The airplane needs to be pointing in a direction 5.71 degrees east of north to compensate for the crosswind and arrive at its destination.
Since the airplane is moving due north and the wind is blowing from west to east, the angle between the airplane's heading and the wind is 90 degrees. We can use vector addition to determine the airplane's resultant velocity, which will point in the direction the airplane needs to be pointing. The magnitude of the resultant velocity can be found using the Pythagorean theorem:
Resultant velocity = [tex]sqrt(airspeed^2 + wind speed^2) = sqrt(200^2 + 20^2) = 201.25 mph[/tex]
The angle between the airplane's heading and the resultant velocity can be found using trigonometry:
[tex]tan(theta) = wind speed / airspeed = 20 / 200 = 0.1[/tex]
[tex]theta = tan^-1(0.1) = 5.71 degrees[/tex]
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if you increase the temperature of a given amount of an ideal gas, what happens to the gas pressure p and the volume v of the gas?
According to Gay Lussac's Law, a gas's pressure is precisely proportional to its Kelvin temperature when kept at a constant volume.The molecules of a gas receive more energ
What happens to an ideal gas's volume as the temperature rises?These instances of how temperature can change a confined gas's volume while maintaining a constant pressure are typical:The volume rises with rising temperature and falls with falling temperature.
when an ideal gas's temperature is raised by?Since internal energy was directly proportional to the temperature, an adiabatic compression raises the temperature of the an ideal gas.
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a figure skater can increase her spin rotation rate from an initial spin rotation rate from an initial rate of 1.0 rev every 1.5 seconds, to a final rate of 2.5 rev/s. if her initial moment of inertia was 4.6 kgm2, what is her final moment of inertia?
The final moment of inertia of the figure skater is approximately 1.23 kgm².
What is the Moment ?
Moment is a concept that refers to a single point in time at which an event or decision must be made. It is often used to describe a critical moment of opportunity or a crucial decision that needs to be made. It can also refer to a specific moment of clarity, when a person suddenly has a realization or an epiphany. The Moment can also refer to a feeling or emotion that can be experienced at a particular time and place. It can be a feeling of joy, love, peace, or sorrow. Whatever the feeling is, it can be a powerful experience that can leave a lasting impression.
We can use the conservation of angular momentum to relate the initial and final moment of inertia of the figure skater:
I_i ω_i = I_f ω_f
where I_i is the initial moment of inertia, ω_i is the initial angular velocity, I_f is the final moment of inertia, and ω_f is the final angular velocity.
We are given that the initial angular velocity is 1.0 rev every 1.5 seconds, which can be converted to radians per second by multiplying by 2π/1 rev:
ω_i = (1.0 rev/1.5 s) * (2π/1 rev) ≈ 4.19 rad/s
We are also given that the final angular velocity is 2.5 rev/s, which can be converted to radians per second by multiplying by 2π/1 rev:
ω_f = 2.5 rev/s * (2π/1 rev) ≈ 15.71 rad/s
Substituting these values into the conservation of angular momentum equation and solving for I_f, we get:
I_f = I_i * (ω_i / ω_f)
I_f = 4.6 kgm² * (4.19 rad/s / 15.71 rad/s)
I_f = 1.23 kgm²
Therefore, the final moment of inertia of the figure skater is approximately 1.23 kgm².
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while an object near the earth's surface is in free fall, its acceleration increases. mass increases. mass decreases. velocity increases.
The correct answer is A) Acceleration increases. When an object is in free fall near the Earth's surface, its velocity increases as it accelerates due to the force of gravity.
This acceleration is constant, and the object's mass does not affect the acceleration rate. As the object accelerates, its velocity increases, and its mass remains constant.
Acceleration is the rate at which velocity changes over time. It is a vector quantity, meaning that it has both magnitude and direction. Acceleration can be caused by a number of factors, such as a change in the speed of an object, a change in direction, or the application of a force. An object is said to be accelerating if it is changing its velocity.
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Please Help And Fast!!!!
A boat’s velocity changes as it reaches the dock.
Which situations would cause the boat’s velocity to change?
Select three that apply.
A. The boat is slowing down.
B. The boat is speeding up.
C. The boat is changing direction.
D. The boat is not changing direction.
If the velocity of the boat is changing, then the boat is changing direction.
option C.
What situations would cause the boat’s velocity to change?
The velocity of a boat can change due to various factors such as;
wind resistance, water currents, engine power, and the boat's interaction with the dock.Additionally, the boat's velocity can change if the boat's pilot applies the brakes or changes the direction of the boat. The boat's velocity can also be influenced by the shape and weight distribution of the boat, the speed of the water, and the presence of other boats and objects in the water.
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You kick a soccer with an initial vertical velocity of 64.1 m/s. How high will it be after 4.5 s?
The maximum height travelled by the ball is 189.23 m.
What is the maximum height travelled by the ball?
The maximum height travelled by the ball is calculated by applying the following kinematic equation as shown below.
h = vt + ¹/₂gt²
where;
v is the initial vertical velocityg is acceleration due to gravityt is the time of motionh = ( 64.1 m/s x 4.5 s ) - ¹/₂ ( 9.8 m/s² ) ( 4.5 s )²
h = 189.23 m
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What is the threshold velocity vthreshold(water) (i. E. , the minimum velocity) for creating Cherenkov light from a charged particle as it travels through water (which has an index of refraction of n=1. 33)?
The threshold velocity (v_threshold) for creating Cherenkov light from a charged particle traveling through water (n=1.33) is 225000000 m/s.
It can be calculated using the formula:
v_threshold = c/n,
where c is the speed of light in a vacuum (approx. 299792458 m/s).
Therefore, v_threshold = 299792458 m/s / 1.33 = 225000000 m/s.
Cherenkov radiation is the emission of electromagnetic radiation when a charged particle travels through a dielectric medium at a velocity greater than the phase velocity of light in that medium.
The Cherenkov effect occurs because when a charged particle moves through a medium, it causes the electromagnetic field in the medium to oscillate.
If the velocity of the charged particle is greater than the phase velocity of light in the medium, the oscillating electromagnetic field creates a cone of radiation known as Cherenkov radiation.
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5) How do the mathematical relationships you figured out about the effects of mass and speed of an object on its kinetic
energy help you make more-accurate predictions for whether a collision would produce damage in some cases and not
others?
The math helps us to determine the amount of kinetic energy an object has based on its mass and speed, and this information can be used to predict whether a collision would produce damage in some cases and not others. By calculating the kinetic energy of two objects, we can determine the amount of energy that would be released upon impact and whether it would be enough to cause damage. This can help us to make more informed decisions about the safety of certain activities or scenarios.
What is energy?
Energy is the ability to do work. It is the capacity to move an object or cause change. It exists in many forms, such as kinetic energy (energy of motion), potential energy (stored energy), thermal energy (heat), electrical energy, chemical energy, and nuclear energy.
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a 6.0-v battery that can store 500.0j of ernergy is connected to a resitor. how much charge must flow between the battery's terminals to completely drain the barrtery if it is fully charged?
Answer:
explain again please meet other people
when is it appropriate to describe a charged object as a point charge, and when is it not appropriate?
Answer: When it slows down or speeds up. Depending on which, it is appropiate.
Explanation:
imped) og 90
Does a 2-kilogram rock have twice the mass
of a 1-kilogram rock? Twice the inertia? Twice
the weight (when weighed in the same loca-b
tion)? (4.5)
urged
bib ord:
Yes, a 2kg rock will have twice the weight and inertia of a 1 kg rock.
What is the weight of an object?
The weight of an object is the measure of the effect of force of gravity on the object.
W = mg
where;
m is the mass of the objectg is acceleration due to gravityThe weight of 2 kg rock and 1 kg rock is calculated as;
W (2) = 2 kg x 9.8 m/s² = 19.6 N
W (1) = 1 kg x 9.8 m/s² = 9.8 N
The weight of 2 kg rock is twice the weight of the 1 kg rock.
Inertia is the measure of reluctance of an object to move or stop moving and it depends on mass, so 2 kg tock will have twice the inertia of 1 kg rock.
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Identify an environmental hazard that you would like to use for this activity. Explain why you chose this risk.
An environmental hazard is a threat posed by natural or human-made conditions that may have a negative impact on the environment, human health or other living organisms.
One example of an environmental hazard is air pollution which can be caused by a range of factors including industrial emissions, vehicle exhaust, and wildfires. Air pollution can have a range of harmful effects on human health including respiratory problems, heart disease and cancer. It can also have negative impacts on wildlife, ecosystems and natural resources.
Other examples of environmental hazards may include toxic waste, climate change, deforestation & water pollution. These hazards may have a range of short and long-term effects on the environment and may require coordinated efforts from governments, individuals and organizations to address and mitigate their impact.
The answer is general because no context is provided.
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the ceiling of an arena is 19 m above the floor. what is the minimum speed that a thrown ball would need to just reach the ceiling?
The minimum speed that a ball should be thrown to reach ceiling is 19.29m/sec.
In regular use and in kinematics, the speed of an article is the extent of the difference in its situation over the long run or the greatness of the difference in its position per unit of time; it is hence a scalar amount. The typical speed of an item in a time period is the distance gone by the article partitioned by the length of the stretch; the immediate speed is the constraint of the typical speed as the span of the time stretch methodologies zero. Speed isn't equivalent to velocity.
We know that to to find the minimum speed at the base location,we need to use third equation of motion which is
v²-u²=2as
Here,v is final velocity which will be zero,u=?,a=9.8m/sec²,S=-19m
So,on putting we get
=>0² - (u²)=2×(-9.8)×19
=>u²=19.6×19
=>u²=372.4
=>u=√372.4
=>u=19.29m/sec.
Hence,minimum speed to throw a ball is 19.29m/sec
.
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a capacitor drawing 8 kvar is placed parallel with an electromagnet that draws 3kw of active power and 4 kvar of reactive power. what effect does this have on the reactive power q provided by the ac power source and the power factor cos.
The power factor is now 0.6, which is an improvement over previous value (which would be lower than 0.6 due to the higher reactive power demand).
Capacitor of 8 kVAR is placed parallel with an electromagnet that draws 3 kW of active power and 4 kVAR of reactive power, resulting circuit becomes a combination of a capacitive and an inductive load.
Net reactive power = [tex]8 kVAR - 4 kVAR = 4 kVAR[/tex]
So, the resulting circuit will have a net reactive power of [tex]4 kVAR[/tex].
The power factor (cos) of the circuit can be calculated as ratio of active power to apparent power:
cos = Active power / Apparent power
The apparent power can be calculated as:
Apparent power = [tex]sqrt(Active power^2 + Reactive power^2)[/tex]
Apparent power = [tex]sqrt(3^2 + 4^2) kVA = 5 kVA[/tex]
So, the power factor of the circuit can be calculated as:
[tex]cos = 3 kW / 5 kVA = 0.6[/tex]
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a small mass m on a string is rotating without friction in a circle. what happens to the tangential velocity of the object
When a small mass m on a string is rotating without friction in a circle, the tangential velocity of the object increases.
How does tangential velocity affect circular motion?Tangential velocity is the linear speed of any object that moving along a circular path. A point on the outside edge of a turntable moves a larger distance in one complete rotation than a point near to the center. In uniform circular motion, the direction of the velocity changes continually, so there is always an associated acceleration, although the speed might be constant.
In this case, work is done on the object, and so its kinetic energy increased. Thus, the tangential velocity had to increase. Another way to consider the problem is that kinetic energy (KE) = L2 / 2I. Thus, the kinetic energy (and so the speed) had to increase. Translational kinetic energy = 1/2Mv cm², so if kinetic energy (KE) increases, so must V (velocity).
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a particle has 1672 mev rest energy, and a mean liftime of 8.2*10^-11 s. it is created and leaves a track 24mm. what is the particles total energy
Total energy of particle is 609.7644meV if its rest energy is 1672meV and mean lifetime is 8.2 ˣ 10⁻¹¹sec.
Rest Energy is a 1980 presentation craftsmanship piece made, established, and recorded by execution craftsman team Marina Abramović and Ulay in Amsterdam, the Netherlands.[1][2][3] Four minutes in length, Abramović has portrayed it as perhaps of the most troublesome piece she has at any point finished, saying -I was not in control.
In Rest Energy we really held a bolt on the heaviness of our bodies, and the bolt is pointed squarely into my heart. We had two little mouthpieces close to our souls, so we could hear our pulses. As our exhibition was advancing, pulses were turning out to be increasingly serious, and however it endured only four minutes and ten seconds, I'm telling you, for me it was for eternity. It was an exhibition about the total and complete trust.[4]
We know very well that rest energy is given by the relation
E=E₀ √(1-v²/c²)
where E₀=rest energy,v is the speed of particle and c is the velocity of light in vacuum and E is the total energy.
So,we have E₀=1672meV,c=3ˣ10⁸m/sec.
v=Total distance/total time
v=(2ˣ3.14ˣ24/1000) /8.2 ˣ 10⁻¹¹
=>v=8.38ˣ10⁸m/sec.
So,E=1672ˣ √1-(8.38)² /3²
=>E=1672× √(1-(0.866)
=>E=1672×0.364
=>E=609.764meV.
Hence,particle total energy is 609.764meV.
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2.2 Forces of 9 N acting horizontally to the right and 5 N in the opposite direction; 12 N acting vertically upwards and 6 N vertically downwards. Forces of 75 N acting vertically downwards and 50 N vertically upwards;
2.3 Forces of 75N acting vertically downwards and 50N vertically downwards;45 N horizontally towards the right and 23N in the opposite direction
(2.2 ) The resultant of the forces are 19 N downwards and 4 N to the right.
(2.3 ) The resultant of the forces are 125 N downwards and 22 N to the right.
What is the resultant force on the object?
The resultant force on the object is the sum of all the forces acting on the object in a particular direction.
for the first given forces,
sum of the vertical forces = 12 N + 50 N - 6 N - 75 N = 19 N downwards
sum of horizontal forces = 9 N - 5 N = 4 N to the right
for the second given forces,
sum of the vertical forces = -75 N - 50 N = 125 N downwards
sum of horizontal forces = 45 N - 23 N = 22 N to the right
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The complete question is below:
2.2 Forces of 9 N acting horizontally to the right and 5 N in the opposite direction; 12 N acting vertically upwards and 6 N vertically downwards. Forces of 75 N acting vertically downwards and 50 N vertically upwards;
2.3 Forces of 75N acting vertically downwards and 50N vertically downwards;45 N horizontally towards the right and 23N in the opposite direction . find the resultant of each forces
You are looking at two bars made of solid gold. The first one has a temperature of 20 °C, while the second one has a temperature of 80 °C. Gold has a melting point of 1948 °C. Which of the following statements are correct?
I The particles in the 20 °C bar are vibrating faster than the particles in the 80 °C bar.
II The particles in both bars are moving around randomly.
III The particles in the 80 °C bar have a higher average kinetic energy.
Group of answer choices
I, II, and III
I and III only
I only
III only
The particles in the 80 °C bar are vibrating faster than the particles in the 20 °C bar.
What is solid?One of the four basic states of matter is solid (the others being liquid, gas, and plasma). The least energetic molecules are those that are tightly packed together and make up solids. A solid is distinguished by its structural rigidity and resistance to external forces.
As the temperature of a solid increases, the vibration of atoms of solid bar increases. Hence, the particles in the 80 °C bar are vibrating faster than the particles in the 20 °C bar.
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earth gains and loses mass true or false
Answer: Earth loses several hundred tons of mass to space every day, significantly more than what we're gaining from dust. So, overall, Earth is getting smaller.
Explanation:
Answer:
true
Explanation:
becuase of the gravity of earth
8. A 5000 kg open railroad car coasts along with a constant speed of 7.0 m/s on a level
track. Snow begins to fall vertically and fills the car at a rate of 2.6 kg/min. Ignoring
friction with the tracks, what is the speed of the car after 100 min?
Answer:
The problem involves finding the effect of added mass on the speed of a moving object, which can be determined using the law of conservation of momentum.
Before the snow starts falling, the initial momentum of the car is 5000 kg * 7.0 m/s = 35000 kg m/s.
As the snow falls, it adds mass to the car, and its momentum increases. The increase in momentum can be calculated as follows:
2.6 kg/min * 100 min = 260 kg
The final momentum of the system (car + snow) is given by:
35000 kg m/s + 260 kg * 0 m/s (since the snow is falling vertically and has no initial velocity relative to the car) = 35000 kg m/s + 260 kg * 0 m/s = 35000 kg m/s
The final velocity of the system (car + snow) can be determined by dividing the final momentum by the total mass:
35000 kg m/s / (5000 kg + 260 kg) = 35000 kg m/s / 5260 kg = 6.64 m/s
So the speed of the car after 100 minutes is 6.64 m/s.
if you heed the sign and slow to 35 mph , what will be your acceleration going around the curve at this constant speed? give your answer in m/s2 .
The acceleration going around the curve at a constant speed of 35 mph is 0 [tex]m/s^2[/tex].
When an object moves at a constant speed in a circular path, it experiences an acceleration known as centripetal acceleration. This acceleration is directed toward the center of the circle and is given by the formula:
acceleration = [tex]v^2[/tex] / r
where v is the velocity of the object and r is the radius of the circular path.
However, if the object is moving at a constant speed, its velocity does not change with respect to time and the acceleration is zero. This means that the car's acceleration going around the curve at a constant speed of 35 mph (15.56 m/s) would be 0 [tex]m/s^2[/tex]. The car's velocity is not changing, so there is no net force causing the car to accelerate.
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free fall objects in free fall will accelerate only due to gravity. the kinematic equation for constant acceleration can be used:
Its value is 9.8 ms-2 when it is close to the earth's surface. Therefore, the acceleration due to gravity (g) is given by = GM/r2.Because kinematics equations are used when the acceleration of the object is constant.
Do the kinematics equations apply to motion in free fall?Therefore, acceleration owing to gravity is the name given to the acceleration of falling objects in free fall.The kinematic equations can be used to analyze any falling object if friction and air resistance are minimal since the acceleration caused by gravity is constant.
Does kinematics include free fall?Therefore, acceleration owing to gravity is the name given to the acceleration of falling objects in free fall.The kinematic equations can be used to analyze any falling object if friction and air resistance are minimal since the acceleration caused by gravity is constant.
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a ball player catches a ball 3.4 s after throwing it vertically upward. with what speed did he throw it, and what height did it reach?
The ball was thrown upward with an initial velocity of 33.32 m/s and reached a maximum height of 94.1 m.
What is speed?Speed is a scalar variable that quantifies how quickly an object's position changes in a particular direction. It is a way to gauge how far you've come in a certain amount of time.
How do you determine it?The following kinematic equations can be used to calculate the ball's initial speed and its highest point:
Vertical displacement (y) is equal to the sum of the initial vertical velocity (vo) and the acceleration (a) times time plus 0.5.
Initial velocity (vo) plus acceleration (a) times time equals final velocity (v).
where a is the acceleration caused by gravity, or -9.8 m/s2.
By setting the ball's end velocity to zero and solving for its beginning velocity and displacement, we can first determine the height to which it can travel.
vo = 9.8 * t
= 9.8 * 3.4
= 33.32 m/s
y = vo * t + 0.5 * (-9.8) * t^2
= 33.32 * 3.4 - 0.5 * 9.8 * (3.4^2)
= 94.1 m
So, the ball was thrown upward with an initial velocity of 33.32 m/s and reached a maximum height of 94.1 m.
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in this experiment, you learned that the acceleration due to gravity is a constant that does not depend on the initial velocity. equation (2.3), however, has a v0 in it. are these two facts consistent? why?
These two facts are consistent because in calculating the value of acceleration due to gravity all other variables are constant.
Equation is derives using
v = u + at
[tex]a=\frac{v-u}{t}[/tex]
This is the equation for an object's final velocity or the velocity at time t when it accelerates with "a." In equation, a does not equal g; rather, it refers to the acceleration of an object that was initially travelling at a speed of u and has since acquired an acceleration.
Since a projectile only experiences the acceleration caused by gravity, we use a = g = 9.81 [tex]\frac{m}{s^{2} }[/tex] in all motion equations for a projectile.
The method used to compute the gravitational acceleration is
g = [tex]\frac{G\times M}{R^{2} }[/tex]; where R is the earth's radius and M is its mass, and G is the gravitational constant of the universe.
As a result, g will always have a constant value of a planet because all of the parameters used to calculate it are constants. similar to earth g = 9.81 [tex]\frac{m}{s^{2} }[/tex] .
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discuss the significance of the law of energy conservation in relation to the flashlight as well as express some new energy sources that are being researched for the near future.
The law of energy conservation states that energy can be neither created nor destroyed, only converted from one form to another. This law is particularly relevant to the flashlight, as it explains why the flashlight needs a power source in order to operate. Without a power source, the flashlight cannot convert electrical energy into light energy.
In terms of new energy sources, research into renewable sources of energy such as solar, wind, and geothermal is becoming increasingly popular. Solar power is the most promising of these sources, as it can provide a clean and renewable form of energy with no emissions. Wind energy is also becoming more popular, as the technology for harnessing wind energy has improved significantly in recent years.
Geothermal energy is also being explored as a potential source of renewable energy, as it has the potential to provide a steady and reliable form of energy. Additionally, research into energy conservation technologies such as LED lighting and energy efficient appliances is being conducted in order to reduce energy consumption and increase energy efficiency.
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a hiker walks 6.7 miles to the east in 5.1 hours then turns around and walks 1.1 miles to the west in 1.0 hours. what was her average velocity during the trip?
To find the average velocity of the hiker during the trip, we need to find the total distance covered and the total time taken 1.28 mph
First, let's find the total distance covered:
6.7 miles to the east
1.1 miles to the west
So, the total distance covered is
6.7 + 1.1 = 7.8 miles.
Next, let's find the total time taken:
5.1 hours to the east
1.0 hours to the west
So, the total time taken is
5.1 + 1.0
= 6.1 hours.
Finally, to find the average velocity, we divide the total distance by the total time:
7.8 miles / 6.1 hours
= 1.28 mph
So, the average velocity of the hiker during the trip was 1.28 mph.
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A camper is about to drink his morning coffee. He pours 400 grams of coffee, initially at 75°C into a 250-g aluminum cup, initially at 16°C. What is the equilibrium temperature of the coffee-cup system, assuming no heat is lost to the surroundings? The specific heat of aluminum is 900 J/kg • K, and the specific heat of coffee is essentially the same as that of water, which is 4186 J/kg • K.
The equilibrium temperature of the coffee-cup system is 67.9 °C.
What is the equilibrium temperature?
The equilibrium temperature of the coffee-cup system is calculated based on the law of conservation of energy as shown below.
Heat lost by the coffee = heat gained by the aluminum
(0.4 kg x 4186 J/kg.K ) ( 75 - T ) = ( 0.25 kg x 900 J/kg.K ) ( T - 15 )
where;
T is the equilibrium temperature125580 - 1674.4T = 225T - 3375
1899.4T = 128,955
T = 128,955 / 1899.4
T = 67.9 °C
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an electric field is produced by the very long, uniformly charged rod drawn above. if the strength of the electric field is e1 at a distance r1 from the axis of the rod, at what distance from the axis is the field strength e1/4?
If the strength of the electric field is e1 at a distance r1 from the axis of the rod, R2 = 4r1 distance from the axis is the field strength e1/4.
Electric field strength = F / q
we will assume the rod has an infinite length
For an infinitely charged rod
E ∝ 1/ r
considering two electric fields E1 and E2 at two different locations as described in the question
E1/E2 = r1/r2 ----- ( 2 )
Calculate for r2 when E2 = E1/4
back to equation 2
E1 / (E1/4) = r1 / r2
∴ r2 = 4r1
Distance is a numerical or on occasion qualitative size of ways a long way aside from objects or points. In physics or ordinary utilization, the distance may additionally confer with a bodily duration or an estimation primarily based on different standards (e.g. "two counties over"). for the reason that spatial cognition is a wealthy supply of conceptual metaphors in human ideas, the term is likewise regularly used metaphorically to mean size of the quantity of difference between similar items (consisting of statistical distance among chance distributions or edit distance among strings of text) or a diploma of separation (as exemplified with the aid of distance between human beings in a social community).
Maximum such notions of distance, each bodily and metaphorical, are formalized in mathematics through the use of the belief of a metric area. In the social sciences, distance can consult with a qualitative size of separation, such as social distance or mental distance.
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if a curve is banked to accommodate cars traveling at 15 m/s, what will happen during an ice storm (no friction with the road) to a car moving at a slower speed?
A automobile will have trouble while going through a curve when there is little friction between the car's tyres and the road during an ice storm and the banking of the road allow vehicles to move at 15 m/s.
The lack of friction will still cause the car to tend to slide towards the outside of the curve even though it is going more slowly. If the car slides off the road or into oncoming traffic, it might be very dangerous.
When the surface of a curving road is inclined towards the horizontal to generate the required centripetal force for a safe turn, the phenomenon known as "banking of roads" takes place.
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a 10.0 kg experimental rocket is catapulted from kennedy space center. it leaves the launch pad with kinetic energy of 1960 j. a) what elements comprise the closed system in this problem and what is the conservative force acting on the experimental rocket? b) how high will the rocket rise?
a). The elements that comprise the system in the question above are kinetic energy and potential energy.
b). The rocket will rise to 20 m high.
Given:
Rocket mass (m) = 10.0 kgInitial kinetic energy (K1) = 1960 Jb)
To calculate the height of the rocket rise, we can use the law of conservation of mechanical energy equation:
K1 + U1 = K2 + U2
U is the potential energy that the rocket has. Its formula is
U = m * g * h
Since we have the mass and acceleration due to gravity, we can calculate the height using that formula.
So,
K1 + U1 = K2 + U2
1960 + U1 = 0 + U2 -> K2 = 0 because at max height, kinetic energy is 0.
U2 = 1960 J
1960 = m * g * h
1960 = 10 * 9.8 * h
h = 20 m
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a ball with mass 0.48 kg moves at a constant speed. a centripetal force of 23 n acts on the ball, causing it to move in a circle with radius 1.7 m. what is the speed of the ball?
Answer:
The speed of the ball can be found using the formula:
v = sqrt(Fc / m) = sqrt(23 N / 0.48 kg) = sqrt(23 / 0.48) m/s
v = approximately 4.53 m/s
The speed of the ball is approximately 9.01 m/s.
The centripetal force acting on a moving object in a circular path is given by the formula:
F = (mv²) / r
where F is the force, m is the mass of the object, v is its speed, and r is the radius of the circular path.
In this case, we know the mass of the ball is 0.48 kg, the centripetal force acting on the ball is 23 N, and the radius of the circular path is 1.7 m. Solving the formula for v, we get:
v = sqrt((Fr) / m)
Plugging in the given values, we get:
v = sqrt((23 N * 1.7 m) / 0.48 kg)
v = sqrt(81.167) m/s
v ≈ 9.01 m/s
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