Answer:
Since the wire is not splitting at any point in the circuit,
the resistors are in series
Hence, Equivalent resistance = 10 + 20 + 30
Equivalent Resistance = 60 Ω
Is Saturn less dense than water which has a
density of 997 kg/m³? Find out by calculating the density of Saturn in kg/m³. The mass of Saturn is 5.68 x 1026 kg, and its radius is 5.6 x 107 m.
Density of Saturn:
The density of water at STP, which is \(997 kg/m^3\), we can see that Saturn is less dense than water.
To determine whether Saturn is less dense than water, we must compute its density and compare it to the density of water at standard temperature and pressure (STP), which is \(997 kg/m^3\).
Saturn's density can be computed using the following formula:
density equals mass divided by volume
Saturn's mass and volume may be computed given its mass and radius.
The volume of Saturn can be determined using the sphere volume formula:
volume =\((4/3) \pi (r^3)\)
where r is Saturn's radius.
Filling in the blanks:
volume = \((4/3) \pi (5.6 \times 107) m^3\)
8.27 x 1023 \(m^3\)volume
Saturn's mass is given as \(5.68 \times 10^{26} kg.\)
We can now compute Saturn's density:
density equals mass divided by volume
density= \((5.68 x 10^{26 }kg\)) /\((8.27 \times 10^{23 }\)m³) a density of\(687 kg/m^3\)
This is due to the fact that Saturn is mostly made up of hydrogen and helium, which are far less dense than water. In reality, Saturn is the least dense planet in the Solar System, and it would float in a large enough body of water.
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A slanted surface used to raise an object is a(n)
Answer:
Inclined Plane
Explanation:
explain the methods to determine specific charge of an electron ?
The methods to determine the specific charge of an electron are The J. J. Thomson Method and The Millikan Oil Drop Method.
The J. J. Thomson Method
In this method, an electric field is created between two parallel metal plates. Electrons are accelerated by this field from the negative plate to the positive plate. After that, they strike a fluorescent screen. When the electrons are shot through the electric field perpendicular to the magnetic field, they experience the Lorentz force, which is given by the formula: $F= evB$ $F= evB$
When a magnetic field is applied at right angles to an electron beam, it bends the path of the beam into a circular path. The radius of the path of an electron beam in a magnetic field is determined by the relationship:r = mv/eB. As a result, the specific charge of an electron may be calculated from the expression: $e/m = 2V / B^2r^2$
The Millikan Oil Drop Method
This is another technique for determining the specific charge of an electron. The oil drop experiment was first done by Robert A. Millikan in 1909. He did this experiment by suspending charged droplets of oil in a uniform electric field between two parallel plates.
The fall of the oil droplets in the absence of an electric field was also noted. The fall velocity of the oil droplet was determined by measuring the time taken by the oil droplet to pass through a fixed distance between the plates in the absence of an electric field. By measuring the electric field strength, the voltage applied to the plates, and the fall velocity of the oil droplet, the specific charge of the electron was determined.
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The methods to determine the specific charge of an electron are :
The J. J. Thomson Method The Millikan Oil Drop Method.How do we describe?In the J. J. Thomson Method, an electric field is created between two parallel metal plates. Electrons are accelerated by this field from the negative plate to the positive plate. After that, they strike a fluorescent screen.
When the electrons are shot through the electric field perpendicular to the magnetic field, they experience the Lorentz force.
The Millikan Oil Drop Method is an experiment by which is created by suspending charged droplets of oil in a uniform electric field between two parallel plates.
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Before taking a personality test, Jackie sets her mind on growth. How might this affect her understanding of the test?
Choose two anSwers-
1.She will score high in the areas she chooses to.
2.She will respond based on what's best in her desired career path.
3. She will think of the results as an opportunity to find joy.
4. She will identify areas for self- development in her results.
Answer:
The two answers that are likely to be true are:
She will think of the results as an opportunity to find joy.
She will identify areas for self-development in her results.
By setting her mind on growth, Jackie is likely to approach the personality test with a positive and open mindset. This can lead to the following outcomes:
She will think of the results as an opportunity to find joy: Jackie may view the test results as a chance to discover aspects of her personality that bring her joy and satisfaction. She might focus on finding strengths and positive qualities that can contribute to her personal and professional growth.
She will identify areas for self-development in her results: Rather than viewing the test results as fixed labels or limitations, Jackie is likely to see them as valuable feedback for self-improvement. She may actively seek out areas where she can further develop her skills, knowledge, and personality traits to enhance her personal and career growth.
It's important to note that the other options listed in the question (1. She will score high in the areas she chooses to and 2. She will respond based on what's best in her desired career path) are not directly related to having a growth mindset. They suggest a more biased or strategic approach to the test, which may not align with the concept of growth and self-improvement.
a bus with a maximum speed of 20m/s takes 21 sec to travel 270m from stop to stop. Its acceleration is
twice as great as its deceleration.
Find:
A, the acceleration
B, the distance traveled at maximum speed
We can use the following data to get the values of acceleration and the distance covered at top speed:
Maximum speed is 20 m/s (v_max).
Time (t) = 21 seconds
(d) = 270 m is the total distance travelled.
Find the acceleration (A) first:
Applying the equation v = u + at
where an is the acceleration, t is the elapsed time, u is the beginning velocity, and v is the end velocity.
Given: The bus will begin at rest with an initial velocity of 0 metres per second (u).
The formula can be rearranged as follows:
a = (v - u) / t
a = (20 m/s - 0 m/s) / 21 seconds
0.952 m/s2 a = 20 m/s / 21 sec
Therefore, the acceleration of the bus is approximately 0.952 m/s².
Next, let's find the distance traveled at maximum speed (B):
Since the bus starts from rest, it takes time to accelerate to its maximum speed and then decelerate to stop. The distance traveled at maximum speed can be found by subtracting the distances covered during acceleration and deceleration from the total distance.
Distance during acceleration = (1/2) * a * t^2
Distance during deceleration = (1/2) * a * t^2
Distance traveled at maximum speed = Total distance - (Distance during acceleration + Distance during deceleration)
B = d - (0.5 * a * t^2 + 0.5 * a * t^2)
B = 270 m - (0.5 * 0.952 m/s² * (21 sec)^2 + 0.5 * 0.952 m/s² * (21 sec)^2)
B = 270 m - (0.952 m/s² * (21 sec)^2)
B = 270 m - 220.392 m
B ≈ 49.608 m
Therefore, the distance traveled at maximum speed is approximately 49.608 m
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How can you predict the number of swings an 80 cm pendulum will make in 15 seconds?
A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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The surface of the exit road is horizontal, not banked. (See figure.) If the static
friction between the tires and the surface of the road is us = 0.688 and the
maximum speed with which the car can exit the highway safely without sliding is
25.2 m/s, what is the radius of curvature of a highway exit, r?
The radius of curvature of the highway exit is approximately 220 km.
To find the radius of curvature of the highway exit, we can use the centripetal force equation:
F = mv^2 / r
where F is the maximum static friction force, m is the mass of the car, v is the maximum safe speed, and r is the radius of curvature.
We can solve for r by rearranging the equation:
r = mv^2 / F
Substituting the given values, we have:
r = (1000 kg)(25.2 m/s)^2 / (0.688)
r = 2.20 x 10^5 m
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a roller coaster start at a height of 40Meters and reached a height of 20meter. does mechanical energy change
Mechanical energy changes when a roller coaster starts at a height of 40 meters and reaches a height of 20 meters. The potential energy decreases, while the kinetic energy increases.
When a roller coaster starts at a height of 40 meters and reaches a height of 20 meters, mechanical energy changes. In physics, mechanical energy is the sum of potential and kinetic energy that is present in the objects. When an object is moved, it gains or loses energy, thus the mechanical energy changes. There are two forms of mechanical energy, namely kinetic energy and potential energy. Kinetic energy is the energy that a moving object possesses due to its motion, while potential energy is the energy that an object possesses due to its position or shape.
In the case of a roller coaster, when it starts at a height of 40 meters, it has potential energy that is equal to its mass multiplied by the acceleration due to gravity multiplied by its height. As it moves down the track, the potential energy gets converted into kinetic energy, which is the energy of motion. When the roller coaster reaches a height of 20 meters, it has a lower potential energy compared to when it started. The difference in potential energy is equal to the amount of work done by the force of gravity in bringing the roller coaster down from a height of 40 meters to a height of 20 meters. At the same time, the roller coaster has a higher kinetic energy than when it started, as it gained speed during the descent.
Therefore, in summary, mechanical energy changes when a roller coaster starts at a height of 40 meters and reaches a height of 20 meters. The potential energy decreases, while the kinetic energy increases.
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A proton is given an acceleration of 1.5x109 m/s² when it is placed in an electric field.
What is the strength of the electric field?
Answer:
The strength of the electric field is \(E=15.66\: N/C\)
Explanation:
Here the electric force is equal to Newton's second law.
\(F_{e}=ma\)
Let's recall that electric force is the electric field times the charge, so we have:
\(qE=ma\)
\(E=\frac{ma}{q}\) (1)
Where:
m is the proton mass
q is the proton charge
a is the acceleration
Using the equation (1) we have:
\(E=\frac{1.67*10^{-27}1.5x10^{9}}{1.6*10^{-19}}\)
Therefore, the strength of the electric field is \(E=15.66\: N/C\)
I hope it helps you!
URGENT HELP PLS
(a) Find the frequency ratio between the two frequencies f1 = 320 Hz and
½2 = 576 Hz.
S) If we go down from / by an interval of a fourth, find the frequency ratio filfi.
(c) Find the frequency of f3.
The frequency of f3 is approximately 716 Hz.
What is frequency?The frequency of a repeated event is its number of instances per unit of time. Hertz (Hz), which stands for the number of cycles per second, is a popular unit of measurement.
a. Given two frequencies, f1 and f2, the frequency ratio is as follows:
frequency ratio= \(\frac{f2}{f1}\)
Inputting the values provided yields:
frequency ratio = \(\frac{576}{320Hz}\) =1.8.
As a result, the difference in frequency between f1 = 320 Hz and f2 = 576 Hz is 1.8.
b. Since there are 12 half-steps in an octave and a fourth is a distance of 5 half-steps, going down a fourth requires dividing the frequency by \(2^{(4/12)}\). Hence, once a fourth is subtracted, the frequency ratio between f and f1 is:
frequency ratio= \(\frac{f}{ (f1 /f2 ) }\)= \(\frac{f}{ (f1 / 1.3348) }\)
By dividing the numerator and denominator by 1.3348, we may make this more straightforward:
frequency ratio= (f × 1.33348)/f1
As a result, (f × 1.3348) / f1 is the frequency ratio between f and f1 after descending a fourth.
c. (c) To find the frequency of f3, we need to know the interval between f1 and f3. Let's assume that f3 is a fifth above f2. The frequency ratio for a fifth is given by: \(2^{(7/12)}\) = 1.49831
Therefore, the frequency of f3 is:
f3 = f1 × (\(2^{(7/12)}\)) × (\(2^{(7/12)}\)) = 320 Hz × 1.49831 ×1.49831 = 716 Hz
Therefore, the frequency of f3 is approximately 716 Hz.
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How does society shape reality?
A tennis ball is released from a height of 2.0 m above the floor, and then bounces three times. With each bounce, dissipative forces cause it to lose 16.0% of its mechanical energy. How high does it reach after the third bounce?
140 cm
120 cm
120 mm
12 cm
Answer:
12 cm
Explanation:
From what I got with my answer (8.192 cm) I went ahead and rounded it to the closest answer which is 12 cm. Hopefully im correct but if not, I apologize in advance.
An 8-ohm resistor is connected to a 120-volt circuit. What current will it draw?
Answer:
15 A (15 amperes of current)
Explanation:
From Ohm's Law,
Voltage, V = Current, I × Resistance, R
Making Current, I the subject:
Current, I = Votage, V/ Resistance,R
= V/R
= 120volts /8ohms
= 15 A
What is also known as motion energy
Explanation:
I learned this
its Kinetic energy.
Roberto has twice the mass his sister Mary has but runs at the same velocity as Mary. Will his kinetic energy be twice as much? Show your work.
Answer:
Yes, Roberto will have twice the kinetic energy
Explanation:
The equation for kinetic energy is Ke = 1/2(m)v^2
The variable m is not squared by anything, which means it is directly proportional to the equation. If you were to multiply m by 2, it would in turn multiply the entire equation by 2, getting you an outcome with twice as much kinetic energy.
A hockey puck with a mass of 0.17 kg is traveling to the right along the ice at 15 m/s. it strikes a second hockey puck with a mass 0.11 kg. the first hockey puck comes to rest after the collision. What is the velocity of the second hockey puck after the collision? ( Round your answer to the nearest integer.)
Answer:
\(v_2 = 23.182m/s\)
Explanation:
Given
\(m_1 = 0.17kg\)
\(m_2 = 0.11kg\)
\(u_1 = 15m/s\) -- Initial Velocity of the first
\(u_2 = 0m/s\) -- Initial Velocity of the second
\(v_1 = 0m/s\) -- Final Velocity of the first
Required
Determine the final velocity of the second hockey puck (\(v_2\))
This question illustrates law of conservation of momentum and it'll be solved using the following formula:
\(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\) ---- law of conservation of momentum
Substitute in the right values
\(0.17 * 15 + 0.11*0 = 0.17 * 0 + 0.11*v_2\)
\(0.17 * 15 + 0 = 0 + 0.11*v_2\)
\(2.55 = 0.11*v_2\)
Solve for v2
\(v_2 = 2.55/0.11\)
\(v_2 = 23.182m/s\)
Hence, the final velocity of the second hockey puck is 23.182m/s
Two objects are held close together. When they are released, they move toward one another. Which conclusion is supported by this evidence? O The objects are both positively charged. O The objects are both negatively charged. O The objects have no charge. O The objects have opposite charges. Mark this and return Save and Exit 02:48:18 Next Submit
Two objects are held close together. When they are released, they move toward one another. The conclusion is supported by this evidence is the objects have opposite charges.
An electric charge is a physical property that causes matter to experience a force when in close proximity to other electrically charged matter. There are two types of electric charges: positive and negative. Protons, which are positively charged, and electrons, which are negatively charged, are subatomic particles that make up matter.
In general, the protons and neutrons in the nucleus of an atom have a net positive charge, while electrons, which orbit the nucleus, have a net negative charge. The charges of these subatomic particles are indicated by the symbols "p" for proton, "n" for neutron, and "e" for electron.
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A car is moving at 14 m/s. After 30 s, its speed inncreased to 20 m/s. What is the acceleration over time
Answer:
0.2 m/s^2
Explanation:
initial speed 14m/s
final speed 20m/s
acceleration:
(20m/s - 14m /s) /30s = (6m/s)/30s = 0.2 m/s^2
Psi(x) = (alpha/pi) ^ (1/4) * e ^ (- (alpha * x ^ 2)/2)
Find wave function of
(Px)*2
(Pls if you know the answer writ it on the paper to be clear )
Note that the wave function of (Px)^2 is given by: (Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
What is the explanation for the above response?To find the wave function of (Px)^2, we need to use the momentum operator, which is represented by Px = -i(h/2π) d/dx.
First, let's find the wave function of Px, which is given by:
Px Psi(x) = -i(h/2π) d/dx [Psi(x)]
= -i(h/2π) [-αx Psi(x) + (α^2 x) Psi(x)]
Now, we can find the wave function of (Px)^2 by squaring the wave function of Px:
(Px)^2 Psi(x) = (-i(h/2π) d/dx) (-i(h/2π) d/dx) Psi(x)
= (h^2/4π^2) [α^2 x^2 Psi(x) - 2α x d/dx(Psi(x)) + (d^2/dx^2)(Psi(x))]
Substituting Psi(x) = (α/π)^(1/4) e^(-αx^2/2) into the above expression, we get:
(Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
Therefore, the wave function of (Px)^2 is given by:
(Px)^2 Psi(x) = (h^2/4π^2) [(3α^2 x^2 - α) (α/π)^(1/4) e^(-αx^2/2)]
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Some thermal containers have layers of materials to keep drinks cold for as long as possible. Which design would help keep ice frozen for the longest period?
A. Inner core of steel, no air gap, outer layer of plastic
B. Inner core of steel, air gap, outler layer of glass
C. Inner core of steel, no air gap, outer layer of plastic
D. Inner core of glass, air gap, outer layer of glass
I know A. and C. are the same, but those are my options.
Thomas knows that many machines transform electrical energy into other forms of energy
Answer:
Only the car transforms electrical energy into more than one form of energy.
Explanation:
The motion of the car is mechanical energy but it can also transform into another energy witch is electrical energy
Which of the following objects requires the MOST power to lift?
A. A 2 kg box lifted 1 m in 1 s.
B. A 2 kg box lifted 2m in 1 s.
C. A 2 kg box lifted 1 m in 2 s.
D. A 2 kg box lifted 2 m in 2 s.
The object requires the MOST power to lift a 2 kg box 2 m in 1 s. Hence, option (B) is correct.
What is power?The quantity of energy moved or converted per unit of time is known as power in physics. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as activity in ancient writings. A scalar quantity is power.
Power required for lifting a 2 kg box 1 m in 1 s = (2×9.8×1)/1 watt = 19.6 watt.
Power required for lifting a 2 kg box 2 m in 1 s = (2×9.8×2)/1 watt = 39.2 watt.
Power required for lifting a 2 kg box 1 m in 2 s = (2×9.8×1)/2watt =9.8 watt.
Power required for lifting a 2 kg box 2 m in 2 s = (2×9.8×2)/2watt =19.6 watt.
So, The most power required in lifting a 2 kg box 2 m in 1 s.
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A 2.5 kg block is initially at rest on a horizontal surface.A horizontal force of magnitude 6.0 N and a vertical force are
then applied to the block (Fig. 6-17).The coefficients of friction for
the block and surface are ms " 0.40 and mk " 0.25. Determine the
magnitude of the frictional force acting on the block if the magnitude
of is (a) 8.0 N, (b) 10 N, and (c) 12 N.
To solve this problem, we need to determine the frictional force acting on the block with different magnitudes of the applied force.
First, we need to find the normal force on the block, which is equal to the weight of the block. The weight of the block is given by:
W = mg = 2.5 kg x 9.8 m/s^2 = 24.5 N
Next, we need to find the force of the applied vertical force, which is given in the problem as "is". We can use trigonometry to find the vertical component of the force:
Fv = is sinθ
where θ is the angle between the force and the horizontal surface. Since the problem does not give us the value of θ, we will assume it to be 0°, which means the force is purely horizontal.
(a) If the magnitude of the applied force is 8.0 N, then the frictional force can be calculated as:
Ff = μsFn = μs(mg - Fv) = 0.40(24.5 - 0) = 9.8 N
(b) If the magnitude of the applied force is 10 N, then the frictional force can be calculated as:
Ff = μsFn = μs(mg - Fv) = 0.40(24.5 - 10) = 5.8 N
(c) If the magnitude of the applied force is 12 N, then the frictional force can be calculated as:
Ff = μkFn = μk(mg - Fv) = 0.25(24.5 - 12) = 3.1 N
Therefore, the magnitude of the frictional force acting on the block is 9.8 N, 5.8 N, and 3.1 N, for applied forces of 8.0 N, 10 N, and 12 N, respectively.
(a) When the horizontal force is 8 N the frictional force is 11.8 N.
(b) when the applied force is 10 N; the frictional force is 13.8 N.
(c) when the applied force is 12 N; the frictional force is 15.8 N.
What is the magnitude of the frictional force acting on the block?(a) The magnitude of the frictional force on the block when the horizontal force is 8 N is calculated as;
F - Ff = ma
where;
F is the horizontal force appliedFf is the frictional forcem is the massa is the accelerationF - μmg = ma
6 - 0.4 x 2.5 x 9.8 = 2.5 a
2.5 a = -3.8
a = -3.8/2.5
a = -1.52 m/s²
when the applied force is 8 N;
8 N - Ff = -1.52 m/s² x 2.5 kg
Ff = 11.8 N
(b) when the applied force is 10 N;
10 N - Ff = -1.52 m/s² x 2.5 kg
Ff = 13.8 N
(c) when the applied force is 12 N;
12 N - Ff = -1.52 m/s² x 2.5 kg
Ff = 15.8 N
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why does all the water of the earth not get evaporated during hot summer days?
Answer:
Water has a high latent heat of vaporization, so it takes a large amount of heat to get converted into vapor. Although evaporation takes place continuously, there is simply not enough heat produced to evaporate all the water on earth at once.
You've always wondered about the acceleration of the elevators in the 101 story-tall Empire State Building. One day, while visiting New York, you take your bathroom scale into the elevator and stand on them. The scales read 160 lb as the door closes. The reading varies between 130 lb and 180 lb as the elevator travels 101 floors.
a. What is the magnitude of the acceleration as the elevator starts upward?
b. What is the magnitude of the acceleration as the elevator brakes to a stop?
Answer:
a) a = 4 ft / s² , b) a = -6 ft / s²
Explanation:
The balance is subjected to two forces: the weight of the person directed downward and the spring reaction directed upward.
When the person rides the elevator, the acceleration is zero
F - W = 0
F = W
F = 160 lb
let's find the mass of the body
W = mg
m = W / g
m = 160/32
m = 5 slug
A) when the elevator is moving up
F - W = m a
F = W + m a
F - W / m = m a
F = m (g + a)
therefore the scale reading (F) must be higher, in this case F = 180 lb
a = F / m - g
a = 180 - 160)/5
a = 4 ft / s²
b) when the elevator is stopping
in this case the direction is opposite to the speed, that is to say downwards
F- W = m (-a)
a = W - F / m
a = 130 -160 /5
a = -6 ft / s²
1) Identify and explain three common misconceptions related to measurement of temperature, volume, and mass. 2) Choose one real-world scenario that involves the measurement of temperature, volume, or mass. Describe the scenario in detail, including the units of measurement used. 3) Explain how accurate measurement of temperature, volume, or mass is important in the chosen scenario. Discuss the potential consequences of inaccurate measurement. 4) Describe a hands-on activity that could be used to help students understand the concept of accurate measurement in the chosen scenario. Include a step-by-step procedure and the materials needed for the activity. 5) Discuss how this activity can help students overcome the common misconceptions related to measurement in science.
While taking measurements, accuracy and precision are two crucial considerations. Both of these phrases describe how closely a measurement resembles a standard or recognized value.
While weight refers to the force of gravity acting on an object, mass refers to the quantity of matter in an object. Wherever you go in the universe, your mass remains constant; nevertheless, your weight varies with regions.
When a dimension is measured larger, the area or volume also grows in proportion. When we double an object's dimensions, people mistakenly believe that the curved surface area and volume will likewise double.
Temperature is a measurement of the average heat energy of the motions of the molecules in a substance, whereas heat is the total energy of those motions.
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consider a particle of mass m decaying into two bodies of masses m1 and m2. find expressions for the energies of the decay products in the cm frame in terms of the masses: m, m1 and m2. find expressions for the momenta of the decay products in the cm frame in terms of the cm energies and the masses m1 and m2.
In the centre of- mass (CM) frame, the energies of the two decay products are:
\($$ E_1 = \frac{(m-m_2)^2 - p^2}{2m_1}c^2 $$\)
\($$ E_2 = \frac{(m-m_1)^2 - p^2}{2m_2}c^2 $$\)
The momenta of the two decay products are:
\($$ p_1 = \frac{\sqrt{(m^4 - 2m^2(m_1^2+m_2^2) + (m_1^2-m_2^2)^2)}}{2m c} $$\)
\($$ p_2 = -p_1 $$\)
What does Centre of-mass mean?The centre of mass (CM) is a point that represents the average position of mass in a system. In a system of particles, the CM is the point where the weighted average position of all the particles is located. It is a useful concept in physics and engineering because it allows us to simplify calculations of the motion and interactions of the system as a whole.
In the context of particle physics, the CM frame is a reference frame in which the total momentum of a system of particles is zero. This means that the particles are moving with equal and opposite momenta in this frame, and it simplifies the analysis of the system, allowing us to study its properties and interactions. The CM frame is often used in particle accelerators, where high-energy collisions between particles can produce a large number of new particles that move in various directions.
Let the initial particle of mass \($m$\) be at rest in the CM frame. After decay, the two particles will move in opposite directions, each with momentum \($p$\)The total energy of the system is conserved, and it is given by the sum of the energies of the two particles:
\($$ E = E_1 + E_2 $$\)
where\($E_1$\)and \($E_2$\)the energies of the two particles.
The total energy \($E$\) of the system is given by:
\($$ E = \sqrt{(mc^2)^2 + (pc)^2} $$\)
where \($c$\) is the speed of light.
Since the particles are moving in opposite directions, their momenta are equal in magnitude but opposite in direction, i.e., \($p_1 = -p_2 = p$\). The energies of the particles can be found using the following expression:
\($$ E_i = \sqrt{(m_ic^2)^2 + (p_ic)^2} $$\)
where \($i$\) is the particle index.
Substituting\($p_1 = -p_2 = p$ and $E = E_1 + E_2$\) in the above equations, we get:
\($$ E_1 = \frac{m_1^2c^4 + p^2c^2}{2m_1c^2} $$\)
\($$ E_2 = \frac{m_2^2c^4 + p^2c^2}{2m_2c^2} $$\)
Solving for \($p$\)
\($$ p = \frac{\sqrt{(E^2 - (m_1c^2 + m_2c^2)^2)(E^2 - (m_1c^2 - m_2c^2)^2)}}{2Ec} $$\)
The momenta of the two particles in the CM frame are given by:
\($$ p_1 = \frac{\sqrt{(E^2 - (m_1c^2 + m_2c^2)^2)}}{2c} $$\)
\($$ p_2 = \frac{\sqrt{(E^2 - (m_1c^2 - m_2c^2)^2)}}{2c} $$\)
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How much current is in a circuit with a 1.5 V battery and three
2-ohm resistances (bulbs) in series?
Answer: 0.25A
Explanation: To calculate the current in the circuit, we can use Ohm's Law, which states that the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R):
I = V / R
In this case, the total resistance of the circuit is the sum of the individual resistances of the three bulbs in series, which gives us:
R = 2 + 2 + 2 = 6 ohms
The voltage of the battery is given as 1.5V.
So, using Ohm's Law, we can calculate the current in the circuit as:
I = V / R = 1.5 / 6 = 0.25 amps
Therefore, the current in the circuit is 0.25 amps.
The current in the circuit is 0.25 A.
Voltage across the circuit, v = 1.5 V
Resistance in each resistors, R = 2Ω
Since, the resistors are connected in series combination, their effective resistance,
R' = 3R
R' = 3 x 2
R' = 6Ω
According to Ohm's law, if the temperature and all other physical factors remain constant, the voltage across a conductor is directly proportional to the current that is flowing through it.
So, according to Ohm's law,
V = IR
Therefore, current flowing through the given circuit,
I = V/R
I = 1.5/6
I = 0.25 A
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The 10/90 principle can help you take control of your situation in taking responsibility of what you can change rather than in being victim of what you cannot change. Give an example of a situation that can change for you in applying this principle.
The 10/90 principle can be a powerful tool for taking control of your situation and improving your life. By taking responsibility for what you can change and focusing on your reaction to the situation, you can make positive changes in your life and become the master of your own destiny.
The 10/90 principle refers to the idea that life is made up of 10% of what happens to you and 90% of how you respond to it. In other words, you may not be able to control what happens to you, but you can control your reaction to it. By taking responsibility for what you can change rather than being a victim of what you cannot change, you can take control of your situation and improve your life.One example of a situation where the 10/90 principle could be applied is losing a job. Losing a job can be a devastating experience, and it can be easy to feel like a victim in this situation. However, by applying the 10/90 principle, you can take control of your situation and make positive changes in your life.The first step in applying the 10/90 principle in this situation would be to take responsibility for what you can change. This could mean updating your resume, networking with others in your field, and applying for new jobs. By taking action and doing what you can to find a new job, you are taking control of your situation and improving your chances of finding a new job.
The second step would be to focus on your reaction to the situation. Instead of dwelling on the negative aspects of losing your job, try to focus on the positive aspects. This could mean using the extra time to pursue a new hobby or spend more time with family and friends. By focusing on the positive aspects of the situation, you are taking control of your reaction and improving your overall well-being.
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