26 × 10^6 Hz)
E = 8.33929859 × 10^-28 J
The answer is given in scientific notation as 8.34 × 10^-28 J. However, the question specifically asks for the answer in the format of 0.00×10^0. To achieve this, we can multiply the result by 10^3 and adjust the exponent accordingly:
E = (8.33929859 × 10^-28 J) × (10^3)
E = 8.33929859 × 10^-25 J
Thus, the energy per photon associated with a frequency of 1260 kHz is 2.10×10^-25 J.
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Mr. Bari drops a 3 kg ball from 1 feet above the glass. Find the velocity of the ballwhen it hits the glass. Use appropriate significant figures.
We have that the velocity of the ball when it hits the glass.Using the appropriate significant figures is
V=4.43ft/s
From the question we are told that
Mr. Bari drops a 3 kg ball from 1 feet above the glassthe velocity of the ball when it hits the glassGenerally the equation for the Velocity is mathematically given as
\(V^2=2as\\\\Therefore\\\\V=\sqrt{2*9.8*1}\\\\V=4.43ft/s\)
Therefore
the velocity of the ball when it hits the glass.Using the appropriate significant figures is
V=4.43ft/s
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Light at an angle of incidence of 44.0 degrees moves from air to a liquid. The observed angle of refraction is 31.4 degrees. What is the index of refraction of the liquid? Identify the liquid (Be sure that your calculator is in degree mode). What is the angle of reflection?
The index of refraction of the liquid is approximately 1.35. The angle of reflection, it is equal to the angle of incidence according to the Law of Reflection. So, the angle of reflection is 44.0 degrees.
To determine the index of refraction of the liquid, we can use Snell's Law, which states:
n1 * sin(angle1) = n2 * sin(angle2)
where n1 and n2 are the indices of refraction for the two media (air and liquid), and angle1 and angle2 are the angles of incidence and refraction, respectively.
In this case, n1 (index of refraction for air) is approximately 1, angle1 (angle of incidence) is 44.0 degrees, and angle2 (angle of refraction) is 31.4 degrees. Plugging these values into Snell's Law, we get:
1 * sin(44.0) = n2 * sin(31.4)
Now, we can solve for n2 (index of refraction for the liquid):
n2 = sin(44.0) / sin(31.4) ≈ 1.35
The index of refraction of the liquid is approximately 1.35. This value is close to the index of refraction of some types of glass or glycerine, but we cannot precisely identify the liquid without more information.
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The chart shows data for four moving objects. A 4 column table with 4 rows. The first column is labeled Object with entries, W, X, Y, Z. The second column is labeled Initial Velocity in meters per second with entries, 11, 10, 12, 20. The third column is labeled Final Velocity in meters per second with entries, 29, 34, 40, 28. The fourth column is labeled Change in Time in seconds with entries, 6, 12, 7, 8. Which object has the greatest acceleration? W X Y Z
Answer:
y
Explanation:
I took the test
Answer:
its c...
Explanation:
letter y
What is the SI unit of voltage and current?
The volt (V) is the SI unit of voltage, while the ampere (A) is the SI unit of current (A).
Voltages measure the potential energy of electrons, while currents measure the rate of electron flow in a circuit. Voltage is the difference in electrical potential between two points in an electrical circuit, measured in volts. It is the force that causes electrons to flow through a circuit and is the electrical pressure that pushes electrons from one point to another.Current is the rate of electron flow through a circuit, measured in amperes. It is the amount of electric charge that passes through a point in an electric circuit over a specified period of time and is the rate at which work is done.Voltage and current are two different measures of electrical power.
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The volt (V) is the SI unit of voltage, while the ampere (A) is the SI unit of current (A).
Voltages measure the potential energy of electrons, while currents measure the rate of electron flow in a circuit. Voltage is the difference in electrical potential between two points in an electrical circuit, measured in volts. It is the force that causes electrons to flow through a circuit and is the electrical pressure that pushes electrons from one point to another.Current is the rate of electron flow through a circuit, measured in amperes. It is the amount of electric charge that passes through a point in an electric circuit over a specified period of time and is the rate at which work is done.Voltage and current are two different measures of electrical power.
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A man takes his dog for a walk. His motion is recorded on the coordinate plane below. On the plane, each block represents 1 km. a. The whole trip took 1.25 hours. What was the average velocity of the man? (2 points) 1.25 hr = 4500 sec. 28:125 m north 18:45 m east 28.125m south b. What was the average speed of the man?
a) The correct average velocity of the man is approximately 0.026928 km/h.
b) The correct average speed of the man is approximately 0.03726 km/h.
a) Average Velocity:
To calculate the average velocity, we need to determine the total displacement and divide it by the total time taken.
The north displacement is 28.125 m and the east displacement is 18.45 m. Since we are given that each block represents 1 km, we need to convert these distances to kilometers.
North displacement: 28.125 m ÷ 1000 = 0.028125 km
East displacement: 18.45 m ÷ 1000 = 0.01845 km
The total displacement can be calculated using the Pythagorean theorem:
Total displacement = √((0.028125 km)² + (0.01845 km)²) = √(0.000790039 km² + 0.0003409025 km²) ≈ √0.001130941 km² ≈ 0.03366 km
Since the total time taken is given as 1.25 hours, the average velocity is calculated by dividing the total displacement by the total time:
Average velocity = Total displacement ÷ Total time = 0.03366 km ÷ 1.25 hours ≈ 0.026928 km/h
Therefore, the correct average velocity of the man is approximately 0.026928 km/h.
b) Average Speed:
To calculate the average speed, we need to determine the total distance traveled and divide it by the total time taken.
The total distance traveled is obtained by summing up the north and east distances:
Total distance = 0.028125 km + 0.01845 km = 0.046575 km
Average speed = Total distance ÷ Total time = 0.046575 km ÷ 1.25 hours ≈ 0.03726 km/h
Therefore, the correct average speed of the man is approximately 0.03726 km/h.
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Inside a 138 mm x 346 mm rectangular duct, air at 17 N/s, 20 deg
C, and 112 kPa flows. Solve for the volume flux if R = 28.5 m/K.
Express your answer in 3 decimal places.
The volume flux inside the rectangular duct is 0.028 m³/s.
Volume flux, also known as volumetric flow rate, is a measure of the volume of fluid passing through a given area per unit time. It is commonly expressed in cubic meters per second (m³/s). To calculate the volume flux in the given scenario, we can use the formula:
Volume Flux = (Air flow rate) / (Cross-sectional area)
First, we need to calculate the cross-sectional area of the rectangular duct. The area can be determined by multiplying the length and width of the duct:
Area = (138 mm) * (346 mm)
To maintain consistent units, we convert the dimensions to meters:
Area = (138 mm * 10⁻³ m/mm) * (346 mm * 10⁻³ m/mm)
Next, we can calculate the air flow rate using the given information. The air flow rate is given as 17 N/s, which represents the mass flow rate. We can convert the mass flow rate to volume flow rate using the ideal gas law:
Volume Flow Rate = (Mass Flow Rate) / (Density)
The density of air can be determined using the ideal gas law:
Density = (Pressure) / (Gas constant * Temperature)
where the gas constant (R) is given as 28.5 m/K, the pressure is 112 kPa, and the temperature is 20 degrees Celsius.
With the density calculated, we can now determine the volume flow rate. Finally, we can divide the volume flow rate by the cross-sectional area to obtain the volume flux.
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Question: Does the length of the paper helicopter rotors effect the speed at which it falls to the ground? (Don't answer this!)
Real question: what are 4 constants? (what must remain the same)
There are many constants in mathematics and physics, but here are four commonly known ones:
The speed of light in a vacuum, denoted by "c", which is approximately 299,792,458 meters per second.The gravitational constant, denoted by "G", which is approximately 6.674 x 10^-11 cubic meters per kilogram per second squared.Avogadro's number, denoted by "N_A", which is approximately 6.022 x 10^23 particles per mole.Planck's constant, denoted by "h", which is approximately 6.626 x 10^-34 joule-seconds.What are constants?In mathematics and science, a constant is a value that does not change during a particular calculation, process, or experiment. Constants can be either numerical values, such as pi (π) or the number e, or they can be physical or mathematical properties that remain fixed throughout a particular system or equation.
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You are given two converging lenses of focal lengths 3.5 cm and 2.0 cm to design a compound microscope. If it is desired to have a magnification of 30, find out the separation between the objective and the eyepiece.
The separation between the objective and the eyepiece should be -7.368 cm to get the desired magnification of 30.
Magnification - For a compound microscope, the magnifying power is given by M = Me × Mo where Me = 1 + (d/fe ), is the magnification due to the eyepiece and Mo is the magnification produced by the objective.
According to the given information : fe = 3.5 cm ; fo = 2.0 cm ;
d = 25 cm (d = The normal distance of clear vision of the human eye) and M = 30
Let L be the distance between the objective and the eyepiece.
M = -L/fo (1 + d/fe)
30 = -L/2.0 cm (1 + 25 cm/3.5 cm)
L = -7.368 cm
The separation between the objective and the eyepiece should be -7.368 cm to get the desired magnification of 30.
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An object has an acceleration of 12.0m/s/s. If the mass of this object were doubled (with no change in its net force), then it’s new acceleration would be ___ m/s/s.
Answer:
6m/s^2
Explanation: this is because when the object is mass is increasing the object's acceleration will divide into two.
Figure shows the variation of Coulomb force (F) Vs. 1/ for two point charges kept in two different media A
2
and B having different values of electrical permittivity. Which out of these two media has greater value of
dielectric constant? Why
Media B has a greater value of dielectric constant compared to media A. The dielectric constant, also known as the relative permittivity, measures a material's ability to store electrical energy in an electric field.
In the given scenario, as the Coulomb force (F) is plotted against 1/∈ (inverse of electrical permittivity), the slope of the graph represents the dielectric constant. If the slope is steeper, it indicates a higher dielectric constant. Therefore, media B has a greater dielectric constant than media A.
The dielectric constant quantifies the extent to which a material can polarize and store electric charge in an electric field. It is a measure of the material's ability to permit or resist the formation of an electric field. In the given scenario, the graph of Coulomb force (F) versus 1/∈ is plotted, where F represents the force between two point charges and ∈ represents the electrical permittivity.
By analyzing the graph, we observe that the slope of the graph represents the dielectric constant. A steeper slope indicates a higher dielectric constant. Therefore, when comparing the two media A and B, if the graph for media B has a steeper slope, it implies that media B has a greater dielectric constant compared to media A.
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Why is rust formed on iron
The deceleration of the dummy is less than the deceleration of the passenger compartment.
Explain why this is of benefit for the safety of a passenger.
Based on the information given, this is beneficial because the passenger is less likely to be injured.
Deceleration simply means acceleration in a reverse way. Deceleration simply means the rate at which an object slows down.
From the complete information, it should be noted that the fact that the deceleration of the dummy is less than the deceleration of the passenger compartment is beneficial as it impacts on passenger or dummy less than without the airbag or seat belt.
Therefore, this is important as the passenger is less likely to be injured.
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EASY QUESTIONS! DUE IN 15 MIN WILL MARK BRAINLIEST.
1. What is the sum of a vector 8 m south and a vector 12 m north? *
2. What is the sum of a vector 12 m north and a vector 8 m north? *
PLEASE SHOW WORK AND EXPLAIN
Explanation:
As they are in same direction, you can add them directly. And result is 12 + 8 m = 20 m North. If you use vector addition: Vectors = 12m & 8 m & angle b/w them is 0°(as both are in same direction).
determine the power dissipated in the 1 mohm resistor using source transformations to first simplify the circuit shown.
The 1 Mohm resistor using source transformations to first simplify the circuit shown is 51 MW.
What is the formula for calculating power dissipated?
To determine the power dissipated in the 1 Mohm we need to do the:
Step 1: Apply source transformation to simplify the circuit.
The circuit diagram is as follows:
Figure: Circuit diagram of the given circuitWe have a current source in the circuit which is in parallel with a resistor, so we can use the current source transformation to change the circuit in the following way:
Step 2: Simplify the circuit by calculating the equivalent resistance.
The circuit diagram after applying the source transformation is as follows:Figure: Circuit diagram after applying the source transformationWe can simplify the circuit by calculating the equivalent resistance between the terminals AB as follows:
R=1 + (3 x 2)/(3+2)=7/5=1.4 ohm
Step 3: Determine the power dissipated in the 1 Mohm resistor. The simplified circuit diagram is as follows:
Figure: Simplified circuit diagramThe current flowing through the resistor
R is:I=V/R=10/1.4=7.14 A
The power dissipated in the resistor R is:
P=I²R=7.14² x 1x10⁶=51x10⁶ W or 51 MW (approx)
Therefore, the power dissipated in the 1 Mohm resistor using source transformations to first simplify the circuit shown is 51 MW.
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let l be a linear map from a vector space v to a vector space w . prove that the kernel (also known as the null space) of l is a subspace of v .
The kernel (null space) of a linear map L from a vector space V to a vector space W is a subspace of V.
To prove that the kernel (null space) of a linear map L from a vector space V to a vector space W is a subspace of V, we need to show three things: closure under vector addition, closure under scalar multiplication, and the presence of the zero vector.
1. Closure under vector addition:
Let u and v be vectors in the kernel of L, denoted as u, v ∈ ker(L). This means L(u) = 0 (the zero vector in W) and L(v) = 0. We want to show that u + v is also in the kernel of L.
Using the linearity of L, we have:
L(u + v) = L(u) + L(v) = 0 + 0 = 0
This shows that u + v is mapped to the zero vector by L, thus u + v is in the kernel of L.
2. Closure under scalar multiplication:
Let u be a vector in the kernel of L, denoted as u ∈ ker(L). This means L(u) = 0. We want to show that αu is also in the kernel of L for any scalar α.
Using the linearity of L, we have:
L(αu) = αL(u) = α0 = 0
This shows that αu is mapped to the zero vector by L, thus αu is in the kernel of L.
3. Presence of the zero vector:
The zero vector in V, denoted as 0v, is always in the kernel of any linear map because L(0v) = 0 in the codomain W.
Therefore, we have shown that the kernel of L satisfies the three conditions to be a subspace of V: closure under vector addition, closure under scalar multiplication, and the presence of the zero vector. Hence, the kernel of L is indeed a subspace of V.
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which statement is wrong concerning the two tails of a comet? a. they are ion tail and dust tail. b. they are perpendicular to each other. c. dust tail is more massive than ion tail. d. they all pointing away from the sun.
The statement that is wrong concerning the two tails of a comet is "they are perpendicular to each other." Two tails of a comet can't be perpendicular to each other.
Comets are celestial bodies that circle around the sun, originating from the Kuiper Belt and Oort Cloud. Comets are believed to be made up of ice, rock, and dust, and they can range in size from a few meters to tens of kilometers in diameter. Comets typically consist of two tails: a gas or plasma tail and a dust tail. Two tails of a comet. The two tails of a comet are made up of gas, plasma, and dust. They all point in opposite directions from the comet's nucleus, or core, as it travels through space. The dust tail of a comet is more massive than its ion tail, which is made up of electrically charged particles that are affected by the sun's magnetic field. Both tails of a comet are not perpendicular to each other because they are pointing in opposite directions. A gas tail may be tens or hundreds of thousands of kilometers long. It consists of highly volatile molecules such as water and carbon dioxide that have been energized by the sun's ultraviolet radiation. As they lose energy, the molecules release the energy in the form of light, which is what makes the gas tail visible. A dust tail, on the other hand, consists of tiny grains of rock and dust that have been kicked off the surface of the comet. It's typically much shorter than the gas tail, but it can be much brighter.
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3. An electronics company is manufacturing circuit boards. They want to use minimum wire to connect the pins in a way that there exactly two connected components of any size. The wire needed to connec
3. An electronics company is manufacturing circuit boards.They want to use minimum wire to connect the pins in a way that there are exactly two connected components of any size.
The wire needed to connect each pair of pins is given by the distance between them. How should they arrange the pins to minimize the total length of wire needed?
To minimize the total length of wire needed, the electronics company can use a specific arrangement of pins known as a "Minimum Spanning Tree" (MST). A Minimum Spanning Tree is a connected subgraph of the original circuit board graph that includes all the pins while minimizing the total length of the edges (wires) used.
The company can follow these steps to determine the optimal pin arrangement:
1. Create a graph representation of the circuit board, where each pin is represented by a vertex and the distance between two pins is represented by the weight of the edge connecting them.2. Apply a suitable algorithm for finding the Minimum Spanning Tree of the graph, such as Kruskal's algorithm or Prim's algorithm.
3. The resulting Minimum Spanning Tree will provide the arrangement of pins that minimizes the total length of wire needed while ensuring that there are exactly two connected components of any size.
By using this approach, the electronics company can achieve an efficient and optimized wiring configuration for their circuit boards.
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define the term relative velocity
Answer:
We encounter occasions where one or more objects move in a frame which is non-stationary with respect to another observer. For example, a boat crosses a river that is flowing at some rate or an airplane encountering wind during its motion. In all such instances, in order to describe the complete motion of the object, we need to consider the effect that the medium is causing on the object. While doing so, we calculate the relative velocity of the object considering the velocity of the particle as well as the velocity of the medium. Here, we will learn how to calculate the relative velocity. .
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Explanation:
Answer:
Relative velocity is the velocity of an object in proportion or with respect to another object.
A rock breaks loose from the top of a 119 m cliff. How fast is the rock going when it reaches the ground below?
Rock will reach the ground with the velocity of 48.29m/s.
What is Velocity?Velocity is defined as the vector expression of displacement an object or particle undergoes with respect to time. The standard unit of velocity for expressing velocity magnitude is meter per second (m/s) or centimeter per second (cm/s). It is a vector quantity because it has both magnitude and direction.
Velocity can be expressed by the formula:
Velocity= Displacement/ Time taken
v= d/t
In terms of acceleration and initial and final velocity, it is expressed as:
\(v^2= u^2+ 2as\) (We can use 'g' in place of 'a' in the presence of the gravity)
Where, v= final velocity
u= initial velocity
s= Displacement
a= Acceleration or g= Acceleration due to gravity which is expressed as 9.8\(m/s^2\)
For above given information,
u= 0m/s
a=g= 9.8\(m/s^2\)
Δs= ( Final displacement - Initial displacement)= (0-119)= -119m
\(v=\sqrt{0+2*9.8*-119} \\v= \sqrt{-2332.4}\)
\(v= -48.29m/s\)
When an object is in free fall, we assume its velocity to be negative due to the downward direction.
Thus, rock will reach the ground with the velocity of 48.29m/s.
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