metal sphere 1 has a positive charge of 9.00 nc . metal sphere 2, which is twice the diameter of sphere 1, is initially uncharged. the spheres are then connected together by a long, thin metal wire. what are the final charges on each sphere?

The given statement "the mantle is partially molten, that's why no S waves travel through it" is false because the mantle is partially molten, but this is not the reason why no S waves travel through it. S waves, or secondary waves, are a type of seismic wave generated during earthquakes.

They cannot travel through liquids, as they require a rigid medium for propagation. The reason S waves don't travel through the mantle is because of the outer core, which is a liquid layer composed mainly of molten iron and nickel. When S waves encounter the outer core, they are absorbed and cannot continue through the liquid.

This creates a shadow zone on the opposite side of the Earth from the earthquake's epicenter, where S waves are not detected. The mantle itself is made up of solid rock with pockets of molten material, and S waves can propagate through the solid parts of the mantle.

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To determine the first, second, and third overtones of the bassoon with a fundamental frequency of 91 Hz, we need to use the formula for the resonant frequencies of a tube with two open ends. Therefore, the first overtone of the bassoon is 143 Hz, the second overtone is 215 Hz, and the third overtone is 286 Hz.

The formula is f = (n/2) * v / L, where f is the frequency, n is the harmonic number, v is the speed of sound, and L is the length of the tube. Since the bassoon has two open ends, we can assume that its length is twice the length of a tube with one open end, which is approximately 60 cm. Therefore, the length of the bassoon can be estimated to be around 120 cm. Using the formula, we can calculate the overtones as follows:
(a) The first overtone is the second harmonic, so n = 2. Plugging in the values, we get f = (2/2) * 343 m/s / 1.2 m = 143 Hz.
(b) The second overtone is the third harmonic, so n = 3. Plugging in the values, we get f = (3/2) * 343 m/s / 1.2 m = 215 Hz.
(c) The third overtone is the fourth harmonic, so n = 4. Plugging in the values, we get f = (4/2) * 343 m/s / 1.2 m = 286 Hz.

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For a resonance tube with two open ends, the frequency of the first overtone is three times the fundamental frequency. The first, second, and third overtones of a bassoon with a fundamental frequency of 91 Hz are 182 Hz, 273 Hz, and 364 Hz, respectively.

Therefore, the first overtone of the bassoon is 273 Hz (91 Hz x 3). The second overtone is five times the fundamental frequency, which is 455 Hz (91 Hz x 5). Finally, the third overtone is seven times the fundamental frequency, which is 637 Hz (91 Hz x 7). These frequencies are all part of the overtone series for a wind instrument, which includes many other frequencies that are higher and lower than these. Understanding the overtone series is important for understanding the sound of instruments and how they produce different notes.

In a resonance tube with two open ends, overtones occur at integer multiples of the fundamental frequency.

(a) The first overtone is the second harmonic, which means it is 2 times the fundamental frequency. For a bassoon with a fundamental frequency of 91 Hz, the first overtone is 2 * 91 Hz = 182 Hz.

(b) The second overtone is the third harmonic, which is 3 times the fundamental frequency. In this case, it is 3 * 91 Hz = 273 Hz.

(c) The third overtone is the fourth harmonic, or 4 times the fundamental frequency. Therefore, it is 4 * 91 Hz = 364 Hz.

In summary, the first, second, and third overtones of a bassoon with a fundamental frequency of 91 Hz are 182 Hz, 273 Hz, and 364 Hz, respectively.

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The total number of complete revolutions the flywheel will make before coming to a stop is 279 revolutions.

To determine the total number of complete revolutions the flywheel will make before coming to a stop, we can break down the problem into each minute of operation and calculate the number of revolutions for each minute.

Given:

Maximum speed of the flywheel: 170 revolutions per minute

Let's calculate the number of revolutions for each minute:

Minute 1: 170 revolutions (maximum speed)

Minute 2: (2/5) * 170 = 68 revolutions

Minute 3: (2/5) * 68 = 27.2 revolutions (rounded to the nearest whole number)

Minute 4: (2/5) * 27.2 = 10.88 revolutions (rounded to the nearest whole number)

Minute 5: (2/5) * 10.88 = 4.352 revolutions (rounded to the nearest whole number)

The pattern continues with the flywheel rotating two-fifths as many times each subsequent minute until it comes to a stop. However, since the values become progressively smaller, we can see that the flywheel will never complete another whole revolution after Minute 5.

Therefore, the total number of complete revolutions the flywheel will make before coming to a stop is 170 + 68 + 27 + 10 + 4 = 279 revolutions.

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When platelets are activated, they undergo a dramatic change in shape. They transform from small, disk-shaped cells to irregularly shaped, spiky cells with long processes that extend outward.

This process is called platelet activation and is a crucial step in blood clot formation.

The activated platelets then release chemicals called thromboxane A2 and serotonin, which cause the nearby platelets to become activated as well.

This leads to the formation of a platelet plug that helps to stop bleeding from an injury. The spiky shape of activated platelets allows them to adhere to damaged blood vessel walls and to each other, forming a strong clot.

Overall, platelet activation and shape change play a critical role in the body's ability to stop bleeding and maintain hemostasis.

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Strictly speaking, the light that meets and passes through a pane of window glass is not the same light that emerges. When light interacts with a pane of window glass, it undergoes several processes that result in its transformation.

As light enters the glass, it encounters the atoms or molecules within the material. These particles absorb and re-emit the incoming light through a process called scattering. This scattering causes a delay and a change in the direction of the light waves, effectively slowing them down.

Additionally, window glass is not perfectly transparent, and it absorbs a small fraction of the light passing through it. This absorption results in a conversion of some of the light's energy into thermal energy, which manifests as heat within the glass.

Due to these interactions, the light that eventually emerges from the other side of the glass is not exactly the same as the incident light. It has experienced scattering, a slight delay, and a partial conversion to heat energy.

However, the emerging light maintains the same general properties, such as its wavelength, color, and intensity. Hence, while it is not precisely the same light, it is a modified version of the original light that entered the glass.

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The spring constant of the bungee cord is approximately 58.97 N/m.

We need to use the equation for the period of simple harmonic motion: T = 2π√(m/k)
where T is the period, m is the mass of the object, and k is the spring constant. We are given the mass of the bungee jumper (m = 75.8 kg) and the period of oscillation (T = 7.25 s), so we can rearrange the equation to solve for k:
k = (4π²m)/T²
Plugging in the values, we get: k = (4π² x 75.8 kg)/(7.25 s)²
k ≈ 266.3 N/m
So the spring constant of the bungee cord is approximately 266.3 N/m.

The answer to your question is that the spring constant of the bungee cord is approximately 266.3 N/m. This can be calculated using the formula k = (4π²m)/T², where m is the mass of the bungee jumper and T is the period of oscillation.
The spring constant of the bungee cord can be calculated using the formula for the period of oscillation in a mass-spring system, which is: T = 2π * sqrt(m / k)
Where T is the period of oscillation (7.25 s), m is the mass of the bungee jumper (75.8 kg), and k is the spring constant we need to find. First, square both sides of the equation: (T^2) / (4π^2) = m / k
Now, rearrange the equation to isolate k:
k = m / ((T^2) / (4π^2))
Plug in the given values for mass and period:
k = 75.8 / ((7.25^2) / (4π^2))
Solve for k:
k ≈ 58.97 N/m

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Answer:

worldwide is the answer

The car traveled a distance of 2.09 m in 3.0 seconds.  

We can use the equation for constant acceleration to solve for the distance traveled:

[tex]v_f^2 = v_i^2 + 2as[/tex]

here [tex]v_f[/tex] is the final velocity, [tex]v_i[/tex]is the initial velocity, a is the acceleration, and s is the time.

In this case, the initial velocity is 4.0 m/s and the acceleration is 2.0 [tex]m/s^2[/tex], so:

[tex]v_i = v_f = 4.0 m/s + 2.0 m/s^2 * 3.0 s[/tex]

= 14.0 m/s

Solve for s:

[tex]3.0 s^2 = 4.0 m/s^2 * 14.0 m/s + 2.0 m/s^2 * 2.0 m/s^2[/tex]

for s, we get:

[tex]s = (4.0 m/s^2 * 14.0 m/s + 2.0 m/s^2 * 2.0 m/s^2)^(1/2)[/tex]

= 2.09 m

Therefore, the car traveled a distance of 2.09 m in 3.0 seconds.  

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Chris is approximately 63.24 meters away from the source of the sound.

We can calculate the distance Chris is from the source of sound using the Inverse-square law formula. The formula states that the sound intensity (I) is inversely proportional to the square of the distance from the source (r²).In other words,

I₁/I₂ = (r₂/r₁)²

Where I₁ and r₁ represent the sound intensity and distance from the source respectively for John, and I₂ and r₂ represent the same for Chris.

To find the distance r₂ for Chris, we can rearrange the formula and substitute the given values as follows:

I₁/I₂ = (r₂/r₁)²r₂ = r₁√(I₁/I₂)r₁ = 2m (given)I₁ = 10(60/10) = 1,000,000 μW/m² (using the formula I = 10(L/10))I₂ = 10(20/10) = 100 μW/m² (using the formula I = 10(L/10))r₂ = 2√(1,000,000/100)≈63.24m

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A galaxy with a small bulge and loose, poorly defined spiral pattern is typically classified as a "late-type" or "low surface brightness" spiral galaxy.

Late-type spiral galaxies are characterized by their loose, open spiral patterns, which are often difficult to discern due to low contrast and irregularity.

They typically have small, faint bulges at their centers and relatively low mass and star formation rates compared to earlier-type spiral galaxies.

The spiral arms of late-type galaxies are often more extended and irregular than those of earlier-type galaxies, with lower concentrations of stars and gas.

The disk of a late-type spiral galaxy is also often thinner and more fragile, making it more susceptible to distortions and disruptions from gravitational interactions with other galaxies.

Examples of late-type spiral galaxies include the Milky Way's neighbor, the Andromeda Galaxy (M31), and the galaxy NGC 2841.

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If planet e has a higher relative velocity compared to planet b, it will experience a larger Doppler shift in the radio signals. On the other hand, if planet b has a higher relative velocity, it will experience a larger Doppler shift.

Firstly, let's define what the Doppler shift is. It is a change in the frequency of waves (in this case, radio signals) due to the relative motion between the source and the observer. When an object is moving away from the observer, the frequency of the waves it emits appears to decrease (called redshift), and when it is moving towards the observer, the frequency appears to increase (called blueshift).

Now, to compare the size of the Doppler shift in the radio signals detected at planets E and B, we need to consider their relative velocities with respect to Earth. Planet B is closer to its star than planet E, meaning it has a smaller orbit and thus a faster orbital velocity. This faster velocity would cause a larger Doppler shift in the radio signals detected at planet B compared to planet E.

Additionally, we also need to take into account the masses of the planets and their respective stars. The larger the mass of the planet or star, the stronger its gravitational pull, and the larger the Doppler shift. However, we do not have enough information to make any conclusions about the masses of the planets and stars in this scenario.

In summary, based on the information provided, we can conclude that the size of the Doppler shift in the radio signals detected at planet B will be larger than the size of the Doppler shift in the radio signals detected at planet E. This is due to planet B's faster orbital velocity around its star compared to planet E.

The size of the Doppler shift in radio signals detected at planets e and b will depend on their respective velocities relative to the source of the radio signals. The Doppler effect causes a change in the frequency of waves (such as radio signals) as the source and the observer move toward or away from each other.

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The force applied to the heavier object (t1) is twice the tension in the string between the masses (t2). This relationship holds true as long as the system remains frictionless and the tension in the string is constant.

The relationship between t1 and t2 in this scenario can be determined by applying Newton's Second Law of Motion. Since the system is frictionless, the net force acting on the objects is equal to the force of tension in the string between the masses.

Let's consider the forces acting on each object individually. Object 1, with mass 2m, experiences a force of tension t2 in the direction of the string and a force of t1 in the direction of the applied force. Object 2, with mass m, experiences only a force of tension t2 in the direction of the string.

Using Newton's Second Law, we can write the equations of motion for each object as follows:

For Object 1:
F_net = t2 - t1 = (2m)a

For Object 2:
F_net = t2 = (m)a

where a represents the acceleration of the system.

Next, we can use these equations to eliminate the acceleration and solve for the relationship between t1 and t2:

t2 - t1 = (2m)a
t2 = (m)a

Substituting the second equation into the first, we get:

(m)a - t1 = (2m)a
t1 = (m)a

Therefore, the relationship between t1 and t2 is:

t1 = 2t2

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Answer:

depends on how you look at light, gaps do not form between photons as light spreads out

Explanation:

The impulse exerted by the floor on the egg is -0.45 kg·m/s.

The impulse exerted on an object can be calculated using the equation I = Δp, where I is the impulse and Δp is the change in momentum of the object. The change in momentum can be determined using the equation Δp = mΔv, where m is the mass of the object and Δv is the change in velocity.

In this case, the egg falls from a height of 90 cm, so it experiences a change in velocity as it falls. Using the equation v = √(2gh), where v is the final velocity, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height, we can calculate the final velocity of the egg upon hitting the floor.

Next, we calculate the initial momentum of the egg using the equation p = mv, where p is the momentum, m is the mass of the egg (5.0 g = 0.005 kg), and v is the initial velocity (0 m/s).

Finally, we subtract the initial momentum from the final momentum to obtain the change in momentum and therefore the impulse exerted by the floor on the egg, which is approximately -0.45 kg·m/s.

The negative sign indicates that the impulse is in the opposite direction to the initial momentum, representing the reversal of motion upon impact with the floor.

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Assuming that both refrigerators have the same weight, the work done in lifting the refrigerator to the truck is the same for both Mr. Montana and Mr. Perry, regardless of the method they used to lift it. However, the force required to lift the refrigerator is different.

Mr. Montana used a ramp to move the refrigerator up to his truck, which means that he applied a smaller force over a longer distance. This is because the ramp reduces the force needed to move the object against gravity, but it increases the distance over which the force is applied. In contrast, Mr. Perry lifted the refrigerator directly, applying a larger force over a shorter distance.

Therefore, Mr. Perry applied more force than Mr. Montana to lift the refrigerator, as he had to lift the entire weight of the refrigerator with his arms. On the other hand, Mr. Montana applied less force because the ramp reduced the force needed to move the refrigerator up to his truck.

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The magnitude of the force that block B exerts on block C is 1.34 N.

According to Newton's third law of motion, the force exerted by block A on block B is equal in magnitude and opposite in direction to the force exerted by block B on block A. Similarly, the force exerted by block B on block C is equal in magnitude and opposite in direction to the force exerted by block C on block B.

Since the system of blocks moves to the right with an acceleration of 1.12 m/s², there must be a net force acting on the system. This net force is caused by the force exerted by block B on block C.

Using Newton's second law of motion (F = ma), we can calculate the force:

Force = mass of block C × acceleration

Force = 1.20 kg × 1.12 m/s²

Force ≈ 1.34 N

Hence, the correct answer is C) 1.34 N.

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Therefore, the current flowing through the wire is: 1600 A. Therefore, the correct answer is (A) 1200 A.  

The current flowing through a wire is given by the equation:

I = V/R

here I is the current, V is the voltage, and R is the resistance of the wire.

The resistance of the wire can be calculated using its resistivity and its length:

R = ρL

here ρ is the resistivity of the metal.

The current can be calculated using the voltage and the resistance:

I = V/R

Therefore, the current flowing through the wire is:

I = 16.0 V/0.0 mm

= 1600 A.

Therefore, the correct answer is (A) 1200 A.  

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The angle at which the sun appears to the fisherman is approximately 0.0009 degrees above the horizon.

We need to determine the position of the sun relative to the observer. The position of the sun in the sky changes throughout the day as it rises and sets, and moves across the sky from east to west. The position of the sun is measured in degrees above or below the horizon. The higher the observer is above the water, the greater their field of vision and the more of the horizon they can see. This will affect the angle at which they see the sun.

Assuming that the fisherman in the boat is at a higher elevation than the diver,
Let's assume that the diver is at sea level, and the fisherman is 10 meters above the water.
tan θ = opposite / adjacent
where θ is the angle we want to calculate, opposite is the height of the fisherman above the water (10 meters), and adjacent is the distance from the fisherman to the horizon (which we can assume is approximately equal to the radius of the earth, or 6,371 kilometers).
tan θ = 10 / 6371000
θ = arctan (10 / 6371000)
θ ≈ 0.0009 degrees

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So the speed of the car and its occupants is approximately 208 m/s (which is about 468 mph!).

First, let's consider the fact that the speed of the tops of the car's wheels (which we'll call v_wheels) is not the same as the speed of the car and its occupants (which we'll call v_car). This is because the car's wheels are rotating while the car is moving forward, so the speed of the wheels is actually greater than the speed of the car.

To calculate the speed of the car and its occupants, we need to use the relationship between the linear speed of an object (the speed of its center of mass) and the angular speed of the object (the speed of its rotation). This relationship is given by the formula:

v = r * w
where v is the linear speed, r is the radius of the object, and w is the angular speed.

In the case of the car's wheels, we know that the linear speed of the tops of the wheels (v_wheels) is 52 m/s. We also know that the radius of the wheels (r) is half the diameter of the wheel, which is typically around 0.5 meters for a car. So we can use these values to solve for the angular speed of the wheels (w):

w = v_wheels / r

w = 52 m/s / 0.5 m

w = 104 rad/s

Now that we know the angular speed of the wheels, we can use the same formula (v = r * w) to find the linear speed of the car and its occupants. We just need to know the radius of the car's motion, which is the distance from the center of the car to the point on the car's surface that is moving forward at the same speed as the car (this is typically the center of mass of the car).

Unfortunately, we don't have this information. However, we can make a reasonable estimate based on the size of the car. Let's assume that the radius of the car's motion is around 2 meters (which would be a typical value for a car). Then we can use the formula to find the linear speed of the car and its occupants:

v_car = r * w
v_car = 2 m * 104 rad/s
v_car = 208 m/s

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Answer:

6 cm

Explanation:

When 4 cm from the mirror the image is 4 cm behind the mirror.  

When the mirror is moved 1 cm towards the man the man is now 3 cm from the mirror and his image is also 3 cm from the mirror.

Thus the distance between the man and his image is now 3+3 = 6 cm.

Compared with the thermal energy and temperature of the sand on a city beach, a very hot cup of hot chocolate has much higher thermal energy and temperature. This is because the hot chocolate has been heated to a high temperature, typically around 65-80°C (149-176°F), whereas the sand on a city beach may only be warmed by the sun to around 30-40°C (86-104°F).

Additionally, the specific heat capacity of sand is much lower than that of liquid, so it takes less thermal energy to heat up sand than it does to heat up hot chocolate. Therefore, the hot chocolate will feel much hotter to the touch and contain more thermal energy than the sand on a city beach.

Compared with the thermal energy and temperature of the sand on a city beach, a very hot cup of hot chocolate has a higher temperature but lower thermal energy. The hot chocolate's higher temperature means it has more intense heat, while the sand's greater thermal energy is due to its larger mass and the heat it has absorbed throughout the day.

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The Maxwell's first equation, also known as Gauss's law for electric fields, states that the electric flux through any closed surface is proportional to the net electric charge enclosed within that surface.

In other words, it relates the electric field to the distribution of electric charges. Mathematically, the equation can be written as ∮E⋅dA = Q/ε₀, where E is the electric field, dA is an infinitesimal surface element, Q is the net electric charge enclosed within the closed surface, and ε₀ is the electric constant.

This equation has important implications in electromagnetism as it helps us understand the behavior of electric fields and charges. It also allows us to calculate the electric field for different charge distributions and to derive other important equations such as Coulomb's law.

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The impedance of an LRC series circuit is given by:

Z = sqrt[R^2 + (Xl - Xc)^2]

where R is the resistance, Xl is the inductive reactance, and Xc is the capacitive reactance. At the frequency where the impedance is minimum, Xl = Xc.

The inductive reactance is given by Xl = 2πfL, and the capacitive reactance is given by Xc = 1/(2πfC). Substituting these expressions into the equation for Z and setting Xl = Xc, we get:

Z = R

Solving for the frequency f, we get:

2πfL = 1/(2πfC)

f = 1/(2πsqrt(LC))

Substituting the given values of R, L, and C, we get:

f = 1/(2πsqrt(24.0 H x 2.0 µF))

f ≈ 0.023 kHz

Therefore, the frequency needed to minimize the impedance is approximately 0.023 kHz. The correct answer is A) 0.023 kHz.

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The term "a change in the forces in one part of a closed system affects the entire system" can be accurately applied to the "force-field analysis." (Option c)

Force-field analysis is a decision-making technique that involves analyzing the pros and cons of a proposed solution. It assumes that any action is affected by the interplay between the forces that support it and the forces that oppose it. It proposes that for an individual to progress or change, the driving force must be greater than the resisting force. Therefore, to attain progress, one must amplify the driving forces and decrease the restraining ones.

This technique is frequently used to aid in the preparation of change and innovation efforts, particularly in the business and healthcare sectors. Thus, the correct answer is option c: force-field analysis.

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a) The rms value of the voltage is D) 71 V.

b) The peak value of the current is A) 141 mA.

(a) The relationship between the peak voltage and the rms voltage in an AC circuit is given by:

V_rms = V_peak / sqrt(2)

Substituting V_peak = 100 V, we get:

V_rms = 100 / sqrt(2) ≈ 70.7 V

Therefore, the answer is D) 71 V.

(b) The relationship between the peak current and the rms current in an AC circuit is given by:

I_peak = I_rms * sqrt(2)

Substituting I_rms = 100 mA, we get:

I_peak = 100 * sqrt(2) ≈ 141 mA

Therefore, the answer is A) 141 mA.

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Answer:Before the collision, the truck had no kinetic energy since it was at rest. The car also had no kinetic energy since it was stationary. Therefore, the initial kinetic energy of the system was zero.

After the collision, the truck and car move with a common speed of 2 m/s. The total mass of the system is:

m = mass of truck + mass of car

m = 8,800 kg + 1,000 kg

m = 9,800 kg

The final kinetic energy of the system is:

KE_final = (1/2) * m * v^2

KE_final = (1/2) * 9,800 kg * (2 m/s)^2

KE_final = 19,600 J

The amount of kinetic energy "lost" in the collision is therefore:

KE_lost = KE_initial - KE_final

KE_lost = 0 J - 19,600 J

KE_lost = -19,600 J

The negative sign indicates that kinetic energy was not conserved in the inelastic collision, and that some of the initial kinetic energy was lost due to deformation and other forms of energy dissipation.

Explanation:

Before the collision, the truck had no kinetic energy since it was at rest. The car also had no kinetic energy since it was stationary. Therefore, the initial kinetic energy of the system was zero.

After the collision, the truck and car move with a common speed of 2 m/s. The total mass of the system is:

m = mass of truck + mass of car

m = 8,800 kg + 1,000 kg

m = 9,800 kg

The final kinetic energy of the system is:

KE_final = (1/2) * m * v^2

KE_final = (1/2) * 9,800 kg * (2 m/s)^2

KE_final = 19,600 J

The amount of kinetic energy "lost" in the collision is therefore:

KE_lost = KE_initial - KE_final

KE_lost = 0 J - 19,600 J

KE_lost = -19,600 J

The negative sign indicates that kinetic energy was not conserved in the inelastic collision, and that some of the initial kinetic energy was lost due to deformation and other forms of energy dissipation.

There are approximately 7,808 turns in the secondary coil.

To determine the number of turns in the secondary coil, we can use the formula for transformer voltage ratio, which states that the ratio of the number of turns in the secondary coil to the number of turns in the primary coil is equal to the ratio of the output voltage to the input voltage. In this case, the input voltage is 21 V and the output voltage is 10,000 V, so the voltage ratio is 10,000/21.

Using this voltage ratio formula, we can write:
number of turns in the secondary coil / 164 = 10,000 / 21

Solving for the number of turns in the secondary coil, we get:
number of turns in the secondary coil = (10,000 / 21) x 164
number of turns in the secondary coil = 7,808 turns (rounded to the nearest whole number)

So there are approximately 7,808 turns in the secondary coil. This allows the transformer to step up the voltage from 21 V to 10,000 V.

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Answer: When You Display Food in Ice, What Should the Food be Held at a Temperature Of?

Explanation:

According to the FDA, food displayed on ice should be held at a temperature of 41°F or below.

{I Hope This Helps! :)}

Answer:

Approximately [tex]6.75\; {\rm m\cdot s^{-1}}[/tex].

Explanation:

Let [tex]u[/tex] denote the initial velocity and let [tex]v[/tex] denote the velocity after launching.

By the conservation of momentum, the sum of momentum would the same before and after launching:

[tex]m_{b}\, u_{b} + m_{r} \, u_{r} = m_{b}\, v_{b} + m_{r}\, v_{r}[/tex].

Assuming that [tex]u_{b} = u_{r} = 0\; {\rm m\cdot s^{-1}}[/tex]:

[tex]m_{b}\, v_{b} + m_{r}\, v_{r} = 0[/tex].

It is given that [tex]v_{b} = 360\; {\rm m\cdot s^{-1}}[/tex] and [tex]m_{r} = 1.6\; {\rm kg}[/tex]. Apply unit conversion and ensure that mass values are measured in the same unit (kilograms):

[tex]m_{b} = 30\; {\rm g} = 30 \times 10^{-3}\; {\rm kg} = 0.030\; {\rm kg}[/tex].

Substitute these values into the equation and solve for [tex]v_{r}[/tex]:

[tex]\begin{aligned}v_{r} &= \frac{-m_{b}\, v_{b}}{m_{r}}\\ &= \frac{-(0.030\; {\rm kg})\, (360\; {\rm m\cdot s^{-1}})}{1.6\; {\rm kg}} \\ &= 6.75\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].

Compared with a sound of 60 decibels, a sound of 80 decibels has an intensity (c) 1000 times greater.



1. The decibel (dB) scale is a logarithmic scale used to measure sound intensity. It is based on the following formula:

dB = 10 * log10(I / I₀)

where dB is the decibel level, I is the intensity of the sound, and I₀ is the reference intensity (usually the threshold of human hearing, 10^-12 watts/m^2).

2. To compare the intensities of two sounds with different decibel levels, you can use the following formula:

I₂ / I₁ = 10^((dB₂ - dB₁)/10)

3. In your question, you have two sounds with decibel levels of 60 dB and 80 dB. To find the ratio of their intensities, plug the values into the formula:

I₂ / I₁ = 10^((80 - 60)/10)

4. Calculate the ratio:

I₂ / I₁ = 10^(20/10) = 10^2 = 1000

So, compared with a sound of 60 decibels, a sound of 80 decibels has an intensity 1000 times greater.

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