Distance (height) and mass determine the amount of ________ energy in an object.

The current sensitivity of a moving coil galvanometer increases with a decrease in its resistance.

What is Current Sensitivity?

Current sensitivity is a measure of the responsiveness of an instrument to the current flowing through it. In particular, it is the deflection produced by a given amount of current passing through a device. The higher the current sensitivity, the smaller the amount of current required to produce a given deflection, and thus the more sensitive the instrument is to changes in current.

This is because the current sensitivity of a galvanometer is defined as the deflection produced per unit of current passed through it. Therefore, a higher current sensitivity means that a smaller current can produce a larger deflection, which can be achieved by decreasing the resistance of the galvanometer. This is because a lower resistance will allow a larger current to flow through the coil, which will result in a larger deflection of the coil.

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Answer:

Resistance

Explanation:

Sensitivity of a moving coil galvanometer can be increased by increasing the number of turns in the coil, the area of coil and magnetic field whereas by decreasing the couple per unit twist of the suspension.

Answer:

B

Explanation:

The more mass an object has, the more gravity it has.

The statement which correctly explains the weight you would experience on each planet is: B. You would weigh less on planet A because it has less mass than  planet B.

Weight can be defined as the force acting on a body or an object as a result of gravity.

Mathematically, the weight of an object is given by the formula;

\(Weight = mg\)

Where;

Hence, we can deduce that the weight and gravity acting on an object is highly dependent on the mass of an object.

Therefore, the higher the mass in a planet, the higher the gravity existing there.

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The kinetic energy of the book after it is slids a distance of 2 meters will be 10 Joules.

The work-energy theorem states that "the work done on an object is the change in its kinetic energy".

Hence;

Kinetic energy = work done

Note that: work-done is expressed as:

Work done = f × d

Where f is force applied and d is distance traveled.

Given that:

Force applied f = 5 newton

Distance d = 2 meters

Work done = ?

Plug these values into the above formula and solve for the workdone.

Work done = f × d

Work done = 5N × 2m

Work done = 10Nm

Work done = 10 Joules

Therefore, the kinetic energy is 10 Joules.

Option B) 10 J is the correct answer.

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The statement that describes the transformation of the graph of function f onto the graph of function g is: The graph shifts 2 units right and 7 units down.

To determine the transformation of the graph of function f onto the graph of function g, we compare the two functions f(x) and g(x) and observe the changes in the equations.

The function f(x) = (1/x - 3) + 1 represents a reciprocal function that is shifted vertically 1 unit up and horizontally 3 units to the right. The reciprocal function is reflected about the line y = x.

The function g(x) = (1/(1 + 4)) + 3 simplifies to g(x) = 4 + 3 = 7, which is a constant function representing a horizontal line at y = 7.

By comparing the equations, we can see that the transformation from f(x) to g(x) involves the following changes:

The term 1/x in f(x) is replaced by the constant 1/(1 + 4) in g(x), resulting in a vertical shift of 7 units up.

The term -3 in f(x) is replaced by 3 in g(x), resulting in a vertical shift of 3 units up.

The +1 in f(x) is replaced by +3 in g(x), resulting in an additional vertical shift of 2 units up.

Therefore, the overall transformation is a shift of 2 units to the right and 7 units down.

Hence, the correct statement is: The graph shifts 2 units right and 7 units down.

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Answer:

In the taller, skinnier cylinder, each tick mark represents 2, while in the larger one, each tick mark represents 50.

Explanation:

If you count the tick marks between each big number, then you can divide, and figure out what amount each tick mark represents.

The pressure of a gas at the triple point of water is 1.50 atm, which means it is at the temperature and pressure where water can exist as a solid, liquid, and gas simultaneously.

To find the pressure of the gas at the temperature at which CO2 solidifies, we need to know the triple point of CO2. The triple point of CO2 is -56.6°C and 5.1 atm.

If the volume of the gas remains unchanged, then its pressure will change with a change in temperature. Using the ideal gas law, PV = nRT, we can find the new pressure of the gas:

P1V1 = P2V2

At the triple point of water:

P1 = 1.50 atm

V1 = V (unchanged)

T1 = 0.01°C (triple point of water)

At the triple point of CO2:

P2 = 5.1 atm

V2 = V1 (unchanged)

T2 = -56.6°C

Using the ideal gas law and solving for P2:

P2 = P1(T2/T1)

P2 = 1.5 x (-56.6+273.15) / (0.01+273.15)

P2 = 0.818 atm

Therefore, the pressure of the gas at the temperature at which CO2 solidifies is 0.818 atm.

Answer:

Force = 607.95 Newton

Explanation:

Given the following data;

Area = 0.00600 m^2

Pressure = 1 atm to Pascal = 101325 Pa

To find the force;

Pressure = Force/area

Force = pressure * area

Substituting into the equation, we have;

Force = 101325 * 0.00600

Force = 607.95 Newton.

Therefore, the amount of force exerted by the air on the stamp is 607.95 Newton.

Answer:

A force is a push or pull upon an object resulting from the object's interaction with another object. Whenever there is an interaction between two objects, there is a force upon each of the objects.

Explanation:

The object distance of the lens is 10 cm and the image distance of the lens is 30 cm.

The object and image distance formed by the lens is calculated by applying the following lens formula.

v + u = 40 ------- (1)

v/u = 3 ------------ (2)

v = 3u

Substitute v into equation (1);

3u + u = 40

4u = 40

u = 40/4

u = 10 cm

The image distance = 3u

= 3 x 10 cm

= 30 cm

Thus, the object distance is 10 cm and the image distance is 30 cm.

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Answer:

V = 7.75 meters per seconds.

Explanation:

Given the following data;

Mass = 100000 Kilograms

Kinetic energy = 3 Megajoules = 3 * 10⁶ Joules

To find the velocity of the train;

Kinetic energy can be defined as an energy possessed by an object or body due to its motion.

Mathematically, kinetic energy is given by the formula;

\( K.E = \frac{1}{2}MV^{2}\)

Where;

K.E represents kinetic energy measured in Joules.

M represents mass measured in kilograms.

V represents velocity measured in metres per seconds square.

Substituting into the formula, we have;

\( 3000000 = \frac{1}{2}*100000*V^{2}\)

Cross-multiplying, we have;

\( 6000000 = 100000V^{2}\)

\( V^{2} = \frac{6000000}{100000} \)

\( V^{2} = 60 \)

Taking the square root of both sides, we have;

\( V = \sqrt {60} \)

V = 7.75 m/s

Mass A = 2000 kg

velocity A = 12 m/s (North)

Mass B= 4000 kg

Velocity B= -8 m/s (South)

We adopt that North is positive and South is negative.

Conservation of momentum (p)

• Pi = Pf

• ma * va + mb*vb = (ma+mb) Vf

Where Vf is the final velocity after the collision.

Replacing:

(2000* 12 ) + (4000*-8)= (2000+4000) vf

24,000- 32,000 = 6,000 vf

-8,000 = 6,000 vf

-8,000 / 6,000 = vf

vf = -1.3334 m/s

vf = 1.3334 m/s , South

a) , it would take approximately 0.4638 seconds for the magnetic energy to decay to 13% of its maximum value.. b)  the voltage across the inductor at the instant when the magnetic energy has decayed to 13% of its maximum value is 6.4 times the initial current in the circuit.

An RL circuit consists of a resistor (R) and an inductor (L) connected in series. When a battery is connected to the circuit, the inductor stores magnetic energy, which creates a magnetic field. When the battery is removed, the magnetic energy in the inductor begins to decay, and the magnetic field collapses, inducing a voltage across the inductor.

a) The time constant (τ) of an RL circuit is given by the formula:

τ = L/R

where L is the inductance in henries, and R is the resistance in ohms. The time constant represents the time required for the magnetic energy to decay to approximately 36.8% of its maximum value.

In this case, L = 5 H and R = 22 ohms. Therefore, the time constant of the circuit is:

τ = L/R = 5 H / 22 ohms = 0.2273 seconds

To calculate the time required for the magnetic energy to decay to 13% of its maximum value, we can use the formula:

t = -ln(0.13) * τ

where ln is the natural logarithm. Plugging in the values, we get:

t = -ln(0.13) * 0.2273 seconds

t = 0.533 seconds

Therefore, it would take approximately 0.533 seconds for the magnetic energy in the inductor to decay to 13% of its maximum value.

b) To find the voltage across the inductor at that instant, we can use the formula:

V = L * di/dt

where V is the voltage across the inductor, L is the inductance, and di/dt is the rate of change of the current in the circuit.

At the instant when the magnetic energy in the inductor has decayed to 13% of its maximum value, the current in the circuit is given by:

I = I0 * e^(-t/τ)

where I0 is the initial current, and e is the mathematical constant approximately equal to 2.71828. Plugging in the values, we get:

I = I0 * e^(-0.533/0.2273)

I = 0.292 * I0

Therefore, the rate of change of current (di/dt) at that instant is given by:

di/dt = I / τ = (0.292 * I0) / 0.2273

Now, we can calculate the voltage across the inductor:

V = L * di/dt = 5 H * (0.292 * I0 / 0.2273)

V = 6.4 * I0 volts

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Answer:

A.

Explanation: both triple by 3

Answer: B

Explanation: It is because the formula for this eq is KE=V^2. In the eq, it says that the mass is triple meaning the KE also must have tripled. For the speed, since it has a formula then you just have 3^2 which is 9.

In order to determine which of the two solutions of salt water is more concentrated, we need to first understand what concentration means and how it is measured. Concentration refers to the amount of solute dissolved in a given amount of solvent. It is typically measured in units of mass per volume, such as grams per liter (g/L) or milligrams per milliliter (mg/mL). so The second solution is more concentrated

When comparing the concentration of two solutions, the one with a higher concentration has more solute dissolved in the same amount of solvent. Therefore, in the picture provided, we can determine which solution is more concentrated by looking at the relative amounts of solute in each solution.If the solutions have the same concentration, then they must have the same amount of solute dissolved in the same amount of solvent. From the picture, we can see that both solutions are in the same size container and have the same amount of solvent (water) in them. Therefore, we can conclude that they have the same concentration of salt.The amount of solute dissolved in a solution can be increased by either adding more solute or by reducing the amount of solvent. If we were to add more salt to one of the solutions, we would increase the concentration of that solution. Alternatively, if we were to evaporate some of the water from one of the solutions, we would reduce the amount of solvent and increase the concentration of that solution.

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Natural gas, hydrogen, electricity, hybrid vehicles, biofuels, five major alternative energy sources in transportation. Producing energy from fossil fuels no releases of greenhouse gases, lowering forms of pollution.

The relative ease with which petroleum-derived fuels may be stored and utilized in internal-combustion engines accounts for their supremacy. However, they need a more intricate storage system than other fossil fuels, such as natural gas, gas, and methanol, which can also be utilized as transportation fuels.

Use your personal automobiles sparingly. When possible, strive to use public transportation. Reduce the car's additional BOOT weight. Unnecessary objects like a flat tire and unwanted luggage—especially hefty ones—in the car might lower its mileage.

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(a) To solve for the mass of the rod, we can use the formula for rotational kinetic energy:

KE = (1/2) * I * w^2

where KE is the rotational kinetic energy, I is the moment of inertia, and w is the angular velocity.

At the beginning, when the bug is at the axis of rotation, the rotational kinetic energy of the rod is:

KE1 = (1/2) * I * w^2 = (1/2) * (3.10×10−3 kg⋅m^2) * (0.37 rad/s)^2 = 0.036 J

When the bug reaches the other end of the rod, the rotational kinetic energy is:

KE2 = (1/2) * I * w^2 = (1/2) * (3.10×10−3 kg⋅m^2) * (0.132 m/s)^2 / (0.480 m)^2 = 3.62×10^-5 J

The change in kinetic energy is due to the work done by the bug as it crawls along the rod. The work done by the bug can be calculated as the product of the force it exerts on the rod and the distance it crawls:

W = F * d

The force the bug exerts on the rod can be calculated using Newton's second law for rotational motion:

τ = I * α

where τ is the torque, α is the angular acceleration, and I is the moment of inertia.

Since the rod is rotating with a constant angular velocity, its angular acceleration is zero, so the net torque on the rod must be zero. This means that the torque exerted by the bug on the rod must be equal and opposite to the torque due to the angular momentum of the rod:

τ_bug = τ_rod

F * d = I * w

F = I * w / d

Substituting the values given, we get:

F = (3.10×10−3 kg⋅m^2) * (0.37 rad/s) / (0.480 m) = 0.0237 N

Now we can use the work-energy principle to find the mass of the rod:

W = KE2 - KE1 = F * d = (1/2) * m * v^2

where m is the mass of the rod and v is the tangential velocity of the bug at the end of the rod.

Substituting the values given, we get:

(1/2) * m * (0.132 m/s)^2 = 3.62×10^-5 J - 0.036 J

Simplifying and solving for m, we get:

m = 0.221 kg

Therefore, the mass of the rod is 0.221 kg.

(b) To find the mass of the bug, we can use the same equation we used to calculate the force it exerted on the rod:

F = I * α / d

where α is the angular acceleration of the rod caused by the bug crawling along it.

Since the rod is a thin uniform rod, its moment of inertia can be calculated as:

I = (1/3) * m * L^2

where L is the length of the rod.

Substituting the values given, we get:

I = (1/3) * (0.221 kg) * (0.480 m)^2 = 0.0202 kg⋅m^2

Now we can calculate the angular acceleration caused by the bug crawling along the rod. Since the rod is rotating with a constant angular velocity, its angular acceleration is given by:

α

Fade

finish

α = (w_f^2 - w_i^2) / (2 * θ)

where w_i is the initial angular velocity of the rod, w_f is the final angular velocity of the rod after the bug has crawled to the end, and θ is the angle through which the bug crawls, which is equal to the length of the rod:

θ = L = 0.480 m

Substituting the values given, we get:

α = (0.132 m/s)^2 / (2 * 0.480 m) = 0.072 rad/s^2

Now we can calculate the force exerted by the bug on the rod:

F = I * α / d = (0.0202 kg⋅m^2) * (0.072 rad/s^2) / (0.480 m) = 0.00303 N

Finally, we can use Newton's second law to find the mass of the bug:

F = m * a

where a is the tangential acceleration of the bug, given by:

a = r * α

where r is the distance from the bug to the axis of rotation, which is equal to the length of the rod minus the distance the bug has crawled, or:

r = L - d = 0.480 m - 0.480 m = 0 m

Therefore, the tangential acceleration of the bug is zero, and its mass is:

m = F / a = 0.00303 N / 0 m/s^2 = undefined

This means that the force exerted by the bug on the rod is not enough to cause any tangential acceleration, and therefore the mass of the bug is negligible compared to the mass of the rod. We can assume that the bug has zero mass for practical purposes.

Explanation:

Both because water can fall in holes and then freeze. However, water can also be chemically react with other elements and substances to wear something away.

Answer:

Yes

Explanation:

because its literally showing they are moving away from the same point

The magnitude of the resultant vector to round the answer to the nearest tenth, we look at the digit in the hundredth's place. If this digit is 5 or greater, we round up. If it is less than 5, we round down.

In the study of physics, we use vectors to represent quantities that have both direction and magnitude. It is often the case that we want to add two or more vectors together to obtain a single vector that represents the net result of these additions. The process of adding two or more vectors together is known as vector addition.The magnitude of the resultant vector is the length of the line that represents it on a scale drawing.

When we add two or more vectors together, the resultant vector is the vector that represents the net result of these additions. To find the magnitude of the resultant vector, we use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In the case of vector addition, the hypotenuse is the resultant vector, and the other two sides are the component vectors. If we have two vectors a and b, the magnitude of the resultant vector is given by the following equation:|R| = √(ax2 + bx2)where R is the resultant vector, a and b are the component vectors, and x is the angle between the vectors.

For example, if the answer is 12.345, we would round it to 12.3.

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Answer:

the correct one is b,  Decrease the launch speed and Low the launch height

Explanation:

Let's find the solution to the problem in order to answer the questions.

The bullet is fired horizontally with a velocity vo, let's find the time or it takes to reach the ground

      y = y₀ + \(v_{oy}\) t - ½ g t²

as it shoots horizontally v_{oy} = 0 and when I reach the floor y = 0

       0 = y₀ - ½ g t2

       t = \(\sqrt{\frac{2y_{o} }{g} }\)

where y₀ is the height of the cliff

at this time the bullet recreates a distance of

       x = v₀ t

we substitute

       x = v₀ \sqrt{\frac{2y_{o} }{g} }

There, to reduce the range of the bullet, we must decrease its speed. This is the magnitude that most affects the distance and to a lesser degree we can decrease the height.

When checking the answers, the correct one is b

Answer:

j120

Explanation:

qll energy for residential is 120 and that's what ruffly is always used for wiring

mvh=1. 654106. 6210=41014m is the de Broglie wavelength of a proton whose kinetic energy is equal to that of the proton.

An electron has an energy of 100,000 eV (100 keV) at a potential difference of 100,000 V (100 kV), and so on. The energy gained by an ion with a double positive charge when it is accelerated through 100 V is 200 eV.

De Broglie wavelength is the length of a particle with kinetic energy E. The wavelength changes to /2 when energy E is added to it.

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Answer:

a very high value of its heat or specific capacity

Explanation:

Water is a compound that has hydrogen in its system, hydrogen atoms can form bonds called hydrogen bridges, they give water a high capacity to store heat, at a macroscopic level these characteristics are reflected in a very high value of its heat or specific capacity

       ce = 4186 J / kg ºC

therefore to change the temperature the water must absorb a lot of energy

The velocity of particle 2 when it is 1cm away from particle 1 is determined as 62.18 m/s.

The electrostatic force between the two charges is calculated as follows;

F = (kq1q2)/(r²)

F = (9 x 10⁹ x 4.5 x 10⁻⁶ x 3.1 x 10⁻⁶)/(0.037)²

F = 91.71 N

F = ma

a = F/m

a = (91.71 N)/(0.0069 kg)

a = 13,291.2 m/s²

v² = u² + 2as

v² = 60² + 2(13,291.2)(0.01)

v² = 3865.82

v = 62.18 m/s

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Answer: The Company has spent $5 million in research and development over the past 12 months developing cutting-edge battery technology which will be incorporated ...

Explanation: uhmmmmmm i dont know this one but it is pretty ez

Answer:

30,000dB

Explanation:

30,000dB because 30 multiplied by a factor of 1000 is 30,000

Hope this helps! :)

The density of mercury can be calculated using the formula:

Density = (mass of mercury) / (volume of mercury)

To calculate the volume of the mercury, we need to subtract the volume of the bottle from the volume of the bottle filled with mercury.

Volume of bottle = Volume of bottle filled with mercury - Volume of mercury

Let's assume that the volume of the bottle filled with mercury is V1 and the volume of the bottle is V2. We can then write:

Density of mercury = (mass of mercury) / (V1 - V2)

Given that the mass of the empty bottle is 20g, we can calculate the mass of the mercury as follows:

Mass of mercury = (mass of bottle filled with mercury) - (mass of empty bottle)

= 360g - 20g

= 340g

The mass of the bottle filled with water is 45g. Therefore, the mass of the mercury in the bottle is:

Mass of mercury = 360g - 45g = 315g

Let's assume that the density of the bottle is negligible. We can then calculate the volume of the mercury as follows:

Volume of mercury = (mass of mercury) / (density of mercury)

Substituting the values we have:

315g / (density of mercury) = (V1 - V2)

We know that the mass of the water in the bottle is 45g, which means that the mass of the mercury is (360g - 45g) = 315g. Therefore, the volume of the mercury is equal to the volume of the water. We can then write:

Volume of mercury = Volume of water = (mass of water) / (density of water)

The density of water is 1 g/cm³. Substituting the values we have:

315g / (density of mercury) = 45g / 1 g/cm³

Solving for the density of mercury, we get:

Density of mercury = (315g * 1 g/cm³) / 45g

= 7 g/cm³

Therefore, the density of mercury is 7 g/cm³.

The order in which the readings will be taken is as follows:

1. Mass of empty bottle

2. Mass of bottle filled with mercury

3. Mass of bottle filled with water (or the mass of the bottle filled with mercury and the mass of the empty bottle, from which we can calculate the mass of the mercury)

4. Volume

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♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Chapter 1

1. Show that the Lorentz transformation is such that the velocity of a light ray

travelling in the x direction is the same for the observer in the frame S and for

the observer in the frame S

.

Solution: Consider a light ray travelling in the x direction. If the light ray

connects two space–time points {t1, x1} and {t2, x2}, we have

c = x2 − x1

t2 − t1

The speed of light observed in the frame S will be

c = x

2 − x

1

t

2 − t

1

= c

γ ((x2 − x1) − βc(t2 − t1))

γ (c(t2 − t1) − β(x2 − x1))

= c

x2 − x1

t2 − t2

− βc

c − β x2 − x1

t2 − t2

= c

2. What is the mean path before decay for a charged pion with a kinetic energy of

1 GeV?

Solution: The pion has a lifetime 2.6 × 10–8 s and a mass of 139.6 MeV. If the

energy is 1 GeV, the velocity of the pion is 99% of the velocity of light (Eq. 1.4).

The mean path before decay is

= 0.99 c γ τ

= 0.99 c

1000 + 139.6

139.6

2.6 10−8 = 63 m

S. Tavernier, Experimental Techniques in Nuclear and Particle Physics, 271

DOI 10.1007/978-3-642-00829-0, C Springer-Verlag Berlin Heidelberg 2010

272 Solutions to Exercises

3. Show that the relativistic expression for the kinetic energy of a particle (Eq. 1.2)

reduces to the non-relativistic expression if the velocity of the particle is small

compared to the velocity of light.

Solution:

E = Ekinetic + m0c2 = m0c2

1 − (v/c)2

≈ m0c2

(1 − 1/2(v/c)2) ≈ m0c2(1 + 1/2(v/c)

2)

= m0c2 +

1

2

m0v2

4. For a Poisson distribution with average value 16, calculate the probability to

observe 12, 16 and 20 as measured value. Calculate the probability density function for a Gaussian distribution with average value 16 and dispersion 4, for the

values x = 12, 16 and 20. Compare the results.

Solution: For a Poisson distribution P(12) = 0.0829, P(16) = 0.1024, P(20) =

0.0418

For a Gaussian distribution, f(12) = 0.0605, f(16) = 0.0997, f(20) = 0.0605

5. Consider a very short-lived particle of mass M decaying into two long-lived particles 1 and 2. Assume you can measure accurately the energies and momenta of

the two long-lived particles. How will you calculate the mass of the short-lived

particle from the known energies and momenta of the two long-lived objects?

Solution: The mass of the short-lived particle, its energy and its momentum are

related by Eq. (1.1). The energy and momentum of the particle are equal to the

sums of the energy and sums of the momenta of the decay products, therefore

M2c4 = (E1 + E2)

2 − c2(P1 + P2)

2

6. Calculate the order of magnitude of the energy levels in atoms and in nuclei

using the ‘particle in a box’ approximation, Eq. (1.9). Use for the dimension of

the atom 10–10 m and for the dimension of the nucleus 10−15 m.

Solution: Atomic energy levels: ≈40 eV; nuclear energy levels: ≈400 MeV.

7 . Show that in a β− or a β+ decay only a very small fraction of the energy derived

from the mass difference goes to the kinetic energy of the final-state nucleon.

The electron is relativistic; therefore this requires a relativistic calculation! Hint:

the 3-body problem can be reduced to a 2-body problem by considering the

electron–neutrino system as one object with a mass of a few MeV.

Solution. Consider the 2-body decay of some heavy object with mass M into

two objects with masses m1 and m2. The kinetic energy of each of the final-state

particles in the overall centre of mass system is found as follows.

Solutions to Exercises 273

Consider two particles with energy and momentum four vectors p1 and p2.

The symbol pi stands for the four-vector {Ei,cpi}. The energy E appearing in this

expression is the total energy E, i.e. the rest energy mc2 plus the kinetic energy.

The four-vector product (p1.p2) is defined as

(p1.p2) =

(

E1E2 − c2 p1 p2

)

A four-vector product is a Lorentz invariant; this quantity can be evaluated in

any reference frame, and the result is the same. Consider now the quantity

(p1.p2)

m1c2

This is a Lorentz invariant. Evaluating this expression in the rest frame of

particle 1 makes clear that this is the energy of particle 2 seen in the rest frame

of particle 1. This remains true also if one of the particles is in fact a system

of particles, for example the system of the two particles 1 and 2. The energy of

particle 2, seen in the overall centre of mass frame of the particles 1 and 2 is

therefore

E∗

2 = (p1 + p2).p2

(p1 + p2)2

We have the following relations:

(p1 + p2)

2 = M2c4

(p1.p2) = 1

2

(

(p1 + p2)

2 − (p1)

2 − (p2)

2

)

= M2c4 − m2

1c4 − m2

2c4

And therefore finally

E∗

2 = M2c4 + m2

2c4 − m2

1c4

2Mc2

Let us now apply the above relation to the decay

N∗ → N + e− + ¯νe + Q

The symbol Q represents the energy liberated in the reaction. Let us denote

by M∗ the mass of the parent nucleus, by M the mass of the final-state nucleus

and by m the mass of the electron–neutrino system. The kinetic energy of the

nucleus in the final state is given by

274 Solutions to Exercises

Ekin = M∗2c4 + M2c4 − m2c4

2M∗c2 − Mc2

= M∗2c4 + M2c4 − m2c4 − 2M∗c2Mc2

2M∗c2

= (M∗ − M)

2 c4 − m2c4

2M∗c2

=

!

mc2 + Q

The energy of the cosmic ray photon is zero. his means that the photon had insufficient energy to create new particles, and instead, it simply scattered off the massive object.

Einstein's energy equation, also known as the mass-energy equivalence, relates the energy E of an object to its mass m and the speed of light c. The equation is:

E = mc^2

where:

E is the energy of the object in joules (J)

m is the mass of the object in kilograms (kg)

c is the speed of light in meters per second (m/s)

This equation means that mass and energy are interchangeable, and that a small amount of mass can be converted into a large amount of energy. The equation is an important consequence of Einstein's theory of special relativity, and it has been confirmed by numerous experiments, including nuclear reactions and particle accelerators.

Here in the Question,

We can use the conservation of momentum and energy to solve this problem. Since the two fragments have equal mass and are moving in opposite directions at the same speed, we know they have equal and opposite momenta. Therefore, the initial momentum of the photon must also be equal and opposite to the total momentum of the fragments.

Let's call the initial momentum of the photon p and the mass of each fragment m. The total momentum of the fragments is:

p' = 2mv

where v is the speed of each fragment, which we know is 0.6c. Therefore, we can write:

p' = 2m(0.6c) = 1.2mc

By conservation of momentum, we have:

p = -p'

where the negative sign indicates that the photon is moving in the opposite direction to the fragments. Therefore:

p = -1.2mc

Now we can use conservation of energy to relate the photon's energy E to its momentum p:

E^2 = p^2c^2 + m^2c^4

Substituting the expression we found for p, we get:

E^2 = (1.2mc)^2c^2 + m^2c^4

E^2 = 1.44m^2c^4 + m^2c^4

E^2 = 1.45m^2c^4

Solving for E, we get:

E = mc^2 * sqrt(1.45)

Plugging in the values for m and c, we get:

E = (0 * 9.0 × 10^16 kg) * sqrt(1.45) = 0

Therefore, The photon from a cosmic ray has no energy. This indicates that the photon was merely scattered off the large object since it lacked the energy to produce new particles.

To learn about Cosmic rays click:

https://brainly.com/question/13960192

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Answer:

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