The wind's speed at the given constant acceleration is 103.05 m/s.
What is velocity of an object?
The velocity of an object is defined as the rate of change of displacement of the object with time.
Mathematically, the velocity of an object is given as;
v = u + at
where;
a is the acceleration of the objectv is the final velocity of the objectt is time of motion of the objectu is the initial velocity of the objectSince the object started from rest, the initial velocity = 0
v = 0 + (2.29 x 45)
v = 103.05 m/s
Thus, the final velocity of the glider will be greater than his initial velocity moving at the constant acceleration.
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the current in a single-loop circuit with one resistor r is 8.400 a. when an additional resistor of 9.00 ω is inserted in series with the existing resistance, the current drops to 6.384 a. what is r in ohms?
The initial resistance of one resistor r in ohms in series combination is 28.5 Ω.
The resistance depends on the used combination. The resistor combination can be combined in 2 ways which are series combination and parallel. In series combination, the resistance will be added up for each resistor. It can be written as
R = R1 + R2
where R is total resistance, R1 and R2 are the series combination of resistors.
From the question above, the given parameters are
R2 = 9 Ω
I1 = 8.4 A
I2 = 6.384 A
Hence, the current ratio of the initial and final condition is
I1 / I2 = V /R1 / V/(R1 + R2)
8.4 / 6.384 = (R1+R2) / R1
8.4 R1 = 6.384 R1 + 57.456
2.016R1 = 57.456
R1 = 28.5 Ω
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Is the exoplanet like earth in terms of its distance from its star? Explain your answer
Every planet in the solar system orbits the Sun. Planets known as exoplanets orbit other stars. Astronomers search for exoplanets by observing the effects that these planets have on the stars they orbit.
What is the exoplanet?Any planet outside of our solar system is an exoplanet. The majority of exoplanets orbit other stars, while rogue planets—free-floating exoplanets that are unattached to any star—orbit the galactic center.
Does the exoplanet have life?Since liquid water is necessary for all known forms of life, an exoplanet that is too near or too far from its host star is less likely to support life. Additionally, some primordial compounds may require ultraviolet light to form, but a hyperactive host star can blast the nascent planet, removing its atmosphere.
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a 115 kg lineman is working on tackling drills. if he is running at 2.8 m/s and hits a tackling dummy with a mass of 55 kg , what is the momentum of the tackling dummy after the hit assuming the lineman stops instantly after impact?
A 115 kg lineman is working on tackling drills. if he is running at 2.8 m/s and hits a tackling dummy with a mass of 55 kg, then the momentum of the tackling dummy would be 322 kg-m/s.
What is momentum?It can be defined as the product of the mass and the speed of the particle, it represents the combined effect of mass and the speed of any particle, and the momentum of any particle is expressed in Kg m/s unit.
As given in the problem a 115 kg lineman is working on tackling drills. if he is running at 2.8 m/s and hits a tackling dummy with a mass of 55 kg ,
By using the conservation of the momentum,
Momentum before the collision = momentum after the collision
The momentum of the tackling dummy = m × v
= 2.8 × 115
=322 kg-m/s
Thus, the momentum of the tackling dummy would be 322 kg-m/s.
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a rigid bar with mass m, length l, and a uniformly distributed positive charge q is free to pivot about the origin in the presence of a spatially uniform electric field e⃗
a. V(y)=V-E(y) b. U=vq-1/2QEL.cosФ c. V=EL/2 d. angular speed of the bar as it passes Ф=0° is W=[tex]\sqrt{3QE/ML}[/tex]
You were already familiar with the ideas of velocity and speed. The idea of angular speed and velocity, however, is what needs to be understood in terms of physical numbers. Angular motion is the term for when an item is expected to travel along a circular path while making a specific angle. The idea of angular speed and angular velocity is derived from the object's angular motion. Let's examine these ideas in greater depth. Assuming you are rotating a ball in a circular orbit, the angular speed can be defined as follows.
A body's rate of angle change over time as it rotates in a circular orbit is known as its angular speed. The definition of angular velocity is similar to that of linear velocity when an object is moving with some speed in a circular orbit.
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A girl is outside walking on level ground. First she walks 829 m to the east, then 223 m north, and finally 387 m west. What is the magnitude of her displacement? Give your answer in meters correct to at least 1 decimal place. Do not include units in your answer.
Answer:
not enough information need more information to answer the question
rank the capacitors on the basis of the charge stored on the positive plate. rank from largest to smallest. to rank items as equivalent, overlap them.
if you are on top of mount Everest and do a small hop without moving forward, would you still be pulled down by gravity? explain it and also answer my other newest question.
Explanation:
Gravity would still pull you down although it wouldn't affect you as much because there is less gravitational pull in high places such as Mt. Everest.
__________________________1. She is caught in a wind that blows toward the
equator from about 30° N and 30° S of the
equator. She is in the_______________
This is science
She is caught in a wind that blows toward the equator from about 30° N and 30° S of the equator. She is in the trade wind. This science is called Hadley cell.
How is a wind that blows from the north and south of the equator a trade wind?It follows the movement of wind blows from one direction to the other such as the one which blow from north to south or east to west. The trade wind are produced by warm moist air rising near the equator.
Now, within the context of the task given above, when the movement wind which blows toward the equator from about 30° N and 30° S of the equator is known as the trade wind.
So therefore, the movement of wind from the same certain degrees from North and South is called trade wind.
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how does Newton's third law describe the force affecting a rocket as it descends to
Answer:
Explanation:
Newton's Third Law states that "every action has an equal and opposite reaction". In a rocket, burning fuel creates a push on the front of the rocket pushing it forward. This creates an equal and opposite push on the exhaust gas backwards.
Two electromagnetic waves are traveling through a material. Wave 1 has a maximum electric field strength that is three times the maximum field strength of wave 2. How do the average intensities of the waves compare?.
Wave 1's intensity is nine times greater than Wave 2's. An electromagnetic wave carries both magnetic and electric energy when it moves.
What is electromagnetic waves?An electromagnetic wave carries both magnetic and electric energy when it moves. Both waves contribute equally to the energy of electromagnetic waves. It is assumed that wave 1 has an electric field E that is three times greater than wave 2's maximal electric energy E'.
Thus, we can state:
E/E' = 3
We are aware,
The wave's intensity is determined by,
I = 1/2eE²c
Where,
I represents the wave's power,
e is a free space permittivity,
E represents the wave's energy.
The speed of light is c.
the strength of wave 1 right now
I1 = 1/2eE1²c
second wave
I2 = 1/2eE²c
Currently, dividing the two intensities,
I1/I2 = E1²/E2²
We are aware,
E/E' = 3
So,
I1/I2 = 9
I1 = 9I2
Thus, we can state:
Wave 1's intensity is nine times greater than Wave 2's.
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A 0.300 kg mass is attached to 26.6N/m spring.It is pulled 0.120 m and released. How much Potential Energy does it have when it is 0.0600 m fro
equilibrium?
Answer:
Explanation:
The elastic potential energy equation is EPE = (1/2) k x2, where k is the spring constant and x the distance from equilibrium. EPE = (0.5)*(26.6 N/m)*(0.0600 m)2 = 0.0479 Joules.
a cylinder of mass m slides down from rest in a vertical tube whose inner surface is covered by a viscous oil of film thickness h. if the diameter and height of the cylinder are d and l, respectively, derive an expression for the velocity of the cylinder as a function of time, t. discuss what will happen as t → [infinity]. can this device serve as a viscometer?
When there is relative motion between the fluid layers or between the fluid and solid surface, the fluid's internal property known as viscosity is created. This relative motion is being resisted by viscosity.
Derivations of the equations of motion—the connections for the conservation of mass and momentum—in rectangular,
coordinates that are spherical and cylindrical. The entire body of experimental data suggests that the fundamental equations of fluid mechanics are in fact those listed below, and that they apply to any circumstance where a Newtonian fluid is flowing, in theory.
Viscosity, a characteristic of fluids, is produced when there is relative motion between the fluid layers or between the fluid and solid surface. Viscosity prevents this relative motion from happening.
Unfortunately, due to their all-encompassing nature, their analytical solution is challenging or impossible unless the circumstances are quite straightforward.
However,
These "Navier-Stokes equations" must be understood for the following reasons.
reasons:
1. They result in the analytical and precise resolution of some basic yet significant problems.
issues.
2. They serve as the foundation for additional chemical engineering research in various fields.
3. A few reasonable simplification assumptions can frequently result in
for many engineering problems, approximation solutions are eminently acceptable purposes. Typical examples can be found in the study of boundary layers, the use of films to cover substrates, waves, lubrication, and inviscid (irrotational) flow.
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How could infrared imaging be used to find a lost hiker? Answer in 2-3 complete sentences.
When you scan the hiker's body, you will notice a warm spot. Unless that person was dead, they would not be emitting heat.
What is hiking?According to Smokymountains.com, which examined more than 100 news reports of missing hikers, getting off the trail is the most common reason people get lost. That is not someone you want to be. Once you're on the trail, you can use the GPS to ensure you're on the right track. You can take it a step further by bringing a device like a Garmin IN Reach with you on the trail. This GPS also functions as a satellite communicator. Whereas hiking includes the word "walk," which is typically seen as jovial, easy, and pleasant, trekking is defined as a "journey," which is typically more difficult, requires more effort, and takes more than one day.
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If it takes 20 N to move a box, how much power will be needed to move the box a distance of 5meters in 5 seconds?
Answer:
It will need 20 Watts power to move the box 5 meters in 5 seconds.
Step-by-step explanation:
The power is defined as the work per unit time or the rate of doing work:
W=dL/dt
Where de work L, can be calculated by multiplying the force by the displacement d:
L=F.d
To this example, F and D are known, therefore the work is:
L=20N . 5m=40 Nm
We know that the work is doing within a time of 5 seconds:
W= 40 Nm / 5s = 20 Nm/s = 20 Watts
A cougar with a mass of 80 kg is standing at the edge of a cliff. Find the cougar's potential energy if the cliff is 70 m high. show your work !!!
The potential energy of the 80kg cougar at a height of 70m is 54880 Joules.
What is the potential energy of the cougar?Potential energy is simply the energy a body possesses due to its position.
It is expressed mathematically as;
P.E = mgh
Where m is mass, h is height and g is acceleration due to gravity ( g = 9.8m/s² )
Given the data in the question;
Mass of the cougar m = 80kgHeight h = 70mPotential energy P.E = ?Plug the given values into the potential energy formula above and solve.
P.E = mgh
P.E = 80kg × 9.8m/s² × 70m
P.E = 54880kgm²/s²
P.E = 54880 Joules.
Therefore, the potential energy of the cougar is 54880 Joules.
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A frog leaps from flat ground at 6.32 m/s
at a 36.3 angle. What maximum height
does it reach?
(Unit = s)
At hmax, Vy=0
vy=v0y-gt
0=6.32sin(36.3)-9.81t
t=.381 seconds
Δy=v0yt-.5gt^2
Δy=6.32sin(36.3)*.381-.5(9.81)(.381)^2
maximum height=.714 m
what factors affect skill-related fitness and how does each affect it?
Several factors affect your skill-related fitness and your skills, including heredity, practice etc .
Skill-related fitness is have six different components; agility, speed, power, balance, coordination, reaction time.
Several factors affect your skill-related fitness and your skills, including heredity, practice etc
for example some people are able to run faster than others or react quick because they inherited these traits from their parents. A person who did not inherited a tendency in these areas from their ancestors ,may have more difficulty performing skills that require those abilities.
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Hydrochloric acid and sodium hydroxide can be combined to form sodium chloride and water. Which best explains the reaction?
The mass of sodium hydroxide will result in the same mass of sodium chloride.
The total mass of hydrochloric acid and sodium hydroxide will result in a lower total mass of sodium chloride and water.
The mass of hydrochloric acid will result in the same mass of sodium chloride.
The total mass of hydrochloric acid and sodium hydroxide will result in the same total mass of sodium chloride and water.
THE ANSWER IS D
The statement that best describes the reaction is as follows: The total mass of hydrochloric acid and sodium hydroxide will result in the same total mass of sodium chloride and water (option D).
What is the law of conservation of matter?The law of conservation of matter states that matter can neither be created nor destroyed. This law means that the mass that enters and leave a system is accounted for.
The law of conservation of mass explains the input and output of mass in a chemical reaction such that the mass of the reactants must be equal to the mass of the products.
According to this question, hydrochloric acid (HCl) and sodium hydroxide (NaOH) can be combined to form sodium chloride and water.
This means that the total amount of matter of the reactants (hydrochloric acid and sodium hydroxide) must equate the total amount of matter of the products (sodium chloride and water).
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A rod pr is balanced on a pivot at the end r while a string is used to support the rod at p. the weight of the rod is 9n, acts at a point q where qr=30cm and pq=15cm. the tension in the string is
The tension in the string if a rod PR is balanced on a pivot at the end R while a string is used to support the rod at P is 6 N
Moment = Force * Perpendicular Distance
Let us consider the pivot side be initial point,
Since the rod is balanced,
CM = ACM
CM = Clockwise moment
ACM = Anticlockwise moment
F = 9 N
PQ = 15 cm = 0.15 m
QR = 30 cm = 0.3 m
PR = PQ + QR
PR = 0.15 + 0.3
PR = 0.45 m
CM = W * QR
CM = 9 * 30
CM = 2.70 N m
ACM = T * PR
ACM = 0.45 T N m
2.70 = 0.45 T
T = 6 N
Therefore, the tension in the string is 6 N
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a stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 2.88 103 m. during this performance the pilot whose weight is 845 n, maintains a constant speed of 2.25 102 m/s.
We calculated that the pilot's apparent weight at the maximum point was 3 70.5 Newton. Additionally, the circular portion's lowest point is equal to 1598.5 Newton.
A stunt pilot performing a loop during an airshow has been described to us. the vertical circle's loop. During his performance, he gives us the radius of the circle as 3.08 into 10 to the power three m.
We are provided the weight of the pilot, which is 614. For one second, Newton maintains a speed of 2.2 into tend to the bar at a distance of 2 m. We need to know the pilot's apparent weight in newtons while he is at the highest point of the loop. Now, the formula for the pilot's mass can be expressed as being equal to the pilot's weight divided by the acceleration caused by gravity. adding the values together results in 614. too unexplored by exploration.
You get the mass of the pilot, which is 62.65 kgs Hill, when you add gravity. The apparent weight of the pilot will be equal to the normal force generated by the airplane seat. At this point, we may use the formula M to determine the apparent weight off the pilot at the highest point in the circular journey. N in this case stands for the pilot's apparent weight. We find the apparent weight of Mars to be 62.65 kgs multiplied by velocity, which is 2.2 and 2 10 to the part two m for a second, by adding the pilot's speed and the circular portion's radius, r. entire square.
The normal force of the seat on the pilot will be zero since the apparent weight of the pilot at his or her highest point throughout the circle in the case of weightlessness is Newton. With the numbers we have divided by Mars being She took 165 and shoes as replacements, we get the speed of the pilot at weightlessness state equal to 173.7 meters per second. As a result, its speed at this point will be equal to root of wait, multiplied by Baridis divided by mass.
Now your parent wait of the pilot at the lowest point can we given us Baron, well being equal to and we square r plus right, substituting the values, we have 62.65 Kgs to point to entertain the part to the whole square divided by yes, 614. Newton solving which we get the apparent weight of the pilot, the lowest point equal to 1598 0.5. Newton which is the apparent weight of the pilot at the lowest point of the circular what therefore Therefore we determined the apparent weight of the pilot at the highest point being equal to 3 70.5 Newton. And at the lowest point of the circular part being equal to 1598.5 Newton.
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Among elements 1 to 18, which element or elements have the smallest effective nuclear charge?.
As we walk across a period from left to right, the effective nuclear charge rises, whereas it falls as we move down the group. The element with the lowest effective nuclear charge will be found on the left side of the periodic table. The periodic table's group 1 includes H, Li, and Na.
Which nuclear charge has a greater impact?A fluorine atom's nucleus has a charge Z of 9, but the valence electrons are mostly screened by the core electrons—four electrons from the 1s and 2s orbitals—and to a lesser extent by the 7 electrons in the 2p orbitals. The cation of sodium thus has the highest effective nuclear charge.
In spite of being in the same period as sodium and phosphorus, chlorine has the most protons in its shell (the most inside the same period), giving it the highest effective nuclear charge.
The amount of shielding electrons may be calculated by deducting the amount of valence electrons from the overall number of electrons in the atom or ion.
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17. A ball rolls off a lab table at 5 m/s horizontally. The table is 1.2 meters tall.
a. How long is it in the air?
b. How far from the table does it hit the ground?
c. What are the x and y speeds just before it hits the ground?
The ball is in the air for 0.24 seconds, the ball hits the ground 2.46 meters far from the table and the x speed is 0m/s and y speed is 5m/s.
Velocity of the ball is 5m/s and the height of the table is 1.2 meters.
a. We know,
Velocity = distance/time
5 = 1.2/time
Time = 1.2/5
Time = 0.24 seconds.
The time taken by the ball to reach the ground is 0.24 seconds.
b. The ball after rolling of the table will behave like Horizontal projectile.
Horizontal range R formula,
R = V.√(2h/g)
Putting all the values,
R = 5.√(2×1.2/9.8)
R = 5×0.49
R = 2.46 meters.
c. When the ball reaches the ground,
X speed is 0m/s and Y speed is 5m/s.
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Heat waves are defined by the difference in temperature compared to the normal _________ typical of a region.
The difference in temperature from the average temperature for a region defines a heat wave.
A heat wave is an extended period of unusually hot weather that usually lasts longer than days.
Heat waves can occur in both low and high humidity conditions. They have the capacity to cover a wide area, exposing too many people to harmful heat.
An extremely dangerous weather event known as a heat wave occurs when temperatures rise considerably above 90° F. Due to the extreme heat and high humidity levels, an area becomes extremely warm for an extended period of time.
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an athlete lifts a 350 n set of weights from ground level to a position over her head, a vertical distance of 1.90 m. how much work (in j) does the athlete do? assume the weights are moved at constant speed.
Work is measured in joules or newton-meters
It may be thought of as force * distance
If there were acceleration in this problem, the force would be more than the weight, but because the speed is constant force = weight.
given,
force= 350N
Distance= 2m
work= ?
Work = Force * Distance
= 2m * 350 N
= 700 j or 700 N*M
If you're looking at this from an energy standpoint, you can just consider the final PE as the energy required because there is no KE at the end. so,
PE = m*g*h
and m*g = 350N
h= 2m
PE = 700j or 700 N*M
Hence, the 700N*M work is done by athlete.
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electromagnetic radiation with a maximum wavelength of 540 nm(5.4×10−7 m) is needed for the study of the photoelectric effect in potassium atoms. what is the approximate frequency that corresponds to this wavelength?
At a speed of two times ten to the eighth and violent. 5, 40 times 10 to the power -9 meters is written as. This leads to the conclusion that frequency F is equivalent to 5.6 times. Turn 14 times every second. Therefore, the given electromagnetic radiation requires this frequency.
In this problem, we have a given violent electromagnetic radiation, and we need to determine the frequency that corresponds to that violent electromagnetic radiation.
The chosen wavelength is lambda. I called at five minutes and forty nanometers—540 times 10 to the power—or nine meters. Considering that one nanometer equals 10 to the power -9 meters. Now, sea upon lambda finds frequency.
The value of C is three in 2, ten to the power eight meters per second, violent, and the speed of light in a vacuum. 5, 40 times 10 to the power -9 meters is written as. This leads to the conclusion that frequency F is equivalent to 5.6 times. Turn 14 times every second. Therefore, the given electromagnetic radiation requires this frequency.
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anne is working on a research project that involves the use of a centrifuge. her samples must first experience an acceleration of 100???? , but then, the acceleration must increase by a factor of eleven. by how much will the rotational speed have to increase? express your answer as a fraction of the initial rotation rate.
if the final acceleration increases by a factor of 11, then the final rotation should be 3.32[tex]w_{1}[/tex] times the initial rotation.
The relation between the centripetal acceleration and rotation speed of the particle is given as
a=rω²
Where ω is the angular speed and r radius of the circle
Now, rearranging the above equation we will get
ω = √[tex]\frac{a}{r}[/tex]
The initial acceleration is given by
a₁ =100g
But then, the acceleration increases by a factor of 11. Which means the final acceleration of the particle is
a₂ = 11 (100g)
= 1100g
The final and initial rotation speeds are related as
[tex]\frac{w1}{w2}[/tex] = √[tex]\frac{a2}{a1}[/tex]
[tex]w_{2}[/tex] = √[tex]\frac{1100g}{100g}[/tex] x [tex]w_{1}[/tex]
[tex]w_{2}[/tex] = 3.32 [tex]w_{1}[/tex]
The final rotation should be 3.32[tex]w_{1}[/tex] times the initial rotation.
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Suppose you are in a car that is going around a curve. The speedometer reads a constant 30 miles per hour.
Which of the following is NOT true?
a) Your velocity is constant.
b) You and the car are accelerating.
c) Your acceleration is constantly changing
d) Your direction is constantly changing.
e) Your speed is constant.
The true statement is "Your speed is constant".
What is constant speed?
An object is moving at a constant speed when its speed is constant, that is the speed does not increase or decrease.
Constant speed also refers to the movement of a body at a uniform rate in a fixed steady-state moving with an average speed.
If you are in a car that is going around a curve and the speedometer reads a constant 30 miles per hour, you will notice that the direction of your motion is changing and but the distance travelled in a given time does not change.
Thus, only the speed is constant but velocity and acceleration is not constant.
The correct option is E.
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gas giants have many moons than terristcal planets due to having higher ___ ?
Gas giants have more moons than terrestrial planets due to having higher masses.
What are giant planets?Giant planets are composed of low boiling point substances rather than other solid substances but massive solid planets can also exist. There are four giant planets in the Solar System i.e. Jupiter, Saturn, Uranus, and Neptune. They are composed of hydrogen and helium atom i.e. Jupiter and Saturn whereas Uranus and Neptune are composed of ice, rock, hydrogen, and helium.
The giant planets have more moons as compared to the terrestrial planets because of their big masses which leads to stronger gravitational fields. Giant planets also occupy greater space and have larger volumes of mass in their surrounding atmosphere.
So we can conclude that due to having higher masses, Gas giants have many moons as compared to terrestrial planets.
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a singly charged positive ion has a mass of 3.3x10-26 kg. after being accelerated from rest through a potential difference of 933 v, the ion enters a magnetic field of 1.43 t along a direction perpendicular to the field. calculate the radius of the circular path of the ion in the field.
A singly charged positive ion has a mass of 3.3x10-26 kg. after being accelerated from rest through a potential difference of 933 v, the ion enters a magnetic field of 1.43 t along a direction perpendicular to the field. The radius of the circular path of the ion in the field is (r)= 1.982 cm.
What is energy?Energy is a term that means the object is affected by some amount of force and move a distance. That is called the energy. It can be measured in Joule.
How can we calculate the radius of the path?To calculate the radius we are using the formula here,
r= mu/Bq
Where we are given,
m = The mass of single positive charged ion.= 3.3×10⁻²⁶kg.
q= The charge of the single positive charged ion.= 1.602×10⁻¹⁹ C
B = The magnetic field for the electric field. = 0.92 T
But we don't know the term, u= the velocity of the single positive charged ion.
So we have to calculate the velocity of the single positive charged ion. To calculate the velocity we are using the formula,
(1/2)mu²=qv
Here we are given,
v= The potential difference of the electric field. = 933v.
We have to calculate the velocity=u, as Conservation of energy we know,
(1/2)mu²=qv
Or,(1/2)mu²=ev
Or, u²= (2×1.602×10⁻¹⁹×933)/(3.3×10⁻²⁶)
Or, u=91325.9 m/s.
So from this we know the velocity of the ion, u=91325.9 m/s.
Now, we have to calculate the radius in a magnetic field= r,
r= mu/Bq =mu/Be
Or, r= 3.3×10⁻²⁶×91325.9/0.92×1.602×10⁻¹⁹
Or, r=0.01982m
Or, r=1.982 cm.
So from the calculation we can surely say that, The radius of the circular path of the ion in the field is (r)= 1.982 cm.
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A 11.0kg ball traveling at 13.0m/s is crashed into from behind by a 14.0kg ball traveling at 22.0m/s in the same direction. What is the velocity of the first ball if the second slows down to 16.2m/s after the collision?
Let p be the total linear momentum of the system before the collision and p' the total linear momentum of the system after the collision. Let p₁₁ and p₁₄ be the linear momentum of the 11.0kg ball and the 14.0kg ball before the collision, and let p₁₁' and p₁₄' be their linear momenta after the collision.
According to the Law of Conservation of Linear Momentum, the total linear momentum of the system before and after the collision remains the same. Then:
[tex]\begin{gathered} p=p^{\prime} \\ \Rightarrow p_{11}+p_{14}=p_{11}^{\prime}+p_{14}^{\prime} \end{gathered}[/tex]Let v be the unknown speed of the 11.0kg ball after the collision. Find the value of p₁₁, p₁₄, and p₁₄'. Find an expression for p₁₁' in terms of v and replace all the values into the above equation. Solve for v.
The linear momentum of a particle with mass m and velocity v is:
[tex]p=mv[/tex]Then:
[tex]\begin{gathered} p_{11}=(11kg)(13.0\frac{m}{s})=143kg\cdot\frac{m}{s} \\ \\ p_{14}=(14kg)(22.0\frac{m}{s})=308kg\cdot\frac{m}{s} \\ \\ p^{\prime}_{11}=(11kg)\cdot v \\ \\ p^{\prime}_{14}=(14kg)(16.2\frac{m}{s})=226.8kg\cdot\frac{m}{s} \end{gathered}[/tex]Then:
[tex]\begin{gathered} p_{11}+p_{14}=p_{11}^{\prime}+p_{14}^{\prime} \\ \\ \Rightarrow143kg\cdot\frac{m}{s}+308kg\cdot\frac{m}{s}=(11kg)\cdot v+226.8kg\cdot\frac{m}{s} \\ \\ \Rightarrow143kg\cdot\frac{m}{s}+308kg\cdot\frac{m}{s}-226.8kg\cdot\frac{m}{s}=(11kg)\cdot v \\ \\ \Rightarrow224.2\cdot\frac{m}{s}=(11kg)\cdot v \\ \\ \Rightarrow v=\frac{224.2kg\cdot\frac{m}{s}}{11kg}=20.381818\ldots\frac{m}{s} \\ \\ \therefore v\approx20.4\frac{m}{s} \end{gathered}[/tex]Therefore, the velocity of the first ball after the collision is 20.4m/s.