A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.
Its circular surfaces are horizontal. What effect will the following changes, each made to the initial system, have on X, the height of the upper surface above the water? The liquids added do not mix with the water, and the cylinder never hits the bottom.

1. The cylinder is replaced with one that has the same density and diameter, but with half the height.
2. Some of the water is removed from the glass.
3. A liquid with a density of 1.06 g/cm3 is poured into the glass.
4. The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm3.
5. A liquid with a density of 0.76 g/cm3 is poured into the glass.
6. The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
Options are: Increase, Decrease, No change

(a) The speed of the center of mass of the spherical shell when it is at the bottom of the bowl is 3.1 m/s when the radius is 80 cm.

(b) The speed of the center of mass of the spherical shell when it is at the bottom of the bowl is 1.1 m/s when the radius is 10 cm.

The speed of the shell at the bottom of the bowl is calculated by applying the principle of conservation of energy.

K.E(rot) + K.E(trans) = P.E

where;

¹/₂mv² + ¹/₂Iω² = mgh

where;

¹/₂mv² + ¹/₂(²/₃Mr²)(v/r)² = mgh

¹/₂v² + ¹/₂(²/₃r²)(v²/r²) = gh

¹/₂v² + ¹/₂(²/₃)(v²) = gh

¹/₂v² + ¹/₃v² = gh

⁵/₆v² = gh

v² = 6gh/5

v = √(6gh/5)

Let the vertical height from the edge of bowl to the bottom , h = R = 80 cm

v = √(6 x 9.8 x 0.8 /5)

v = 3.1 m/s

v = √(6gh/5)

v = √(6 x 9.8 x 0.1 /5)

v = 1.1 m/s

Thus, the speed of the center of mass of the spherical shell when it is at the bottom of the bowl is 3.1 m/s when the radius is 80 cm.

The speed of the center of mass of the spherical shell when it is at the bottom of the bowl is 1.1 m/s when the radius is 10 cm.

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(a) Walking 73.2 m at 1.22 m/s would take

[tex]\dfrac{73.2\,\rm m}{1.22 \frac{\rm m}{\rm s}} = 60 \,\rm s[/tex]

and running 13.2 m at 3.02 m/s would take

[tex]\dfrac{13.2\,\rm m}{3.02\frac{\rm m}{\rm s}} \approx 4.37\,\rm s[/tex]

You've undergone a total displacement of 73.2 + 13.2 = 86.4 m in a matter of approximatly 64.37 s, so your average velocity is

[tex]\dfrac{\Delta x}{\Delta t} = \dfrac{86.4\,\mathrm m}{64.37\,\rm s} \approx \boxed{1.34\dfrac{\rm m}{\rm s}}[/tex]

(b) In the first 1.00 min = 60 s, you undergo a displacement of

[tex](60\,\mathrm s) \left(1.22 \dfrac{\rm m}{\rm s}\right) = 73.2 \,\rm m[/tex]

and in the second minute, you undergo a displacement of

[tex](60\,\mathrm s) \left(3.05\dfrac{\rm m}{\rm s}\right) = 183 \,\rm m[/tex]

Your total displacement is then 73.2 + 183 = 256.2 m in a matter of 2.00 min = 120 s, so your average velocity is

[tex]\dfrac{\Delta x}{\Delta t} = \dfrac{256.2\,\mathrm m}{120\,\rm s} \approx \boxed{2.14\dfrac{\rm m}{\rm s}}[/tex]

(c) For part (a), your displacement [tex]x(t)[/tex] (in m) at time [tex]t[/tex] (in s) is given by

[tex]x(t) = \begin{cases}1.22t & \text{for } 0 \le t \le 60 \\ 73.2 + 3.02 (t-60) & \text{for } t > 60\end{cases}[/tex]

and for part (b), your displacement is given by the very similar

[tex]x(t) = \begin{cases}1.22 t & \text{for } 0 \le t \le 60 \\ 73.2 + 3.05(t-60) & \text{for } t > 60 \end{cases}[/tex]

See the attached plots. The average velocity for the given situation is the slope of the dotted line.

Enthalpy changes are always lower than their expected values due to faulty measurements; option D.

Enthalpy changes refers to the changes in the heat content of substances in the course of a reaction.

Enthalpy changes occurs as a result of bond breaking and bond formation in the reactant molecules and product molecules respectively.

Enthalpy changes are measured from the changes in temperature that are observed in the course of a given reaction.

Due to faulty measurements in a particular experiment measuring enthalpy changes, enthalpy changes are always lower than their expected values.

Therefore, accurate measurements are required if results as close as possible to the actual enthalpy changes are to be obtained.

In conclusion, enthalpy changes measure the heat changes that occur during a particular chemical reaction.

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The formular for calculating half life is:

T1/2=0.693/Π

(a) The magnitude of the velocity of the 1000 kg car after the collision is 10.5 m/s.

(b) The direction of the velocity of the 1000 kg car after the collision is 8.2 ⁰ north west.

(c) The ratio of the kinetic energy of the two cars just after the collision to that just before the collision is 0.72.

Apply the principle of conservation of linear momentum as follows;

m₁u₁  +  m₂u₂ = m₁v₁x  +  m₂v₂x

where;

750(0) + 1000(13) = 750(4 cos 30)   +   1000v₂x

13000 = 2,598.1  +   1000v₂x

10,401.9 = 1000v₂x

v₂x  =  10.4 m/s

m₁u₁  +  m₂u₂ = m₁v₁y  +  m₂v₂y

750(0) + 1000(0) = 750(4 sin 30)   +   1000v₂y

0 = 1500 +  1000v₂y

v₂y  = -1500/1000

v₂y  = -1.5 m/s

v = √(v₂ₓ² + v₂y²)

v = √[(10.4)² + (-1.5)²]

v = 10.5 m/s

tanθ = v₂y/v₂ₓ

tanθ = -1.5/10.4

tanθ =  -0.144

θ = arc tan(-0.144)

θ = 8.2 ⁰ north west

K.Ei = 0.5m₁u₁²  +  0.5m₂u₂²

K.Ei = 0.5(750)(0)²  +  0.5(1000)(13)²

K.Ei = 84,500 J

K.Ef = 0.5(750)(4)²  +  0.5(1000)(10.5)²

K.Ef = 61,125 J

K.Ef/K.Ei = 61,125/84,500

K.Ef/K.Ei = 0.72

Thus, the magnitude of the velocity of the 1000 kg car after the collision is 10.5 m/s.

The direction of the velocity of the 1000 kg car after the collision is 8.2 ⁰ north west.

The ratio of the kinetic energy of the two cars just after the collision to that just before the collision is 0.72.

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Answer:

The four inner planets have shorter orbits, slower spin, no rings, and they are made of rock and metal. The four outer planets have longer orbits and spins, a composition of gases and liquids, numerous moons, and rings. The outer planets are made of hydrogen and helium, so they are called gas giants.

4. a poor insulator

If rest other things are kept constant or unchanged then a good conductor can be termed as a poor insulator.

Answer:

4 conductors and insulators are opposites of each other.

Explanation:

(a) The speeds of the tips of both rotors; main rotor 181.02 m/s and  tail rotor 223.8 m/s.

(b) The speed of the main rotor is 52.8 % speed of sound, and the speed of the tail rotor is 65.2 % speed of sound.

v = ωr

where;

v(main rotor) = (449 rev/min x 2π rad x 1 min/60s) x (0.5 x 7.7 m)

v(main rotor) = 181.02 m/s

v(tail rotor) = (4,150 rev/min x 2π rad x 1 min/60s) x (0.5 x 1.03 m)

v(tail rotor) = 223.8 m/s

% speed (main motor) = 181.02/343 = 0.528 = 52.8 %

% speed (tail motor) = 223.8/343 = 0.652 = 65.2 %

Thus, the speed of the main rotor is 52.8 % speed of sound, and the speed of the tail rotor is 65.2 % speed of sound.

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There wouldn't be any life on Earth and no climate if it weren't for the Sun.

The spherical form of the Earth results in changes in the amount of sunlight that reaches the surface at various latitudes, giving rise to various climatic zones. Seasons are caused by the tilt of the Earth's axis of rotation in relation to the ecliptic plane.

The surface of the sun is around 6000 C hot; at this temperature, the solar mostly produces visible light. The Earth radiates infrared energy back into space to maintain its energy balance after being warmed by incoming solar radiation. The Earth's surface has an average temperature of 15 C, and at this temperature, the planet emits infrared light.

Carbon dioxide, methane, nitrous oxide, and other atmospheric greenhouse gases let solar energy to pass through but absorb infrared radiation that the planet emits back into space. This feature is not shared by other atmospheric elements like oxygen and nitrogen. These greenhouse gases re-emit infrared radiation in all directions to maintain energy balance, some of which is aimed at the Earth's surface and warms it. More greenhouse gases will increase infrared absorption and raise surface temperatures. This is comparable to how much blanket you cover yourself with at night. The blanket's thickness affects how warm you feel. The result of heat brought on by rising levels of greenhouse gases in the atmosphere is climate change.

In the course of billions of years, the Sun will continue to get hotter and brighter, rendering the Earth uninhabitable.

Additionally, all fossil fuels (coal, petroleum, and natural gas) and renewable energy are directly and indirectly derived from the sun (wind, solar, biomass, and hydroelectric).

Thank you,

Eddie

The amplitude of the red colored wave is 1 unit and the amplitude of the red colored wave is 2.1 unit.

The amplitude of a wave is the maximum displacement of the wave. It can also be described at the maximum upward displacement of a wave curve.

From the graph, the amplitude of the red colored wave is 1 unit.

From the graph, the amplitude of the red colored wave is 2.1 unit.

Thus, the amplitude of the red colored wave is 1 unit and the amplitude of the red colored wave is 2.1 unit.

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Based on the given data about, volume, mass, and density of the spheres;

The density, mass, volume, and shape of an object determines whether it will float or sink in water.

For an object to float, it will displace its own weight of the fluid in which it floats. This is according to Archimedes' principle which states that the upward force acting on a body immersed fully or partially in a fluid, is equal to the weight of the fluid displaced.

Considering the given scenarios:

1. The new sphere has a density of ρ > ρ0 and a mass of m = m0.

This means that the volume of new sphere is smaller than the volume of the original sphere, therefore, the water level will fall,

2. The new sphere has a mass of m > m0 and a radius of r = r0.

This means that the new sphere will have a greater volume and mass. However, the density may be greater or less.. Therefore, the water level may rise or fall.

3. The new sphere has a radius of r = r0 and a density of ρ > ρ0.

The new sphere has equal volume, greater density and mass than the original sphere. Therefore, the water level will rise.

In conclusion, the level of the water in the container depends on the volume, mass and density of the object placed in it.

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Data:

We apply the following formula

Q = mcₑΔT

    Q = mcₑ (T - T₀)

We substitute Our data in the formula and solve:

Q = 0.210 g * 4.18 J / g K (305 k - 292.2 k)

Q = 11.23 J

The distance from the wall you would stand and hear no sound at all is 0.83 m.

The speed of a wave is the rate of change of distance traveled by a wave with time.

The distance at which the wave will have zero amplitude, there will be no sound at all since amplitude of a sound is proportional to intensity of the sound.

The point of zero amplitude, L = λ/₂

Where;

λ is wavelength of the wave

The wavelength of the wave is calculated as follows;

λ = V/f

where;

λ = 332/200

λ = 1.66 m

L = 1.66/2

L = 0.83 m

Thus, the distance from the wall you would stand and hear no sound at all is 0.83 m.

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Answer:

The second universal law, the law of vibration, posits that everything (every atom, object, and living thing) is in constant motion, vibrating at a specific frequency.

Explanation:

Please mark brainly

The second universal law defines this.

The second universal law, also known as the Law of Vibration, The Law of Vibration states that everything in the universe is in a constant state of movement. We refer to these movements as vibration, and the speed or rate at which something vibrates is called its frequency. The only difference between one object and another is its vibration rate.

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Q.1 Calculate the different accelerations from the graph

At initial point (let O) the velocity was 0 m/s to reach point A when the velocity was 5 m/s it took nearly 3 seconds as we all know that acceleration is nothing but the change in velocity per unit time

[tex]a \: = \frac{dv}{t} [/tex]

[tex]a = \frac{5 - 0}{3} = \frac{5}{3} \: m/ {s}^{2} [/tex]

Similarly from point A to point B the acceleration was

[tex]a = \frac{dv}{t} = \frac{7 - 5}{3} = \frac{2}{3} m/s²[/tex]

From Point B to C the velocity was constant so the acceleration at that point would be zero.

in the same way we can calculate acceleration for rest other points.

Q.2 Explain why a Merry-Go-Round and a Ferris Wheel have a constant acceleration when they are moving?

We all know that Velocity is nothing but the speed with direction. Merry Go Round and a Ferris Wheel has constant speed but dynamic direction due to which the magnitude of velocity at every point differs with different sign hence it have a constant acceleration.

The correct answer choice concerning weight and energy balance which is most accurate is the optimal amount of physical activity needed to maintain weight is unclear.

Energy balance refers to the way in balance is achieved when intake of energy is equal to energy expended.

Energy refers to the impetus behind all motion and all activity. If is also the capacity to do work. Energy is measured in a unit dimensioned in mass × distance²/time² (ML²/T²) or the equivalent.

So therefore, the correct answer choice concerning weight and energy balance which is most accurate is the optimal amount of physical activity needed to maintain weight is unclear.

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Answer:

B Gravitational potential energy

Explanation:

(a) The velocity of 0.2 kg after the collision is 30.48 m/s and the velocity of the 0.3 kg mass is 119.92 m/s.

(b) The velocity of their center of mass before collision is 60.24 m/s and after the collision is 84.14 m/s.

Apply the principle of conservation of linear momentum to determine the velocity of the balls;

m₁u₁ + m₂u₂ = m₁v₁  + m₂v₂

0.2(150) + (0.3)(-0.4) = 0.2v₁ + 0.3v₂

29.88 = 0.2v₁ + 0.3v₂

Apply one directional linear velocity

u₁ + v₁ = u₂ + v₂

v₁ = u₂ + v₂ - u₁

v₁ = -0.4 + v₂ - 150

v₁ = v₂ - 150.4

Substitute the value of v₁ into the first equation;

29.88 = 0.2(v₂ - 150.4) + 0.3v₂

29.88 = 0.2v₂ - 30.08 + 0.3v₂

59.96 = 0.5v₂

v₂ = 59.96/0.5

v₂ = 119.92 m/s

v₁ = 119.92 - 150.4

v₁ = -30.48 m/s

V(cm) = (0.2 x 150  +  0.3 x 0.4) / (0.2 + 0.3)

V(cm) = 60.24 m/s

V(cm) = (0.2 x 30.48 +  0.3 x 119.92) / (0.2 + 0.3)

V(cm) = 84.14 m/s

Thus, the velocity of 0.2 kg after the collision is 30.48 m/s and the velocity of the 0.3 kg mass is 119.92 m/s.

The velocity of their center of mass before collision is 60.24 m/s and after the collision is 84.14 m/s.

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1. Alpha

Number next to Th is 231

(because 231 + 4 = 235)

The other number below the 4 is 2 - helium

(because 90 + 2 = 92)

2. Beta

Missing numbers are zero and one. Same as the one below it.

3. Beta

11 is the number above the C

(because 11 + 0 = 11)

5 is the number next to the B

(because 5 + 1 = 6)

Basically, the missing numbers must balance on both side of the equation; creating the elements you've started of with, meaning if you where to add the right side of the equation up - you should end up with the same protons and mass numbers you began with.

Hope this helps!

The potential energy (P.E) of X at r is less than P.E at s.

The total energy (T.E) of Y is less than total energy (T.E) of X.

The PE of Y at v is greater than the PE of Z at c.

The speed of Y at i is .greater than that at v.

The kinetic energy (KE) of z at u is less than that at n.

The PE of Y at s is less than the PE of X at c.

The PE of X at c is less than the PE of Z at c.

The PE of X at c is less than the PE of Z at c.

The potential energy (P.E) of X at r is less than P.E at s due to greater displacement at s.

The total energy (T.E) of Y is less than total energy (T.E) of X because X has greater displacement from the planet.

The PE of Y at v is greater than the PE of Z at c due to greater displacement at v.

The speed of Y at i is .greater than that at v because i is closer to the planet than v.

The kinetic energy (KE) of z at u is less than that at n because n is closer to the planet and will have greater velocity.

The PE of Y at s is less than the PE of X at c, because position c has greater displacement.

The TE of Z is greater than the TE of X due to greater displacement of Z from the planet.

The PE of X at c is less than the PE of Z at c due to greater displacement of Z from c.

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Radius of the circular loop is 0.0091m.

Magnetic field is the area around a magnet where the magnetism influence is felt .

B =(μ)I/2r

μ= Magnetic permeability =4(π)*10^(-7)

I= current flowing through the loop

r= radius of the loop

=0.0091m

Thus, we can conclude that the radius of the loop is 0.0091m .

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Answer:

150 J

Explanation:

Moving 3 times higher will increase the   P E  x 3   = 150 J

Answer:

A personal mission statement defines who you are as a person (or as a team member where you work) and identifies your purpose, whether that's in the office or simply in life.

Explanation:

It explains how you aim to pursue that purpose, and why it matters so much to you.

The angular speed such a cylinder must have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth is 0.046 rad/s.

The angular speed such a cylinder must have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth is calculated as follows;

a = v²/r

v² = ar

(ωr)² = ar

ω²r² = ar

ω²r = a

ω² = a/r

ω = √(a/r)

where;

ω = √(g/r)

ω =  √(9.8/4554.4)

ω = 0.046 rad/s

Thus, the angular speed such a cylinder must have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth is 0.046 rad/s.

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Let us assume a man travelled from a point A to a point B over a distance 'd'. After a while he travels the same distance back to point A.

Therefore, since his initial and final positions are the same, displacement is equal to zero, and the distance travelled is (d + d) = 2d, which is not zero.

Example:

Imagine a person walks 10 meters forward and then turns around and walks 10 meters back to the starting point. In this case, the displacement is zero (starting point to ending point), but the distance traveled is 20 meters (10 meters forward + 10 meters backward).

⇒ Acids taste sour, react with metals, react with carbonates, and turn blue litmus paper red. Bases taste bitter, feel slippery, do not react with carbonates and turn red litmus paper blue.

The study of acids and bases is crucial to chemistry. The Lewis acid/base motif, which broadens the concept of an acid and base beyond H+ and OH- ions, is one of the most relevant theories.

Acids are ionic compounds, which means they have a positive or negative charge. In water, these ionic compounds separate to create hydrogen ions, or H+.

The quantity of H+ ions in the solution determines how strong an acid is. Acid is stronger the more H+ there is. Bases are ionic substances that separate in water to produce the negatively charged hydroxide ion (OH-). The quantity of Hydroxide ions in a base determines its strength (OH-). The strength of the base increases with OH- ion concentration.

Hope this helps,

- Eddie.

Answer:

Explanation:

Answer:

See below

Explanation:

vf = vo + at        when it reaches top vf = 0    vo = 10m/s      a = -9.81 m/s^2

0 =   10  + (-9.81) t  

t = 1.02 seconds to reach max

time up = time down   so    roundtrip =  2.04 seconds

When light is incident parallel to the principal axis and then strikes a lens, the light will refract through the focal point on the opposite side of the lens.

To find the answer, we have to know about the rules followed by drawing ray-diagram.

Thus, we can conclude that, when light is incident parallel to the principal axis and then strikes a lens, the light will refract through the focal point on the opposite side of the lens.

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Because the voltage stays the same while the amps grow, parallel batteries last longer. It will still be a 12 volt system if you connect two 12v 50ah batteries in parallel, but because the amps quadruple to 100ah, the batteries will last longer. Charges are spread among the bulbs in a parallel circuit because they are flowing in several directions over multiple paths. As a result, each bulb will have less charge since the charge is travelling in multiple directions, and the lights will shine less brightly. On the other hand, in a series circuit, there is only one channel and only one location for the charge to travel, meaning that all of the charge is directed at a single lightbulb. As a result, the lightbulb will shine more brilliantly since there is no need to spread the energy. The rule of conservation of energy is not broken because of the difference in power; instead, smaller resistance causes bigger current, which results in brighter lights. The energy traveling from the source to the bulbs remains constant. Because higher power means that more energy in a given time goes quicker from the source to the bulb, brighter lights require more power rather than energy. Because the energy traveling from the source to the bulbs remains constant, the rule of conservation of energy is not being broken; rather, there is merely a difference in power as a result of smaller resistance leading to bigger current, which will result in brighter lights. This means that brighter lights require more power rather than energy since higher power enables more energy to go from the source to the bulb more quickly.

Thank you,

Eddie

Answer:

100 368 J

Explanation:

Heat lost by the water = heat gained by the air ( which the 'frige works to expel and keep at 4 degrees)

specific heat for water ( in joules) :  4182 J / kg-C

    3 kg *  4182 J / kg-C  * (12-4 C) = 100 368 J