a toy duck is floating on the water. the average density of the duck is rhod = 620 kg/m3, while the density of water is rho = 1.0 x 103 kg/m3. the volume of the duck is vd = 0.000125 m3.

The angular speed required so that the angular acceleration is equal to the free fall acceleration on earth is 0.047 rad/s².

The centripetal acceleration of a  is given by,

a = w²r

r is the radius,

r = D/2

a = w²D/2

D is the diameter of cylinder.

Also,

The free-fall acceleration has to be equal to the angular acceleration,

g = angular acceleration

a = g

w²D/2 = g

w = √(2g/D)

Putting values,

w = √(2x9.8/D)

D = 5.38 miles.

1 mile = 1609m

5 miles = 8931.4 m

So, we get,

w = √(2x9.8/8931.4)

w = 0.047 rad/s²

So, the angular speed that is required is 0.047 rad/s².

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When we do this, we find that , the acceleration due to gravity at the surface of Mars, is equal to 296 newtons, which is the weight force exerted by the astronaut on Mars's surface, divided by 80 kilograms, which is the astronaut's mass .

what is the weight of a 80-kg astronaut at the surface of mars?

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A thermometer that always reads three degrees off, is reliable but not valid.

Reliability of a measuring instrument refers to the consistency of the measurement. It always give the same reading for the same temperature, however it is not correct as it is reads three degrees off. So we can say it is reliable, we can use it by calibrating it.

On the other hand it is not valid, as it gives the incorrect value of the temperature by reading the three degrees off. It does not give the reading that is suppose to. So it is not valid, or we can say the reading of this thermometer is not valid. Hence the correct option is E.

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In order to calculate the speed of an object, we need to use the formula:

Speed = (2 x Energy) / Mass

So, using the information given in the question:

Speed = (2 x 129000 J) / 100 kg

To find the speed, we need to divide the energy by the mass and then multiply by 2.

Speed = 2580 m/s

So, the 100kg object is rolling down the hill at a speed of 2580 m/s (or approximately 5800 mph)

The student should arrange the motion detectors in a way that allows them to measure the velocity of both carts before and after the collision.

The student could place one detector at the start of the collision and one at the end of the collision. This would allow them to measure the velocity of each cart before and after the collision. The mass of each cart can be measured using the mass balance.

With this information, the student can calculate the momentum of each cart before and after the collision and verify that the total momentum of the system is conserved.

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In accordance with gas laws, when a sample of gas is heated frtom 35 c to 70 c , its volume increases.

Gas Laws are laws that govern how a gas's pressure, volume, and temperature are related. According to Charles' Law (one of the gas laws), at constant temperature, for a fixed amount of gas, its volume is directly proportional to its temperature.

Ideal gas law equation : PV=nRT

According to Charles's gas law, V ∝ T

V1/V2 = T1/T2

According to given question, T1 (in kelvin) = 35+273 = 308K

T2 (in kelvin) = 70+273 = 343K

Hence, V1/V2 = 308/343 = >1

Thus, we can infer that when temperature rises, an ideal gas' volume increases.

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Answer:  Energy is transferred between organisms in food webs from producers to consumers. The energy is used by organisms to carry out complex tasks. The vast majority of energy that exists in food webs originates from the sun and is converted (transformed) into chemical energy by the process of photosynthesis in plants.

Answer: 0.914 km/hour or 914 meters/hour

Explanation:

To calculate Joanne's speed, we need to divide the distance she traveled by the time it took her to travel that distance. In this case, she walked a total distance of 0.4 km south + 0.5 km north + 0.7 km = 1.6 km. To find her speed, we divide the distance traveled by the time it took:

Speed = 1.6 km / 1.75 hours

= 0.914 km/hour or 914 meters/hour

Velocity, on the other hand, is a vector quantity that describes an object's speed and direction. In this case, Joanne walked 0.4 km south and then 0.5 km north and then 0.7km to forever 21 so her direction is not constant. Therefore, her velocity would be zero, because her displacement is zero.

The change in kinetic energy of the particle is determined by the change in potential energy of the particle which is acted on by a force.

What is force?
Force is a physical quantity that is a measurement of an interaction that occurs between two objects or systems. It is a vector quantity, meaning it has magnitude and direction. Force can cause an object to accelerate, decelerate, or remain at a constant speed. Examples of forces include gravitational force, electrostatic force, and electromagnetic force. Force is a key concept in classical mechanics, and is fundamental to understanding how objects interact in the physical world. Force is also used to describe energy, momentum, and torque. Understanding force can help us better understand how the physical world works.

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A special (speci) observation would be made if the ceiling decreased from 1,000 ft to 900 ft agl.

The global standard code for hourly and unique surface weather measurements is SPECI.

A SPECI message is the same as a METAR but is broadcast only when necessary. It is a unique observation message that draws attention to any noteworthy change that has occurred since the last METAR or SPECI was published.

Aeronautical decision making is a systematic approach to the mental process used by aircraft pilots to consistently to determine the best course of action in response to a given set of circumstances.

Inflight briefing should be requested in those cases where an update to a previous briefing needs to be obtained over an aircraft's radio.

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The pressure developed in the system is 180 Kn/m² and force that will be exerted by each output piston is 2.25 KN.

A physical force applied to an object is referred to as pressure. The force applied is perpendicular to the surface of the objects per unit area. F/A is the fundamental formula for pressure (Force per unit area). Pascals are a unit of pressure (Pa). Absolute, atmospheric, differential, and gauge pressures are different types of pressure. Have you ever noticed that when using a straw to drink something, you actually suck the air out of the straw? While taking a drink, you are actually exerting "Pressure."

a) Actual force applied F' = 50 x 9 = 450 N

so,

Pressure

= 450 / (25 x 10⁻⁴)

= 180000 N/m²

= 180 Kn/m²

b) force at each output = 180 x 250 x 10⁻⁴/2 =2.25 KN

Thus, The pressure developed in the system is 180 Kn/m² and force that will be exerted by each output piston is 2.25 KN.

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Hence, the value of Tfinal will be =18.01786 C

The temperature of the final mixture can be calculated using the law of conservation of energy, which states that the total energy of a system remains constant.

The change in energy of the water is equal to the heat absorbed by the water from the silver pellet.

Q = mcΔT

where Q is the heat absorbed,

m is the mass of the water,

c is the specific heat capacity of water,

and ΔT is the change in temperature.

The heat absorbed by the water can be calculated as follows:

Q = mcΔT = 270 g * 4.18 J/g°C * (Tfinal - 18°C) = mcΔT

The heat absorbed by the water can be calculated as follows:

Q = mcΔT = 1.2 g * 0.24 J/g°C * (88°C - Tfinal) = mcΔT

Solving for Tfinal, we get:

Tfinal = 18°C + (Q / mc)

= 18°C + [1.2 g * 0.24 J/g°C * (88°C - Tfinal)] / [270 g * 4.18 J/g°C]

=18 + [1.2*0.24*(88-18)]/[270*4.18]

=18+(20.16/1128.6)

=18+0.01786

=18.01786 C

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The new temperature of gas is 3/2 times of old temperature when a gas at and atmospheric pressure fills a cylinder.

Given the initial volume of cylinder = V1

The initial pressure of gas = P1

The initial temperature of gas = T1

Let the volume of new cylinder = V2

It is given that V2 = 3V1

Let the pressure of new cylinder = P2

It is given that P2 = 1/2P1

Let the new temperature of cylinder = T2

We know that from thermodynamic gas laws that PV = nRT where R is gas constant and n is the number of moles.

Then, P1V1/T1 = P2V2/T2 keeping n constant.

P1V1/T1 = 1/2P1 x 3V1/T2

T2/T1 = 3/2 = 1.5

Then T2 = 3/2T1

Hence the new temperature of gas is 3/2 times of old temperature.

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(1) The orbital speed of the moon is  463.3 m/s.

(2) The mass of the planet is 2.055 x 10²² kg.

The orbital speed of the moon is calculated by applying the following equation as shown below.

v = √ ( GM / r )

where;

v = √ ( 6.67 x 10⁻¹¹ x 2.4 x 10²⁰ / 5.17 x 10⁷ )

v = 17.6 m/s

The orbital speed of the planet is calculated as;

V = 2πr / T

since the planet is similar to earth, period of one complete rotation = 24 hours.

radius of planet = radius of earth = 6,371 km = 6,371,000 m

V = ( 2π x 6371000) / ( 24 x 60 x 60 s )

V = 463.3 m/s

The mass of the planet is calculated as follows;

V = √(GM/r)

V² = ( GM/r )

M = ( V²r ) / ( G )

M = ( 463.3²  x 6371000) / ( 6.67 x 10⁻¹¹ )

M = 2.055 x 10²² kg

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The increase in the strength of the magnetic field will make the magnetic filed lines more closer to each other at the magnetic poles.

The magnetic field lines show how powerful the magnet is. This magnetic field will have a wider region of coverage for a powerful magnet. The magnetic field lines appear to all diverge or converge at the poles, as shown in the illustration above. This indicates that the region where a magnet's external magnetic field is highest.

The magnetic south pole is the point at which all magnetic field lines converge for all magnets, while the magnetic north pole is the point at which all magnetic field lines diverge.

The magnet's north pole is where magnetic lines of force begin, and its south pole is where they terminate. At the poles, magnetic field lines are closest to one another, and the distance at which they are separated from the magnet changes.

Magnetic force lines never cross one another. But they come closer when the field strength is increased.

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The impulse exerted on the ball by the bat is 4.8 Ns. The result is obtained by using the Impulse-Momentum Theorem.

The Impulse-Momentum Theorem states that impulse of an object equals to the change of the momentum. It can be expressed as

I = Δp

I = mΔv

Where

A baseball is thrown with

Find the magnitude of the impulse exerted on the ball by the bat!

The impulse exerted by the bat is

I = mΔv

I = m(v₁ - v₀)

I = 0.15(78 - 46)

I = 0.15(32)

I = 4.8 Ns

Hence, the bat exerts the impulse of 4.8 Ns.

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Enthalpy are given as a)334.99 kJ; b)5.46 moles; c)63.3 kJ/mol;

d)189.9 kJ/mol; e)The reaction that would have an enthalpy change of -2xAH is:

6 C →9 A + 3 B.

a) If you have 5.30 moles of A, the quantity of heat absorbed can be calculated as follows:

AH = 63.3 kJ/mol

moles of A = 5.30 moles

Heat absorbed = moles of A * AH

Heat absorbed = 5.30 moles * 63.3 kJ/mol = 334.99 kJ

b) If the reaction absorbs 345 kJ of heat, the quantity of moles of C produced can be calculated as follows:

Heat absorbed = 345 kJ

AH = 63.3 kJ/mol

Moles of C = Heat absorbed / AH

Moles of C = 345 kJ / 63.3 kJ/mol = 5.46 moles

c) For the reaction 2 C →3 A + B, the enthalpy change can be calculated using the equation:

AH = -AH(reversed reaction)

AH = -63.3 kJ/mol

AH = 63.3 kJ/mol

d) For the reaction 9 A + 3 B →6 C, the enthalpy change can be calculated as follows:

Enthalpy change for the reaction = 9 * AH(3 A + B 2 C) / 3 = 9 * 63.3 kJ/mol / 3 = 189.9 kJ/mol

e) The reaction that would have an enthalpy change of -2xAH is:

6 C →9 A + 3 B

Enthalpy change for the reaction = 9 * 63.3 kJ/mol / 6 = 189.9 kJ/mol * -2 = -379.8 kJ/mol.

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The spatial pulse length is 0.75 mm, if the pulse has 3 cycles each with a wavelength of 0.25 mm.

Spatial pulse length in ultrasound imaging is used to determine for how much time an ultrasound wave exists in space. It is equal to the number of cycle times the wavelength of the pulse. A higher axial resolution is due to the shorter spatial length. Spatial pulse length can be decreased by using the higher frequency transducer or by heavier damping.

Spatial pulse length(SPL) = Number of cycle in each pulse × wavelength

Spatial pulse length(SPL) = 3 × 0.25 = 0.75 mm

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The statement which is not correct regarding geothermal energy is that it can be locally depleted due to heavy use.

Geothermal energy is the energy in the form of heat, which is generated inside the earth. Temperature inside the earth increases at the rate of 25°C/km. When temperature reaches 700-1300°C, the rock becomes magma. This magma comes in the mantle or upper core layer.

Due to the high temperature magma heats up the attached rock and thereby water inside the permeable layers of the Earth. This warm water is utilized to run the turbine and generate electricity. It is a renewable source of energy which cannot be depleted by anyone. So the statement C is not true.

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The magnitude of the force that the charged sphere exerts on the line of charge is zero.

Electric force is the attracting or repulsive interaction between any two charged things. Similar to any force, Newton's laws of motion describe how it affects the target body and how it does so.

The the magnitude of the force  is = kQ₁Q₂/r²

= (9×10⁹) × 2.00 × 10⁻⁶ × 5.80 × 10⁻⁹ × dl/x²

But these forces are equal and in opposite direction,  the magnitude of the force that the charged sphere exerts on the line of charge is zero.

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Answer:

B

Explanation:

F = ma        'a'  in this case is the acceleration of gravity (9.81 m/s^2) PLUS the acceleration of the elevator (2 m/s^2 )

F = 60 kg ( 9.81 + 2 ) m/s^2 = 708.6 N    

The women exerts a force of 294N on the floor of cab which is moving upwards with an acceleration of 2 m/s2.

"the question is asking force exerted by woman on the floor of cab and not the net force"

The force exerted by a woman on the floor of the cab is equal to her weight, which is the force of gravity acting on her mass. According to Newton's second law of motion, this force is equal to the product of her mass and acceleration.

So, the force exerted by the woman is given by:

F = m * a = 60 kg * 2 m/s^2 = 120 N

Therefore, the answer is (d) 294 N.

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The tension needed to properly tune a grand piano string can be calculated using the equation T = (μL2f2)/(4L2), which is 130.31N.

μ is the mass per unit length of the string, L is the length of the string's vibrating section, and f is the string's frequency. Therefore, to calculate the tension, we need to first calculate the mass per unit length, which is equal to the mass of the string divided by the length of the vibrating section.

In this case, the mass per unit length is 400g divided by 1.90m, which equals 210.53 g/m.

Now we can calculate the tension.

Plugging in the values to the equation, the tension is (210.53g/m×1.90m2×275Hz2)/(4×1.90m2)

=130.31N.

Therefore, the tension needed to tune this string properly is 130.31 N.

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The amount of force is referred to as the magnitude of a force. Hence, option B is correct.

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Answer:

Explanation:

It will take 13.33 s for the stuntman's car to reach 200 m. The car will land in 4.48 s and the car will land 178.72 m from the cliff horizontally.

a. To find the time it takes the car to go 200 m, we need to find the final velocity of the car, which can be calculated using the formula vf = vi + at, where vi is the initial velocity, a is the acceleration, and t is the time.

Since the car is slowing down, the acceleration is negative, so we can use the formula:

t = (vf - vi) / a = (0 - 40) / -3 = 13.33 s

b. To find the time it takes the car to land, we need to find the time it takes for the car to fall the 120 m height. This can be found using the formula:

t = √(2d / g), where d is the distance fallen and g is the acceleration due to gravity (9.8 m/s²).

t = √(2 x 120 / 9.8) = 4.48 s

c. To find the horizontal distance the car lands from the cliff, we need to find the horizontal distance the car travels during the time it falls. This can be found using the formula:

d = vi x t = 40 x 4.48 = 178.72 m.

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The average speed of the car on this trip is 76.4 km/h, which is the total distance travelled divided by the total time taken.

The average velocity, on the other hand, is 0 km/h, as the car has travelled in a straight line and has not changed direction. Therefore, the difference between the average speed and the average velocity is 76.4 km/h.

It is important to note that the average speed and velocity are two different measures of the same quantity. The difference between them can be seen in terms of the direction of the car's displacement. While the average speed gives the total distance travelled, the average velocity gives the direction in which the car has been travelling, and its magnitude.

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Answer:

Explanation:

2πr²

When Galileo observed Venus, he saw something that didn't fit with the Ptolemaic model for the Solar System and it was option a. Venus shows phases, instead of always looking nearly full at times.

In October 1610, Galileo made his first telescopic views of Venus. He was eager to find out if Venus has phases like the Moon did. Before the telescope was created, Venus and the other planets appeared to be blazing stars. Galileo was able to determine that Venus circled the Sun, not the Earth, by observing the phases of the planet.

The centuries-old notion that the sun and planets rotated around Earth were disproved by Galileo Galilei's observation that Venus appeared in our sky in phases that were comparable to those of the Earth's Moon. This proved that Venus orbited the sun.

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The ratio of the mass of an electron to its rest mass when it is moving with a kinetic energy of 20 MeV can be calculated using the equation of special relativity and assuming that the speed of the electron is much less than the speed of light. The result is that the mass of the electron is 39.22 times its rest mass.

The ratio of the mass of an electron to its rest mass can be calculated from its kinetic energy using the equation of special relativity, which states that the total energy of an object is equal to its rest mass multiplied by the square of the speed of light, plus its kinetic energy.

The rest mass of an electron is 0.51 MeV, so its total energy is given by:

[tex]E[/tex] = [tex]0.51 MeV*c^{2} + KE[/tex]

Where c is the speed of light, and KE is its kinetic energy.

Since the kinetic energy of the electron is 20 MeV, we have:

[tex]E = (0.51 MeV) * (c²) + 20 MeV[/tex]

And the total energy can be divided by the rest mass of the electron and the square of the speed of light to obtain the ratio of its mass to its rest mass:

 [tex]m/m0[/tex] = [tex]\frac{E}{0.51 MeV * c^{2} }[/tex]

[tex]m/m0[/tex] = [tex]\frac{0.51 MeV*c^{2} + 20 MeV}{0.51 MeV }[/tex]

We can simplify the calculation by assuming that the speed of the electron is much less than the speed of light, so that we can ignore the term (0.51 MeV * c^2).

In that case, we have:

[tex]m/m0[/tex] = [tex]\frac{20MeV}{0.51MeV}[/tex]

[tex]m/m0 = 39.22[/tex]

So the ratio of the mass of an electron to its rest mass when it is moving with a kinetic energy of 20 MeV is 39.22.

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