State in which all electrons are at their lowest possible energy level

Answer:

The temperature required is near about 3 million kelvin

Explanation:

The brilliance of the star results from the nuclear reaction that take place in the core of the star and radiate a huge amount of thermal energy resulting from the fusion of hydrogen into helium.

For this reaction to take place, the temperature of the star's core must be near about 3 million kelvin.

The hydrogen atoms collide and starts and the energy from the collision results in the heating of the gas cloud. As the temperature comes to near about [tex]1.5\times 10^{7 {\circ}C[/tex], the nuclear fusion reaction takes place in the core of the gas cloud.

The huge amount of thermal energy from the nuclear reaction gives the gas cloud a brilliance resulting in a protostar.

The core temperature necessary for hydrogen fusion to begin in a star is approximately 15,000,000 Kelvin, marking its entry into the main sequence. With hydrogen's exhaustion, fusion of helium and other more complex elements happen, each needing significantly higher temperatures.

Hydrogen fusion, also known as thermonuclear fusion, initiates within a star when its core temperature reaches approximately 15,000,000 Kelvin (K). At these temperatures, all molecules dissociate into atoms, and the atoms ionize, forming plasma. This process of hydrogen fusion occurring in the core of a star is critical for a star's energy balance and longevity.

A star reaches the main sequence when its core temperature is high enough (about 12 million K) to fuse hydrogen into helium. However, once the hydrogen fuel is exhausted in a star's core, fusion of helium, and later, other more complex elements can occur, with each requiring significantly higher temperatures than previous fusion reactions.

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Answer:

ρ = 1061 kg/m³

Explanation:

The pressure at the top pf the box is clearly different from the pressure at the bottom of of the  box due to the depth. So the problem can be solve the following way:

Difference in pressure =  density * acceleration due to gravity * height

ΔP = ρgΔh

112 000 Pa - 109 400 Pa = ρ * 9.8 m/s² * 0.25 m

                                     ρ = 1061 kg/m³

The density of the fluid can be calculated using the formula P=hρg, where P is the pressure, h is the height or depth, ρ is the density, and g is the acceleration due to gravity. The pressure difference is due to the fluid itself and can be used to find the density when the height and acceleration due to gravity are given.

The student's question is about finding the density of a fluid given the pressure at the top and bottom of the cube. The key to finding this is using the formula that relates pressure, depth, and density in a fluid, which is P=hρg where P is the pressure, h is the height or depth, ρ is the density, and g is the acceleration due to gravity.

Given that the difference in pressure between the bottom and top of the cube is 112.00 kPa - 109.40 kPa = 2.60 kPa, this represents the change in hydrostatic pressure due to the fluid itself. Now, convert this pressure difference from kPa to Pa (since 1 kPa = 1000 Pa), we get 2.60 kPa * 1000 = 2600 Pa.

The height of the cube is given as 25.0 cm which needs to be converted to meters (since 1m = 100 cm), giving us a height of 0.25 m. We can calculate the density of the fluid using the rearranged formula ρ = P/gh. Substituting known values: ρ = 2600 Pa / (9.81 m/s² * 0.25 m). The answer will then give us the density of the fluid.

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After defining variables and initial conditions, analyzing the block's motion before collision, and applying the conservation of momentum principle, we found that the block had been falling for approximately 0.198 seconds before colliding with the bullet.

1. Defining Variables and Initial Conditions:

m: Mass of the bullet (0.026 kg)

v_b: Velocity of the bullet before collision (750 m/s)

M: Mass of the block (5 kg)

v_f: Final velocity of the block before collision (unknown)

t: Time the block falls before collision (unknown)

V: Final velocity of the combined bullet-block system after collision (unknown)

2. Analyzing Block's Motion before Collision:

The block is initially dropped from rest, so its initial velocity (v_o) is 0 m/s.

The block experiences acceleration due to gravity (g) in the downward direction, represented by a negative sign (-g).

We want to find the final velocity (v_f) of the block just before the collision using the kinematic equation:

v_f = v_o + at

Since v_o = 0 and a = -g, we get:

v_f = -gt

3. Applying Conservation of Momentum:

During the collision, momentum is conserved, meaning the total momentum before the collision equals the total momentum after.

Before the collision, the momentum is the sum of the bullet's momentum (mv_b) and the block's momentum (Mv_f).

After the collision, the combined bullet-block system moves together with a final velocity (V).

We can express the conservation of momentum equation as:

mv_b + Mv_f = (m + M)V

4. Solving for Time (t):

Substitute the expressions for v_f and V from previous steps:

(0.026)(750) + (5)(-gt) = (0.026 + 5)(gt)

Simplify and solve for t:

19.5 - 49t = 49.2548t

98.7548t = 19.5

t = 0.198 seconds

Therefore, the block had been falling for 0.198 seconds before the collision with the bullet.

Answer:

(a). The total moment of inertia of the system is 0.0233 kg-m².

(b). The kinetic energy is 0.0011 J.

Explanation:

Given that,

Mass of each particle m= 0.85 kg

Length = 5.6 cm

Mass of each rod M= 1.2 kg

Angular speed = 0.30 rad/s

The moment of inertia of the rod  between  axis of rotation and mass  is

[tex]I_{1}=\dfrac{Md^2}{3}[/tex]

The moment of inertia of the rod  between masses about center of mass is

[tex]I_{cm}=\dfrac{Md^2}{12}[/tex]

Moment of inertial of the rod between masses about point O is

[tex]I_{2}=M(d+\dfrac{d}{2})^2+\dfrac{Md^2}{12}[/tex]

Moment of inertia of two masses is

[tex]I_{m}=md^2+m(2d)^2[/tex]

(a). We need to calculate the total moment of inertia of the system

Using formula of moment of inertia

[tex]I_{t}=I_{1}+I_{2}+I_{m}[/tex]

Put the value into the formula

[tex]I_{t}=\dfrac{Md^2}{3}+M(d+\dfrac{d}{2})^2+\dfrac{Md^2}{12}+md^2+m(2d)^2[/tex]

[tex]I_{t}=\dfrac{Md^2}{3}+\dfrac{9Md^2}{4}+\dfrac{Md^2}{12}+md^2+4md^2[/tex]

[tex]I_{t}=\dfrac{32Md^2}{12}+5md^2[/tex]

[tex]I_{t}=2.67Md^2+md^2[/tex]

Put the value into the formula

[tex]I_{t}=2.67\times1.2\times(5.6\times10^{-2})^2+5\times0.85\times(5.6\times10^{-2})^2[/tex]

[tex]I_{t}=0.0233\ kg-m^{2}[/tex]

(b). We need to calculate the kinetic energy

Using formula of kinetic energy

[tex]K.E=\dfrac{1}{2}I\omega^2[/tex]

Put the value into the formula

[tex]K.E=\dfrac{1}{2}\times0.0233\times(0.30)^2[/tex]

[tex]K.E=0.0011\ J[/tex]

Hence, (a). The total moment of inertia of the system is 0.0233 kg-m².

(b). The kinetic energy is 0.0011 J.

The rotational inertia of the combination is 0.041 kg·m² and the kinetic energy is 80.93 J.

The rotational inertia (moment of inertia) of the combination can be calculated using the formula I = 2mL², where m is the mass and L is the length of the rod. Substituting the given values, the rotational inertia is 0.041 kg·m².

The kinetic energy of rotation can be calculated using the formula K = ½Iω², where I is the moment of inertia and ω is the angular velocity. Substituting the given values, the kinetic energy is 80.93 J.

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1) False

2) True

3) The distance is 17 m

4) The displacement is 2 m south

5) She did not give the direction as either left, or negative.

6) The average speed is 28 mph

7) The average velocity is 12 mph north

8) The average speed is 0.27 m/s

9) False

10) False

Explanation:

1)

Speed is a scalar quantity which tells how fast an object is moving regardless of its direction, and it is calculated as:

[tex]speed=\frac{d}{t}[/tex]

where d is the distance covered by the object and t is the time taken. Being a scalar quantity, speed consists only of a value and its units, so no direction needs to be specified.

2)

Velocity is a vector quantity, defined as

[tex]velocity = \frac{d}{t}[/tex]

where d is the displacement of the object (a vector connecting the initial position to the final position of motion) and t is the time taken. Being a vector, velocity has both a magnitude and a direction (the same direction as the displacement), so direction here should also be specified.

3)

The distance travelled by the object is just the total length of the path taken, regardless of the direction of each part of the motion.

Here the object moves:

10 meters to the right

7 meters to the left

So, the distance travelled is

d = 10 + 7 = 17 m

4)

The displacement is a vector connecting the initial position to the final position of motion, so we have to compare the starting position with the final position.

Taking x = 0 as initial position, and north as positive direction:

- The object moves 5 m north first (+5)

- The object moves 7 m south (-7)

So, the displacement is

d = +5 + (-7) = -2 m

which means 2 meters south.

5)

As we said previously, displacement is a vector connecting the initial position to the final position of motion. Being a vector, it must have:

- A magnitude (the shortest distance between the initial and final position, in a straight line)

- A direction

Here Jenny reported only the magnitude (3 meters), but not the direction, so she forgot to include the direction of the displacement (which is to the left).

6)

The average speed is given by

[tex]speed=\frac{d}{t}[/tex]

where d is the distance and t is the time taken.

The distance is just the total length covered, so:

d = 5 + 2 = 7 miles

The time taken is

t = 1/4 h = 0.25 h

So, the average speed is

[tex]speed=\frac{7}{0.25}=28 mph[/tex]

7)

The average velocity is given by

[tex]velocity=\frac{d}{t}[/tex]

where d is the displacement and t is the time taken.

The displacement is, taking north as positive direction:

d = +5 + (-2) = 3 miles (north)

The time taken is

t = 1/4 h = 0.25 h

So, the average velocity is

[tex]velocity=\frac{3}{0.25}=12 mph[/tex] (north)

8)

We can calculate the average speed by adding the single measurements and dividing by the number of trials done:

[tex]speed_{avg}=\frac{s_1+s_2+s_3}{3}[/tex]

where in this case, N = 3. For this experiment we have:

[tex]s_1 = \frac{0.75 m}{2.5s}=0.30 m/s\\s_2 = \frac{0.75 m}{2.75 s}=0.27 m/s\\s_3=\frac{0.75 m}{2.98 s}=0.25 s[/tex]

So the average is

[tex]speed_{avg}=\frac{0.30+0.27+0.25}{3}=0.27 m/s[/tex]

9)

Data are said to be:

- Accurate, when the average value of the measurements is close to the actual value

- Precise, when the spread of the measurements done in the different trials is small

Therefore, the first part of the sentence "Data that is accurate, is data that is really close to the actual value" is correct, and the second part "data that is precise is data that is repeated over and over again" is not correct, since we may have several measurements but their spread may be large.

10)

As we said in part 9):

- Accuracy refers to how close the measured value is to the actual value

- Precision refers to the spread (or the uncertainty) on the measured value: the smaller it is, the better the precision

For instance, let's assume that the actual value of a certain variable is 3.0. If we get the following set of data:

2.4, 2.5, 2.4, 2.3

it is precise (the spread is small) but not accurate (since the average, 2.4, is far from the actual value)

while the following set:

3.1, 3.6, 2.4, 3.0

is accurate (the average is around 3.0, so close to the actual value), but not precise (the spread is very large).

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Answer:

c. Jupiter's greater mass compresses it more, thus increasing its density.

Explanation:

The mass of Jupiter is greater in its interior, this mass compresses Jupiter to some extent. Thus, its density is increased. Now, more mass is compressed in the lesser volume. Hence, its size does not increase enormously. On the other hand the mass of Saturn is lesser  and also density lower. this gives Saturn a reasonably higher volume.

Hence, option C is correct.

Saturn appears almost as large as Jupiter due to its lower mass leading to less gravitational compression of its hydrogen and helium composition, resulting in a larger volume for its mass. The correct answer from the provided choices is c. Jupiter's greater mass compresses it more, thus increasing its density.

The reason why Saturn appears almost as large as Jupiter despite having a smaller mass is largely due to its composition and structure. We see that Jupiter, which is 318 times more massive than Earth, has a significantly higher density because its greater mass compresses the planets' internal hydrogen and helium more than Saturn, which is about 25% as massive as Jupiter. In comparison, Saturn's lower mass results in less compression and hence a larger volume for its mass. So, the correct answer is c. Jupiter's greater mass compresses it more, thus increasing its density.

Jupiter and Saturn are both composed mainly of hydrogen and helium, which become liquid at great depths due to their large size and the resulting high pressure. However, Saturn, with its lower density, is the least dense planet in the solar system, even less dense than water. Contrary to the choices provided, Saturn's rings do not play a significant role in making the planet appear larger in terms of its physical size, and the effect of distance from the Sun on the compactness of the planets is negligible compared to the impact of their massive gravitational compression.

When a region of rarefaction from one sound wave overlaps with a similar region in another wave, they cause constructive interference. The result is an increased amplitude, which makes the sound louder.

When a region of rarefaction of one sound wave overlaps with a region of rarefaction in another sound wave, it results in constructive interference. This is because both the waves are essentially 'in sync', and they amplify each other. The amplitude of the resulting wave increases, and in terms of sound, this means that the sound becomes louder, because amplitude is directly related to the volume or loudness of the sound. Hence, the correct answer is: Constructive interference; the sound becomes louder because the amplitude increases.

For instance, if you're playing two sounds of the same frequency and amplitude together, and their waves align such that their areas of rarefaction meet, the combined sound would be louder than the individual sounds. This is a direct application of the physics concept of wave interference.

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Answer:

fumaroles or smokers

Explanation:

Fumaroles: they are gaseous emissions from lavas in craters at more or less elevated temperatures. Its composition varies according to the temperature of the lavas, in such a way that it changes since the fumaroles appear until their extinction.

Water flows in the form of steam continuously through the cracks of a volcano or volcanic surface because its temperature exceeds 100 °C.

Groups of fumaroles

- Dry fumaroles: They are those that come off the melting lava, in the vicinity of the crater. Its temperature is higher than 500oC. They are mainly composed of sodium, potassium and sulfur dioxide and carbon dioxide.

- Acid fumaroles: with temperatures between 300oC and 400oC, they are constituted by a large amount of water vapor, with hydrochloric acid and sulphurous anhydride.

- Alkaline fumaroles: Temperature close to 100oC, contain water vapor with hydrogen sulfide and ammonium chloride.

Answer:

[tex]\frac{v_p}{v_a}=1.268[/tex]

Explanation:

1) Basic concepts

Apogee: is the maximum distance for an object orbiting the Earth. For this case the distance for the apogee would be the sum of radius for the earth and 2289 km.

Perigee: Minimum distance of an object orbiting the Earth. For this case the distance for the perigee would be the sum of radius for the earth and 459 km.

A good approximation for these terms are related to the figure atached.

Isolated system: That happens when the system is not subdued to an external torque, on this case the change of angular momentum would be 0.

2) Notation and data

[tex]r_{earth}[/tex] radius for the Earth, looking for this value on a book we got [tex]r_{earth}=6.37x10^{3}km[/tex]

[tex]r_p =459km +r_{earth}=459km +6.37x10^3 km=6.829x10^3 km[/tex], represent the radius for perigee

[tex]r_a =2289km +r_{earth}=2289km +6.37x10^3 km=8.659x10^3 km[/tex], represent the radius for perigee

[tex]T=112.7min[/tex], period

[tex]v_p[/tex] velocity of the perigee

[tex]v_p[/tex] velocity of the apogee

[tex]r=\frac{v_p}{v_a}[/tex] is the variable of interest represented the ratio for the speed of the perigee to the speed of the apogee

3) Formulas to use

We don't have torque from the gravitational force since is a centered force. So the change of momentum is 0

[tex]\Delta L=0[/tex]   (1)

[tex]L_a=L_p[/tex]   (2)

From the definition of angular momentum we have [tex]L_i=mv_i r_i[/tex], replacing this into equation (2) we got:

[tex]mv_a r_a =mv_p r_p[/tex]   (3)

We can cancel the mass on both sides

[tex]v_a r_a =v_p r_p[/tex]   (4)

And solving [tex]\frac{v_p}{v_a}[/tex] we got:

[tex]\frac{v_p}{v_a}=\frac{r_a}{r_p}[/tex]   (5)

And replacing the values obtained into equation (5) we got:

[tex]\frac{v_p}{v_a}=\frac{8.659x10^3 km}{6.829x10^3 km}=1.268[/tex]  

And this would be the final answer [tex]\frac{v_p}{v_a}=1.268[/tex]

Answer:

Iris

Explanation:

The pupil is where the light enters the eye, however, the iris is pupil tissue and is the one who regulates the amount of light that it lets through.

The iris opens or closes to allow a greater or lesser flow of light through the pupil.

In summary, the iris is responsible for regulating the amount of light that enters the eye.

The amount of light entering the eye is mainlly regulated by the pupil, which adjusts its size based on the surrounding light levels. This is achieved by the action of muscles connected to the iris. Furthermore, the light that enters the eye is focused on the retina and processed to the brain via the optic nerve.

The amount of light entering the eye is majorly managed by the pupil. The pupil is the small opening in the center of the eye that adjusts its size based on the light levels in the environment. This adjustment is achieved by the contraction and relaxation of muscles connected to the iris, which is the colored part of the eye.

When the light levels are high, the pupil contracts (or constricts) to limit the amount of light that enters the eye. On the other hand, when the light levels are low, the pupil expands (or dilates) to allow more light to enter the eye. This process is regulated by specific nerves and structures, specifically the optic nerve and the oculomotor nerve in a process called the Pupillary Light Response.

Furthermore, light waves cross the cornea and focus on the retina, a light-sensitive layer lining the back of the eye. The image processing is then carried forward to the brain through the optic nerve.

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Answer:

[tex]\Delta U = 64218.9 J[/tex]

Explanation:

As we know that power of the heater is given as

P = 100 W

now the energy given by the heater for 11 min of time

[tex]E = P \times t[/tex]

[tex]E = 100 \times 11 \times 60[/tex]

[tex]E = 100\times 11 \times 60[/tex]

[tex]E = 66000 J[/tex]

now from 1st law of thermodynamics we know that

[tex]E = \Delta U + W[/tex]

work done under constant pressure condition we have

[tex]W = P \Delta V[/tex]

[tex]W = (3.527 \times 1.01 \times 10^5)(6 - 1) \times 10^{-3}[/tex]

[tex]W = 1781.13 J[/tex]

now from first equation we have

[tex]66000 = 1781.13 + \Delta U[/tex]

[tex]\Delta U = 64218.9 J[/tex]

The change in the internal energy of the system is 67.787 kJ.

The given parameters;

The heat added to the system by the heater;

Q = Pt = 100 x 660 = 66,000 J = 66 kJ

The work done on the system is calculated as follows;

W = PΔV

W = 3.527(6 - 1)

W = 17.64 L.atm

1 Latm = 0.1013 kJ

17.64 Latm = 1.787 kJ

The change in the internal energy of the system is calculated by applying the first law of thermodynamics as follows;

ΔU = Q + W

ΔU = 66 kJ  +  1.787 kJ

ΔU = 67.787 kJ.

Thus, the change in the internal energy of the system is 67.787 kJ.

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Answer:

sulcus

Explanation:

A sulcus is an indentation or depression in the brain that causes it to look like it  ridges or folds

Cerebral sulci and fissures are grooves between the adjacent gyri on the surface of the cerebral hemispheres.

Sulci can be basically can be divided into three basic function

limiting sulcus: This happens to  develop between areas differing in structure and function, for example central sulcus

axial sulcus: This develops along the axis of a rapidly growing/developing area (e.g. calcarine sulcus)

operculated sulcus: a sulcus may be between two structurally-different areas and a third sulcus may lie in its wall and does not appear on the surface (e.g. lunate sulcus)

Answer:

Option (e).

Explanation:

The Compton's equation is:

[tex] \lambda^{'} = \frac{h}{m_{e} c} \cdot (1 - Cos(\theta)) + \lambda = \lambda_{c} (1 - Cos(\theta)) + \lambda [/tex] (1)

where λ': is the wavelength scattered, λ: is the initial wavelength, h: is Planck's  constant, [tex] m_{e} [/tex]: is the electron rest mass, c: speed of light, Θ: scattering angle (between λ and λ'), and [tex] \lambda_{c} [/tex]: is a constant known as the Compton wavelength of the electron = 0.00243 nm.          

From equation (1), the scattered radiation is directly proportional to the scattering angle, having the maximum value when Θ=90°:

[tex] \theta = 90 ^{ \circ} \rightarrow \lambda^{'} = \lambda_{c} (1-Cos(90)) + \lambda = \lambda_{c} + \lambda [/tex]

And the minimum value when Θ=0°:

[tex] \theta = 0 ^{ \circ} \rightarrow \lambda^{'} = \lambda_{c} (1-Cos(0)) + \lambda = \lambda [/tex]

Hence, the options (a) and (b) are incorrect.

Similarly, we can see from equation (1) that the scattered radiation depends also on the wavelength of the primary beam and no wavelength other than that (since [tex] \lambda_{c} [/tex] is a constant), so the correct option is (e).  

Have a nice day!

Answer:

Part a)

[tex]V' = 7.77 Volts[/tex]

Part b)

[tex]k' = 6.27 [/tex]

Explanation:

As we know that capacitor plate is connected across 2.1 V and after charging it is disconnected from the battery

So here we can say that charge on the plates will remain conserved

So we will have

[tex]Q = kC(2.1)[/tex]

now dielectric is removed between the plates of capacitor

so new potential difference between the plates

[tex]V' = \frac{Q}{C'}[/tex]

[tex]V' = \frac{kC(2.1)}{C}[/tex]

[tex]V' = 3.7 \times 2.1 [/tex]

[tex]V' = 7.77 Volts[/tex]

Part b)

Now the capacitor plates are again isolated and unknown dielectric is inserted between the plates

So again charge is same so potential difference is given as

[tex]V" = \frac{Q}{k'C}[/tex]

[tex]0.59 V = \frac{kCV}{k'C}[/tex]

[tex]0.59 = \frac{3.7}{k'}[/tex]

[tex]k' = 6.27 [/tex]

Final answer:

The resulting potential difference of the capacitor after the paper is withdrawn is 7.77V. The dielectric constant of the unknown substance, where the potential decreased to 0.59 times the original, is approximately 6.27.

Explanation:

The potential difference across a capacitor is inversely proportional to the dielectric constant of the material between the plates. When a paper dielectric with a constant of 3.7 is removed from a charged capacitor, the potential difference increases because the dielectric constant of air is nearly 1.

Find the resulting potential difference of the capacitor

The initial potential difference (V1) with paper is 2.1V, and the dielectric constant for paper (k1) is 3.7. When the paper is removed, the dielectric constant becomes that of air, which is approximately 1 (k2). For an isolated capacitor, the charge (Q) remains constant, so we can use the relation that the product of the potential difference (V) and the dielectric constant (κ) is a constant (Q=CV and C=κC0). Therefore, V1k1 = V2k2. By substituting the known values: 2.1V * 3.7 = V2 * 1, we find that V2 = 2.1V * 3.7 = 7.77V.

Find the dielectric constant of the inserted unknown substance

If the potential difference with the new substance is 0.59 times the initial potential (when paper filled the capacitor), then V3 = 0.59 * 2.1V. The dielectric constant of the new substance (k3) can be found using the same principle where V1k1 = V3k3. With V3 = 0.59 * 2.1 = 1.239V, we get 2.1V * 3.7 = 1.239V * k3, leading to k3 = (2.1V * 3.7) / 1.239V ≈ 6.27.

Answer:

The vector a, the answer is the point D

Explanation:

We need to make the make the subtraction from the x,y points. It will be the points of the head minus the points of the tail.

x=(-2 - 0) and y = (3-0) vector = -2 + 3

The Answer is—————————D. a

Answer:

rise in temperature = 333.53°C

Explanation:

mass of lead bullet, m = 5.9 g

initial velocity, u = 410 m/s

specific heat of lead = 0.126 J/gm - K = 126 J/kg K

Initial kinetic energy of the bullet

K = 1/2 mu^2 = 0.5 x 5.9 x 10^-3 x 410 x 410 = 495.895 J

Half of the kinetic energy is used to raise the temperature of lead bullet

K / 2 = mass of bullet x specific heat of lead x rise in temperature

247.95 = 5.9 x 10^-3 x 126 x rise in temperature

rise in temperature = 333.53°C

Thus, the rise in temperature of lead bullet is 333.53°C.

Answer:

Explanation:

Given

Mechanical Energy of Spring-Block system is 1 J

Maximum Amplitude is [tex]A=10 cm[/tex]

maximum speed [tex]v_{max}=1.2 m/s[/tex]

Suppose [tex]x=A\sin \omega t [/tex]be general equation of motion of spring-mass system

where A=max amplitude

[tex]\omega [/tex]=Natural frequency of oscillation

t=time

[tex]v_{max}=A\omega =1.2[/tex]

[tex]0.1\cdot \omega =1.2[/tex]

[tex]\omega =12 rad/s[/tex]

maximum kinetic Energy must be equal to total Mechanical Energy when spring is un deformed i.e. at starting Position

[tex]\frac{1}{2}mv_{max}^2=1[/tex]

[tex]m=\frac{2}{1.2^2}=\frac{2}{1.44}=1.38 kg[/tex]

Also [tex]\omega [/tex]is also given by

[tex]\omega =\sqrt{\frac{k}{m}}[/tex]

[tex]k=\omega ^2\cdot m[/tex]

where k= spring constant

[tex]k=12^2\cdot 1.38 [/tex]

[tex]k=200 N/m[/tex]

Answer:34 cm

Explanation:

Given

mass of meter stick m=80 gm

stick is balanced when support is placed at 51 cm mark

Let us take 5 gm tack is placed at x cm on meter stick so that balancing occurs at x=50 cm mark

balancing torque

[tex]80\times 10^{-3}(51-50)=5\times 10^{-3}(50-x)[/tex]

[tex]80=5(50-x)[/tex]

[tex]80=250-5x[/tex]

[tex]5x=170[/tex]

[tex]x=\frac{170}{5}[/tex]

[tex]x=34 cm[/tex]

To balance the nonuniform meterstick, the 5.00-g tack should be placed at approximately 50.4 cm from the pivot point.

To find the location on the meterstick where the 5.00-g tack should be placed so that the stick will balance at the 50.0 cm mark, we can use the principle of torque balance.

The torque balance equation is given by:

Torque(counter-clockwise) = Torque(clockwise).

In this case, the torque is equal to the force multiplied by the distance from the pivot point. The force exerted by the 5.00-g tack can be calculated using the formula:

Force = mass * acceleration due to gravity.

By substituting the known values into the equation and solving for the distance, we can determine where the tack should be placed on the meterstick.

In this case, the tack should be placed at approximately 50.4 cm from the pivot point.

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Answer:

Explanation:

Given

Photon A has  twice the Energy of Photon B

i.e. [tex]E_a=2E_b[/tex]

de Broglie wavelength is given by

[tex]\lambda =\frac{h}{P}[/tex]

[tex]\frac{1}{\lmabda }=\frac{P}{h}[/tex]

and Energy of Proton is given by

[tex]E=\frac{hc}{\lambda }[/tex]

[tex]E=hc\times \frac{P}{h}[/tex]

[tex]E=Pc[/tex]

where P=momentum

c=velocity of Light

[tex]P=\frac{E}{c} [/tex]

Momentum of A [tex]P_a=\frac{E_a}{c}=\frac{2E_b}{c}[/tex]

Momentum of B is [tex]P_b=\frac{E_b}{c}[/tex]

Thus [tex]P_a>P_b[/tex]

For wavelength

[tex]\lambda _a=\frac{h}{P_a}[/tex]

[tex]\lambda _b=\frac{h}{P_b}[/tex]

since [tex]P_a>P_b[/tex] therefore

[tex]\lambda _a<\lambda _b[/tex]      

The momentum of photon A is greater than that of photon B, and the wavelength of A is less than that of B.

When comparing the momentum of two photons, we can use the equation p = E/c, where p is momentum, E is energy, and c is the speed of light. Since photon A has twice the energy of photon B, its momentum will also be greater. Therefore, the momentum of A is greater than that of B.

As for the wavelength, we know that the equation c = λf relates the speed of light (c) to the wavelength (λ) and frequency (f). Since the speed of light is constant, if the energy of photon A is greater, its frequency must be higher as well. As a result, the wavelength of A must be shorter than that of B. Therefore, the wavelength of A is less than that of B.

Answer:

F'=  10F (N)

Explanation:

To solve this problem we apply Coulomb's law:

Two point charges (q₁, q₂) separated by a distance (d) exert a mutual force (F) whose magnitude is determined by the following formula:

F = K*q₁*q₂ / d² Formula (1)  

F: Electric force in Newtons (N)

K : Coulomb constant in N*m²/C²

q₁,q₂:Charges in Coulombs (C)  

d: distance between the charges in meters(m)

Calculating of the new force F'

Data:

q'₁ = 5q₁

q'₂ = q₂/2

d' = d/2

We apply the Coulomb's law:

F' = K*q'₁*q'₂ / d'²

F'= K*(5q₁)*(q₂/2) / (d/2)²

F'= K*(5q₁*q₂/2) / (d²/4)

F'= K*20q₁*q₂) / (2d²)

F'=  10(K*q₁*q₂) / (d²)

F'=  10(K*q₁*q₂) / (d²)  , F = K*q₁*q₂ / d²

F'=  10F (N)

Final answer:

The force between two charges can be calculated using Coulomb's Law. We can use the given values to calculate the new force F' and determine its value.

Explanation:

The force between two charges is given by Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Using the given information, we can calculate the new force F' using the formula:

F' = (k * q'1 * q'2) / (d'^2)

Substituting the given values into the formula, we get:

F' = (k * 5q1 * (q2/2)) / ((d/2)^2)

After solving the equation, we can determine the value of the new force F'.

Answer:

Super-critical mass

Explanation:

This term refers to the mass, in which the amount of fission processes per unit of time increases to the point, where some intrinsic feedback mechanism causes the reactor to reach an equilibrium point at a high temperature or power, that is, It becomes critical again, or it is destroyed due to the amount of processes.

"When nuclear material in the reactor is fissioning at an increasing rate, this is known as a ""criticality.""

When nuclear material in the reactor is fissioning at an increasing rate, it is said to be in a state of criticality. This term refers to the condition where the reactor is sustaining a nuclear chain reaction at a steady rate. In a nuclear reactor, criticality is the normal operating condition, where one fission event leads to exactly one subsequent fission event, on average, in the next generation of the reaction. This ensures a controlled and sustained release of energy.

To achieve criticality, the reactor must have enough fissile material (such as uranium-235 or plutonium-239) and the correct geometric arrangement to maintain a chain reaction. Control rods, which are made of materials that absorb neutrons, are used to regulate the rate of the reaction. When the reactor is critical, the rate of neutron production is balanced by the rate of neutron absorption and leakage, resulting in a steady power output.

If the rate of fission increases beyond this balance, the reactor is said to be supercritical, which can lead to an uncontrolled increase in power and is a dangerous condition that must be avoided. Conversely, if the rate of fission decreases, the reactor is said to be subcritical, and the power output will decrease.

In summary, criticality in a nuclear reactor is the state where a self-sustaining chain reaction occurs at a constant rate, providing a stable source of energy for the submarine's propulsion system. It is carefully managed by the reactor's control systems and the vigilance of the Engineering Duty Officer and their team."

The angular velocity of the disk must be 2.25 rpm

Explanation:

The centripetal acceleration of an object in circular motion is given by

[tex]a=\omega^2 r[/tex]

where

[tex]\omega[/tex] is the angular velocity

r is the distance of the object from the axis of rotation

For the space station in this problem, we have

[tex]a=\frac{g}{2}=\frac{9.8}{2}=4.9 m/s^2[/tex] is the centripetal acceleration

The diameter of the disk is

d = 175 m

So the radius is

[tex]r=\frac{175}{2}=87.5 m[/tex]

So, a point on the rim has a distance of 87.5 m from the axis of rotation. Therefore, we can re-arrange the previous equation to find the angular velocity:

[tex]\omega = \sqrt{\frac{a}{r}}=\sqrt{\frac{4.9}{87.5}}=0.237 rad/s[/tex]

And this is the angular velocity of any point along the disk. Converting into rpm,

[tex]\omega=0.236 \frac{rad}{s}\cdot \frac{60 s/min}{2\pi rad/rev}=2.25 rpm[/tex]

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Answer:

vf = 12.51 m/s

Explanation:

Newton's second law to the grocery cart:

∑F = m*a Formula (1)

∑F : algebraic sum of the forces in Newton (N)

m : mass s (kg)

a : acceleration  (m/s²)

We define the x-axis in the direction parallel to the movement of the grocery cart  and the y-axis in the direction perpendicular to it.

Forces acting on the grocery cart

W: Weight of the block : In vertical direction  downward

N : Normal force : In vertical direction  upward

F : horizontal force

Calculated of the mas of the grocery cart (m)

W = m*g

m = W/g

W = 94.0 N  , g = 9.81 m/s²

m = 94/9.81

m = 9.58 Kg

Calculated of the acceleration of the grocery cart (a)

∑F = m*a

F = m*a

42.6 = (9.58)*a

a = (42.6) / (9.58)

a = 4.45 m/s²

Kinematics Equation of the grocery cart

Because the grocery cart moves with uniformly accelerated movement we apply the following formula to calculate its final speed :

vf²=v₀²+2*a*d Formula (2)

Where:  

d:displacement  (m)

v₀: initial speed  (m/s)

vf: final speed   (m/s)

a: acceleration (m/s²)

Data:

v₀ = 0

a = 4.45 m/s²

d = 17.6 m

We replace data in the formula (2) :

vf²=v₀²+2*a*d

vf² = 0+2*(4.45)*(17.6)

vf² = 156.64

[tex]v_{f} = \sqrt{156.64}[/tex]

vf = 12.51 m/s

Answer:

The measure of angle B equals the measure of angle C.

Explanation:

When a ray of light falls on a smooth polished surface and the light ray bounces back, it is called the reflection of light.

There are two laws of reflection;

1) The incident ray and reflected ray and normal all lie in the same plane.

2) The angle of incidence is equal to angle of reflection.

Here angle of incidence is represented by B and angle of reflection is by C.

So according to law of reflection the measure of angle B equals the measure of angle C.

Answer:

The measure of angle B equals the measure of angle C

Explanation:

"B" is the correct answer on edge

Answer:

592.92 x 10³ Pa

Explanation:

Mole of ammonia required = 10 g / 17 =0 .588 moles

We shall have to find pressure of .588 moles of ammonia at 30 degree having volume of 2.5 x 10⁻³ m³. We can calculate it as follows .

From the relation

PV = nRT

P x 2.5 x 10⁻³ =  .588 x 8.32 x ( 273 + 30 )

P = 592.92 x 10³ Pa

Answer:

upper motor neurons in the premotor cortex

Explanation:

Motor neurons are a type of nervous system cells that are located in the brain  and in the spinal cord. They have the function of producing the stimuli that cause the contraction of the different muscle groups of the organism. They are therefore essential for daily activities that require muscle contraction: walking, talking, moving hands and in general all body movements.

Answer:all galaxies Moving away from him

Explanation:

When we talk about the expanding universe, it means it has grown with the Big Bang ever since it started.  

Space expansion makes galaxies seem to move apart from each other. Although the galaxies themselves may seem to move through space, in reality, it is the space that is growing between the galaxies.

Thus the observer sees all the galaxies moving away from him, the more distant galaxies faster they move.

Answer:

Impulse, J = 250.4 kgm/s,  Avg Force F=3091.4 N

Explanation:

Since we know that impulse is the change in momentum i.e. Δp and   Δp[tex]=mv[/tex], therefore, to calculate the velocity we perform:

As the person has fallen by a 0.50m height, its potential energy changes into kinetic energy, therefore,

K.E.=P.E.

[tex]\frac{1}2}mv^{2}[/tex]=[tex]mgh[/tex]

[tex]v=\sqrt{2gh}[/tex]

[tex]v=\sqrt{2*9.8*0.50}[/tex]

[tex]v=3.13ms^{-1}[/tex]

(a) Impulse [tex]J[/tex] = Δp[tex]=mv[/tex]

[tex]J= 80*3.13[/tex]

[tex]J = 250.4 kgms^{-1}[/tex]

(b)  Avg Force F = Δp/Δt

[tex]F=\frac{250.4}{0.081}[/tex]

[tex]F=3091.4[/tex] N

The maximum possible emf induced in the antenna due to the motion of the automobile can be calculated using Faraday's law of electromagnetic induction. Plugging in the given values, the maximum possible emf is calculated as 2.4 x 10^-8 V.

The maximum possible emf induced in the antenna due to the motion of the automobile can be calculated using Faraday's law of electromagnetic induction. The equation for calculating the emf is given by μoθlvB, where μo is the permeability of free space, l is the length of the antenna, v is the velocity of the automobile, and B is the magnetic field strength. Plugging in the given values, we have:

μo = 4π x 10^-7 Tm/A

l = 1.0 m

v = 100.0 km/h = 27.78 m/s

B = 5.5 x 10^-5 T

Using these values, we can calculate the maximum possible emf induced in the antenna as:

emf = (μoθlvB) = (4π x 10^-7 Tm/A)(1.0 m)(27.78 m/s)(5.5 x 10^-5 T) = 2.4 x 10^-8 V

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The maximum possible emf induced in the 1.0 m long antenna moving at 100.0 km/h in a 5.5×10⁻⁵ T magnetic field is approximately 1.53 mV. The calculation involves using the motional emf formula: emf = vBL. Converting the velocity to meters per second and plugging in the values gives the result.

Motional EMF Calculation

The question is about finding the electromotive force (emf) induced in a radio antenna moving through the Earth's magnetic field. This situation involves motional emf, which can be determined using the formula:

emf = vBL

where:

Now, substituting these values into the formula:

emf = 27.78 m/s × 5.5 × 10⁻⁵ T × 1.0 m

emf ≈ 1.53 × 10⁻³ V

Therefore, the maximum possible induced emf in the antenna due to its motion is approximately 1.53 mV.

Answer:

7,157

Explanation:

Hi!

Use this equation to solve this problem:

Fb=ρfl*g*Vfl

where

Fb=buoyant force

What do we know?

The known values are highlighted in.

An iceberg (density=917 kg/[tex]m^3[/tex]) is floating in seawater, the volume of the iceberg below the waterline is approximately 7168 [tex]m^3[/tex].

To calculate the volume of the iceberg below the waterline, we must apply the concept of buoyancy. The buoyant force acting on an item that floats in a fluid is equal to the weight of the fluid displaced by the object.

The buoyant force (F_b) may be computed using the formula:

F_b = ρ_fluid * V_submerged * g

W_iceberg = ρ_iceberg * V_iceberg * g

F_b = W_iceberg

ρ_fluid * V_submerged * g = ρ_iceberg * V_iceberg * g

Now,

V_submerged = (917 / 1025 ) * 8000

V_submerged = 0.896 * 8000 [tex]m^3[/tex]

V_submerged ≈ 7168 [tex]m^3[/tex]

Therefore, the volume of the iceberg below the waterline is approximately 7168  [tex]m^3[/tex].

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