The calculated distance is 20 km.
Speed indicates how quickly something, or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. For instance, if a car drives 120 miles in 2 hours, we may calculate the speed as 120 x 2 = 60 miles per hour. The units for speed are determined by the units of distance and time.
Recognizing that the gap between the trains is closing at a constant rate of 20 km/h,
the total time that elapses before they crash is
t=(20km)/(20km/h)
=1.0h.
During this time, the bird travels a distance of
x=vt
=(20km/1.0h)
=20km.
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A car travels 10km for 3h, then travels 15km for another 6h, finally travels 3km for 5h. What is the average speed or the car?
The average speed of the car that travels 10km for 3h, then travels 15km for another 6h, finally travels 3km for 5h is 2km/hr.
How to calculate average speed?The average speed of a moving object can be calculated by dividing the distance moved by the substance by the time taken.
Average speed = Distance/time
According to this question, a car travels 10km for 3h, then travels 15km for another 6h, finally travels 3km for 5h.
The total distance of the car is 10km + 15km + 3km = 28kmThe total time = 3h + 6h + 5h = 14hAverage speed = 28km ÷ 14h = 2km/hr
Therefore, the average speed of the car that travels 10km for 3h, then travels 15km for another 6h, finally travels 3km for 5h is 2km/hr.
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(ii) Write down, using figures and unit abbreviations: six thousand watts; four
hundred pascals.
a) 6000 Pa
b) 400 Pa
The watt (abbreviated W) is the International System of Units' (SI) standard unit of power (energy per unit time), the equivalent of one joule per second. The watt is used to specify the rate at which electrical energy is dissipated, or the rate at which electromagnetic energy is radiated, absorbed, or dissipated.
One pascal can be defined as the pressure exerted on a surface of area 1m2 by a force of 1N that acts normally on it.
in statement six thousand watt
six thousand in figure will be = 6000
since , its unit is in watt it can be written as = 6000 W
in statement four hundred pascals
four hundred in figures will be = 400
having unit pascal = Pa
which can be written as = 400 Pa
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How do I solve this???
If a toy rocket is launched vertically and rises to a height of 250 meters, then the initial velocity of the toy rocket would be 70 m / s.
What are the three equations of motion?
There are three equations of motion given by Newton,
v = u + at
S = ut + 1/2×a×t²
v² - u² = 2×a×s
As given in the problem, a toy rocket is launched vertically and rises to a height of 250 meters, we have to find the initial velocity of the launch,
By using the third equation of motion given by Newton,
v² - u² = 2×a×s
0² - u² = 2×(-9.81)×250
u² = 4905
u = 70 m / s
Thus, the initial velocity of the toy rocket would be 70 m / s.
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What is the equivalent resistance of a circuit that contains four 75.0 Ω
resistors connected in series to a 100.0 V battery?
Ο Α. 300.0 Ω
Ο Β. 750.0 Ω
Ο C. 1.33 Ω
Ο D. 175.0 Ω
Answer:
Ο Α. 300.0 Ω
Explanation:
The equivalent resistance of a circuit that contains four 75.0 Ω in series combination 300Ω
What is a parallel and series combination of resistance?When two or more resistors are connected between two same points, they are said to be connected in parallel combination(as shown in fig). The equivalent resistance is the reciprocal and the sum of reciprocals of all resistance connected in parallel combination.
1/Rs = 1/R₁ + 1/R₂ + 1/R₃...........+ 1/R(n).
where Rs is the equivalent or total resistance of the circuit.
In parallel combination, same potential difference exists across each resistor. But current through each resistance is different.
When two or more resistors are connected one after other, they are said to be connected in series as shown in figure. in this combination voltage difference across each resistance is different which is given by ohms law. current flowing through each resistance is same.
equivalent resistance for series combination is given by,
R(s) = R₁ + R₂ + R₃...........+R(n).
Given,
R₁ + R₂ = R₃ = R₄ = 75Ω
For series combination,
R(s) = R₁ + R₂ + R₃+R₄
R(s) = 75+75+75+75
R(s) = 300 Ω
Hence option A is correct.
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Review. (b) Is this statement true for all angular displacements, for all displacements less than 180° , or only for small angular displacements? Explain.
Small angle approximation is used. Thus, the magnetic dipole displaced from the equilibrium acts as a torsional pendulum only for a small angle.
What is angular displacement?The angle (measured in radians, degrees, or revolutions) through which a point spins around a particular axis or center is known as the angular displacement of a body. Because a body rotates about its axis, its motion cannot simply be analyzed as a particle because it constantly changes its speed and acceleration (t). It is less complicated to think of a body as rigid while dealing with its rotation. When all of the particle separations remain constant during a body's motion—for instance, when its mass is not flying off—the body is said to be rigid. Realistically, everything is susceptible to deformation, but the effects are little and insignificant.
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A wire 2.80m in length carries a current of 5.00A in a region where a uniform magnetic field has a magnitude of 0.390T. Calculate the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is (c) 120° .
The force on the wire will be
F = 3.16 Newton
We have a current carrying wire in a uniform magnetic field.
We have to determine the magnitude of the magnetic force on the wire assuming the angle between the magnetic field and the current is 60.0°.
What is the magnitude of force acting on a current (I) carrying wire of length (L) placed in a Magnetic field (B)?The force on the current carrying wire will be -
F = IBL sinθ
According to the question, we have -
L = 2.80 m
I = 5 A
B = 0.39 T
Therefore -
F = IBL sinθ
F = 5 x 0.39 x 2.80 x sin(120)
F = 5.46 x sin(120)
F = 5.46 x 0.58
F = 3.16 Newton
Hence, the force on the wire will be
F = 3.16 Newton
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The magnitude of the magnetic force on the wire 4.728 N.
To find the magnetic force, the values given are:
Length A = 2.80m
Current I = 5 A
Magnetic field B = 0.390 T
Angle = 120° .
What is meant by magnetic force?
The attraction or repulsion that arises between electrically charged particles because of their motion is called Magnetic force.Magnetic force is the basic force which is responsible for such effects as the action of electric motors and the attraction of magnets.A force experienced through the magnetic field with some moving charges is perpendicular to its own velocity.The formula to find the magnetic force,F =iBLsinθ Newton
Substituting the values given,
Magnetic force,
F = 5 A × 0.390 T × 2.80 m × Sin 120°
= 5 A × 0.390 T × 2.80 m × 0.8660254
F = 4.728 N.
The magnitude of the magnetic force on the wire 4.728 N.
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The rest energy of an electron is 0.511MeV. The rest energy of a proton is 938MeV. Assume both particles have kinetic energies of 2.00MeV. Find the speed of (a) the electron
The speed of the electron is 0.98c, given that the rest energy of an electron is 0.511MeV and the rest energy of a proton is 938MeV, with both particles having kinetic energies of 2.00MeV.
A particle's total energy and the rest energy follow the laws of physics and the theory of relativity. The energy of any particle is equal to mass times the speed of the light-squared relatively.
Where; E=γ.〖mc〗^2
γ is the ratio of total energy to rest energy of the particle.
m_0 is known as the rest mass of the particle.
Rest energy can be written as: E_0=〖m_0 c〗^2
γ=K/E_0 +1 (1)
γ=1/(√1-v^2/c^2 ) (2)
Putting the values of the electron energy into equation (1):
γ=2.00MeV/0.511MeV+1
γ= 3.91 + 1
γ=4.91
From equation (2),
γ=1/(√1-v^2/c^2 )
Squaring both sides of the equation,
γ^2=1/(1-v^2/c^2 )
1/γ^2 =1-v^2/c^2
v^2/c^2 =1-1/γ^2
v/c=√1-1/γ^2
Making v subject of the formula,
v=√1-1/γ^2 ×c (3)
Inserting the values in the equation,
v=√1-1/〖4.91〗^2 ×c
v=√1-1/24.11×c
v=√0.959×c
v=0.98×c
v=0.98c
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Fossil fuels, hydroelectric power, and wind power ultimately get their energy from _______.
Answer: I would say that the answer to your question is "Nature"
Explanation: Everything that you've listed is related to nature.
"4. Two long, parallel wires each carry the same current I in the same direction (Fig. OQ 30.4) . Is the total magnetic field at the point P midway between the wires (a) zero,(b) directed into the page,(c) directed out of the page,(d) directed to the left, or (e) directed to the right?"
Total magnetic field at the point P midway between the wires is Zero.
The higher wire's contribution to the magnetic field at point P is directed into the page, whereas the lower wire's contribution is directed out of the page. These two oppositely directed contributions to the magnetic field have identical magnitudes and cancel each other out since point P is equally spaced from the two wires and the currents flowing through them are of equal magnitude.
Define magnitude?The term "magnitude" refers to an object's greatest size and direction. Scalar and vector quantities both use magnitude as a common factor. We are aware that scalar quantities are those that have just magnitude by definition. Those quantities with both magnitude and direction are considered vector quantities. It can also be used to describe how far an object has travelled or how much an object weighs in terms of its magnitude.
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A series R L Circuit has components with the following values: L=20.0mH, C=100 nF, R=20.0 Ω , and ΔVmax = 100V, with Δv=ΔVmax sin Ω t . Find (b) the amplitude of the current. at. the resonant frequency,
The amplitude of the current at resonant frequency is 5 A
What is a R L C circuit?R L C is acronym representing Resistor Inductor and Capacitor. A circuit containing Resistor, Inductor, and Capacitor is called R L C circuit. The connection of the circuit can be in series or in parallel;
For connection in series, like we have the end of the connection point of the resistor marks the beginning of the connection point of the inductor and the end of the inductor marks the beginning of the connection point for the capacitor. The sequence of the connection may not be exactly R L C however connection of the three components end to end represents the R L C series connection
How to solve for current. I at resonant frequencyGiven values:
L=20.0mH,
C=100 nF,
R=20.0 Ω ,
ΔVmax = 100V
I = ΔVmax / R
I = 100 / 20
I = 5.0 Amp
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The rotor in a certain electric motor is a flat, rectangular coil with 80 turns of wire and dimensions 2.50 cm by 4.00 cm . The rotor rotates in a uniform magnetic field of 0.800 T . When the plane of the rotor is perpendicular to the direction of the magnetic field, the rotor carries a current of 10.0 mA . In this orientation, the magnetic moment of the rotor is directed opposite the magnetic field. The rotor then turns through one-half revolution. This process is repeated to cause the rotor to turn steadily at an angular speed of 3.60×10³ rev/min. (b) Find the peak power output of the motor.
The Peak power output of the motor is 0.452 Watt
To find the peak power output, the given values are,
No .of turns of the wire = 80
Dimensions is given as, 2.50 cm by 4.00 cm
Magnetic field = 0.800 T.
current = 10 mA.
Angular speed = 3.60 ×10³ rev/min
What is Peak power output?Peak power output can be also known as Peak work rate.If the output was greatest or the work production was very high in the given amount of time then it is known as Peak power output.This peak power is depends on the force, distance and time.The formula for peak power output,
Pout = τ * ω
where,
Pout - output power watts (W),
τ - torque Newton meters (Nm),
ω - angular speed radians per second (rad/s).
Calculating angular speed as here rotational speed of the motor in rpm is given:
ω = rpm * 2π / 60
where,
ω – angular speed, radians per second (rad/s),
rpm – rotational speed in revolutions per minute,
π – mathematical constant pi (3.14),
60 – number of seconds in a minute.
So, the formula is,
Peak power output = τ *rpm * 2π / 60
τ = NIAB sinθ Nm
= 80×10×10⁻³×0.0250×0.040×0.800× Sin 90°
= 2 × 6.4 × 10 ⁻⁴
= 1.2 × 10⁻⁴ Nm.
Peak power output = 1.2 × 10⁻⁴ ×3.60×10³ × 2π / 60
= 0.452 Watt
Thus, the peak power output is 0.452 Watt.
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as a star's size increases, its luminosity increases . as a star's temperature increases , its luminosity increases
A bigger star has a bigger surface.The ability to emit more light and energy is made possible by the greater surface area.The luminosity of a star is also influenced by temperature.
Two red stars have surface temperatures of 3000 K, but Star A's luminosity is about 5% of the Sun's and Star B's luminosity is about 32,000 times the luminosity of the Sun. How much bigger is star B than star AThe radius of star B is nearly 800 times greater than that of star A.
When two stars with a 3000K surface temperature are present.
The star A is about 5% brighter than the star B, which is about 32,000 imes brighter.In light of the fact that brightness is a property of both stars and suns, star B will have a radius that is 800 times greater than star A's.
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Two solid spheres, both of radius 5cm , carry identical total charges of 2 μC. Sphere A is a good conductor. Sphere B is an insulator, and its charge is distributed uniformly throughout its volume. (i) How do the magnitudes of the electric fields they separately create at a radial distance of 6cm compare? (a) EA>EB=0 (b) EA>EB>0 (c) EA=EB>0 (d) 0
The magnitude of their relation compares by the given relation E_A= E_B > 0 (c) when two solid spheres, both of radius 5cm, carry identical total charges of 2 μC, given that Sphere A is a good conductor. Sphere B is an insulator, and its charge is distributed uniformly throughout its volume
Both spheres produce identical fields at the outer locations, much like particles do at the cores, due to the spherically symmetric charge distributions. However, the magnitude of the electric field in charge A is equal to the magnitude of the electric field in charge B greater than zero.
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Simplify this hypothesis about the Michelson-Morley experiment.
"If the speed of light were constant with respect to the proposed ether through which Earth was moving, then that motion could be detected by comparing the speed of light in the direction of Earth's motion.”
The Michelson-Morley test set out to test whether or not or not the ether becomes an absolute reference body by measuring the velocity of light with admire to the shifting Earth. It became hypothesized that the rate of light ought to alternate with a change within the Earth's velocity across the solar.
The outcomes of the Michelson-Morley experiment found no interference styles which means that the velocity of light is equal in a vacuum. This brought about the realization that mild does now not require any medium to travel. The results of the Michelson-Morley experiment supported Einstein's principle of unique relativity.
It turned into hypothesized that the rate of mild ought to trade with a change in the Earth's pace around the sun. however, no such exchange in velocity of light turned into observed and this became called the null result. Michelson and Morley were capable of degree the velocity of light by means of seeking out interference fringes among the mild which had surpassed via the 2 perpendicular palms of their equipment.
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A car moves 92 km due east, then 56 km due west. what is its total displacement?
By using vector, the total displacement is 36 km.
We need to know about vectors to solve this problem. Vector has magnitude and also direction. Displacement is included in vector. It can be written as
s = sx i + sy j + sz k
where s is displacement, sx is displacement on x-axis, sy is displacement on y-axis and sz us displacement on z-axis.
From the question above, we know that
east = positive x
west = negative x
s1 = 92i km
s2 = -56i km
Hence, the total displacement is
s = s1 + s2
s = 92i - 56i
s = 36i
Find the magnitude
|s| = √sx²
|s| = √36²
|s| = 36 km
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Shakib says that 25 meters per second is a velocity. Vania says that 25 meters per second is a speed. Who do you agree with?
Vania is correct in her saying that 25 meters per second is speed as in 25 meter per seconds nothing represents the direction in which the speed is pointing.
What is speed?Speed is a physical quantity that represents the change in distance per unit time it is a scalar quantity and its SI unit is meter per second. Speed only has magnitude but does not have direction.
What is velocity?Velocity is a physical quantity that represents the change in displacement per unit time it is electric quantity and its SI unit is meter per second. Velocity has both magnitude and direction.
Given:
The physical quantity is 25 meters per second.
According to the question Shakib points out that 25 meters per second is velocity, but Shakib is wrong in saying so as in 25 meters per second nothing represents the direction of this quantity.
Here from the given data we can only know the magnitude of the physical quantity but not wear it is pointing towards to.
On the other hand one ya says that 25 m per second is a physical quantity that represents speed and her reasoning is that 25 m per second gives the magnitude as well as the SI units of speed and do not point out in a particular direction therefore the quantity must be speed.
Hence, Vania is correct in her saying that 25 meters per second is speed as in 25 meter per seconds nothing represents the direction in which the speed is pointing.
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A person walks 15 km in 2 hour 30 minutes. Calculate his average speed.
Answer:
6 kilometers per hour
Explanation:
Distance = 15km
Time= 2 hours 30 minutes
Speed = Distance / Time
Speed = 15 / 2.5
Speed = 6 km per hour.
a horizontal clothesline is tied between 2 poles, 10 meters apart. when a mass of 1 kilograms is tied to the middle of the clothesline, it sags a distance of 1 meters. what is the magnitude of the tension on the ends of the clothesline?
By analyzing the vector, the clothesline tension is 25 N.
We need to know about vectors to solve this problem. Force is included in vectors that have magnitude and direction. It can be written as
F = (Fx i + Fy j) N
where F is the force vector, Fx is the x-axis component and Fy is the y-axis component.
From the question we know that :
x = 10 m
(midpoint = 5m)
y = 1 m
m = 1 kg
Find the weight
W = m . g
W = 1 x 10
W = 10N
There are two y-axis components of the tension that hold the clothes. Because of static conditions, we can write
∑Fy = 0
Ty + Ty - W = 0
2Ty - 10 = 0
2Tsinθ - 10 = 0
Find sinθ
sinθ = y/x
sinθ = 1/5
Substitute the sinθ
2Tsinθ - 10 = 0
2T(1/5) - 10 = 0
2T/5 = 10
T = 25 N
Hence, the clothesline tension is 25 N.
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Find the vector using parallelogram law [and Pythagoras theorem (h² = a² + o²) h being the hypothenuse, a being the adjacent side and o being the opposite side]
The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a2 + b2, are equal to the squares on the legs.
What is Pythagorean Theorem called?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. The Pythagorean equation, which is typically used to express this theorem, can be expressed as an equation linking the lengths of the legs (a, b), and the hypotenuse (c):
There are several ways to generalize the theorem, including to higher-dimensional spaces, non-Euclidean spaces, objects other than right triangles, and even things that are not triangles at all but n-dimensional solids. The Pythagorean theorem has garnered interest outside of mathematics as a representation of mathematical mystique, power, or obscurity; there are numerous references to it in popular works of fiction, dramas, musicals, songs, stamps, and cartoons.
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a small turbo prop commuter airplane accelerates before taking off calculate the acceleration of the planbe
The calculated acceleration is for plane and in 19 s 2.63 m/s2 and 475.25 m respectively.
An object's velocity can alter depending on whether it moves faster or slower or in a different direction. A few instances of acceleration include an apple falling, the moon orbiting the earth, or a car being halted at a set of traffic lights.
We employ the following equation to resolve the first portion of this problem.
Vf = 50 m/s final speed
Initial speed: 0 V
t=time
a=acceleration
a=(Vf-Vo)/t
a= (50-0)/19=2.63m/s^2
The following equation is used for this problem's second component.
X=(Vf^2-Vo^2)/2a
X= (50^2-0^2)/ (2*2.63)
=475.25m
The complete question is- A small turbo prop commuter airplane, starting from rest on a New York airport runway, accelerated for 19.0s before taking off. It's speed at takeoff is 50.0 m/s. Calculate the acceleration of the plane, assuming it remains constant. Part B) In this problem, how far did the plane move while accelerating for 19.0s?
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question 53 a 250 ft long span separates a dc power supply from a lamp which draws 25 a of current. if 14 awg wire is used (note that two wires are needed for a total of 500 ft), calculate the amount of power wasted in the wire.
A bulb that consumes 25 A of current is separated from a dc power source by a span of 250 feet. Calculate the amount of power lost in the cable if 14 AWG wire is used (keep in mind that two wires are required for a total length of 500 ft).
How much energy is lost?The answer is 34%, according to the Energy Information Administration (EIA). In other words, by the time the power reaches the consumer metre, 66% of the raw energy needed to generate it has been lost.
The biggest televisions in particular might be the most energy-hungry of all entertainment devices, according to Brian Horne, Senior Insights & Analytics Consultant, Energy Saving Trust. Regardless of its energy rating, a television will use more energy the bigger it is.
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An electron and a proton, moving in opposite directions, are accelerated from rest through the same potential difference. Which particle has the longer wavelength? (a) The electron does. (b) The proton does.(c) Both are the same.(d) Neither has a wavelength.
The electron has the longer wavelength which is option (a) .
De Broglie proposed that because light has both wave and particle properties, matter exhibits both wave and particle properties. This property has been explained as the dual behavior of matter.De Broglie's relationship is given by [tex]\lambda=\frac{h}{mv}[/tex] .....(1) where λ is known as de Broglie wavelength and m is mass of the particle , v i velocity of the particle ,h = Plank’s constant .As mass of electron is less that the mass of the proton .
From equation (1) it is clear that de Broglie wavelength is inversely proportional to the square root of the mass of the material.
Hence , so de Broglie wavelength of electron will be greater than that of proton.
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The height of a person is 1.65 m. Express it into cm and mm
Answer:
1.65 m = 165 cm = 1650 mm
Explanation:
Hope this helps :)
Answer:
1.65 m = 165cm
1.65 m = 1,650mm
Explanation:
1.65 m = 165cm
for converting m to cm ▶ meters×100 ▶ 1.65×100=165cm
1.65 m = 1,650mm
for converting m to mm ▶ meters×1,000 ▶ 1.65×1,000=1,650mm
Hope it helps!!!
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Force pairs definition
The statements which are true about Newton's Third Law force pairs include the following:
A force pair is only created when there are equal and opposite forces on a system. Force pairs point in opposite directions. Force pairs have the same magnitudes. Force pairs should never be on the same free body diagram. What is Newton's Third Law of Motion?Newton's Third Law of Motion states that for every action there is an equal but opposite reaction. This ultimately implies that, in every interaction, there is a pair of forces (force pairs) acting on the two interacting objects.
In Science, force pairs are also referred to as action-reaction pairs, which are forces acting on different object and have the same (equal) magnitude but opposite in direction.
What is a free body diagram?A free body diagram can be defined as a graphical illustration which is typically used to visualize moments, tension, and applied forces that are acting on an isolated or rigid body (object), while using arrows pointing in the direction of these forces.
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Complete Question:
Which of the following statements are true about Newton's 3rd law force pairs? There may be more than one correct answer.
If there is a force on a system, then there must be a force pair present on a different system. A force pair is only created when there are equal and opposite forces on a system. Force pairs point in the same direction. Force pairs point in opposite directions. Force pairs can have different magnitudes. Force pairs have the same magnitudes. Force pairs should never be on the same free body diagram. Force pairs should be on the same free body diagram if they are present.if a force f⃗ acts on an object as that object moves through a displacement s⃗ , the work done by that force equals the scalar product of f⃗ and s⃗ : w
If a force f acts on an object as that object moves through a displacement s , the work done by that force equals the scalar product of f and s : w . This is because when the object moves, the force applied to it changes in magnitude and direction.
Therefore, multiplying this change in Force by the distance traveled.
What connection exists between an object's work and its displacement?The distance and direction that an object is moved are known as displacement. While force and displacement are indirectly proportional, work and force are directly proportional. W= Fd is the equation illustrating the relationship.F stands for force in newtons, W for work measured in joules, and d for distance in meters.To learn more about displacement, visit:
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A reconnaissance plane flies 430 km away from its base at 680 m/s, then flies back to its base at 1020 m/s. what is its average speed? answer in units of m/s.
The average speed of the plane is 816 m/s.
We need to know about the average speed to solve this problem. The average speed can be determined as the total distance divided by the total time. It can be written as
v = d / t
where v is average speed, d is distance and t is time.
From the question above, we know that
d1 = d2 = 430 km
v1 = 680 m/s
v2 = 1020 m/s
Because of the distance is the same, we can calculate the average speed as
v = 2d / (t1 + t2)
v = 2.d / (d/v1 + d/v2)
v = 2/(1/v1 + 1/v2)
v = 2/(1/680 + 1/1020)
v = 816 m/s
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Based on the information you have seen, in which sport do the players have a greater change of hitting a home run? Use your understanding of forces to explain.
Then step off and then throw to the base where the infraction occurred. There is no need to tell an umpire what you are appealing the players have a greater change of hitting a home run.
What is home run?In baseball, a home run (abbreviated HR) is scored when the batter is able to safely round the bases and get to home plate in one play without any errors from the opposing team's defense. Typically, a home run is obtained by launching the ball over the outfield fence in between the foul poles (or by striking either foul pole) without allowing it to touch the field. A much less frequent type of home run is one that occurs "within the park," in which the batter makes it safely home while the ball is still in play on the field.
A hit, a run scored, and a run batted in (RBI) are all given to the batter when a home run is hit.
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A uniform magnetic field of magnitude 0.150 T is directed along the positive x axis. A positron moving at a speed of 5.00×10⁶ m/s enters the field along a direction that makes an angle of Ф = 85.0° with the x axis (Fig. P 29.73 ). The motion of the particle is expected to be a helix as described in Section 29.2. Calculate (a) the pitch p
The pitch of the helical path of positron is, [tex]p=1.038 \times 10^{-4}[/tex]
Explain the trajectory's radius?The radius of a circular arc that most closely resembles the curve at a given point on a projectile's trajectory is the radius of the trajectory, which reveals the direction in which the projectile is curving at that particular location.
Given:
Magnitude of magnetic field, [tex]B=0.150\;T[/tex]
Speed of position, [tex]v=5 \times 10^{6}\;m/s[/tex]
Angle, [tex]\;\theta=85^{\circ}[/tex]
The motion of the particle is expected to be a helix.
(a)
We know that,
[tex]Pitch,\;p=V_{11} \times T[/tex]
Where,
[tex]V_{11}=parallel\;velocity\;to\;magnetic\;field[/tex]
[tex]T=Time\;period=\frac{2 \times \pi \times m}{q \times B}[/tex]
[tex]Mass\;of\;positron,\;m=9.1 \times 10^{-31}\;kg\\[/tex]
[tex]Change\;of\;positron,\;q=+1e=1.6 \times 10^{-19}\;kg[/tex]
Substitute the known values in pitch equation,
[tex]p=Vcos\theta\frac{2\times \pi \times m}{q\times B}[/tex]
[tex]p=(5\times 10^{6)} cos85^{\circ}\;\frac{2\times \pi \times 9.1 \times 10^{-31} }{1.6 \times 10^{-19} \times 0.150}[/tex]
By solving the above equation, we get
[tex]p=1.038 \times 10^{-4}[/tex]
Therefore,
[tex]p=1.038 \times 10^{-4}[/tex]
(b)
We know that,
[tex]Radius\;of\;trajectory,\;r=\frac{m \times V_{1} }{q \times B}[/tex]
Where,
[tex]V_{1}=perpendicular\;velocity\;to\;magnetic\;field[/tex]
[tex]m=mass\;of\;positron=9.1 \times 10^{-31} \;kg[/tex]
[tex]q=charge\;of\;positron=+1e=1.6 \times 10^{-19}\;kg[/tex]
Substitute the known values in the radius of trajectory equation,
[tex]Radius\;of\;trajectory,\;r=\frac{m}{q \times B}\;(Vsin\theta)[/tex]
[tex]Radius\;of\;trajectory,\;r=\frac{9.1 \times 10^{-31} \times 5 \times 10^{6} \times sin85^{\circ}}{1.6 \times 10^{-19} \times 0.150}[/tex]
By solving the above equation, We get,
[tex]r=1.88 \times 10^{-4} \;m[/tex]
Therefore, The radius of the trajectory is,
[tex]r=1.88 \times 10^{-4} \;m[/tex]
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Suppose our Sun is about to explode. In an effort to escape, we depart in a spacecraft at v=0.800 c and head toward the star Tau Ceti, 12.0 ly away. When we reach the midpoint of our journey from the Earth, we see our Sun explode, and, unfortunately, at the same instant, we see Tau Ceti explode as well.(a) In the spacecraft's frame of reference, should we conclude that the two explosions occurred simultaneously? If not, which occurred first?
Sun exploded 16 years after Tau Ceti.
Considering a scenario in which the Sun is going to explode.
In order to escape the explosion, we depart in a spacecraft with a speed of v = 0.8c.
The star Tau Ceti is 12 life years away.
At the midpoint of the journey, the Sun as well as Tau Ceti explode. at the same instant.
Now, the distance between the Sun and the spacecraft:
L = L(p) √( 1 - (v/c)²)
L = (6 ly) √[1 - (0.8)²] = 3.6 ly
Now, we observe Sun to be flying away from us at a speed of 0.8c whereas the light from the Sun approaches at a speed 1c. Therefore, the gap between the Sun and the blast of the Sun wave is opened at a speed of 1.8c.
Therefore, the time passed ever since the Sun exploded is:
t = 3.60 ly / 1.80c = 2 years.
Now, we observe Tau Ceti moving toward us at a speed of 0.8c, whereas the light from the blast approaches at a speed of 1c which is only 0.2c faster. Then the gap between the Tau Ceti and its blast wave is 3.60 ly and growing at a speed of 0.2c.
Therefore, the time for which it has been opening is:
t = 3.60 ly/ 0.20c
t = 18 years.
Therefore, Tau Ceti exploded 16 years before the Sun.
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Suppose you perform Young's double-slit experiment with the slit separation slightly smaller than the wavelength of the light. As a screen, you use a large half-cylinder with its axis along the midline between the slits. What interference pattern will you see on the interior surface of the cylinder?(a) bright and dark fringes so closely spaced as to be indistinguishable (b) one central bright fringe and two dark fringes only (c) a completely bright screen with no dark fringes (d) one central dark fringe and two bright fringes only (e) a completely dark screen with no bright fringes
The interference pattern that you you see on the interior surface of the cylinder is (a) bright and dark fringes so closely spaced as to be indistinguishable
What is Young's double slit experiment?Young's double slit experiment is the experiment performed in 1801 by Thomas Young to prove that light is a wave.
Since you are performing Young's double-slit experiment with the slit separation slightly smaller than the wavelength of the light and as a screen, you use a large half-cylinder with its axis along the midline between the slits.
What interference pattern will you see on the interior surface of the cylinder?Now, we know that the interference pattern of a Young's double slit experiment is as a result of diffraction.
What is interference pattern?Interference pattern is the pattern observed due to the vectorial combination of waves
What is diffraction?Diffraction is the property of a wave in which a wave spreads out as it passes through an opening.
Now, we know that diffraction occurs when a wave goes through an aperture or opening smaller than its wavelength.
Now, the smaller the opening compared to the wavelength of the wave, the more the diffraction you would observe bright and dark fringes so closely spaced as to be indistinguishable.
So, the interference pattern that you you see on the interior surface of the cylinder is (a) bright and dark fringes so closely spaced as to be indistinguishable
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