In the Soapbox Derby in, young participants build non-motorized cars with very low-friction wheels. Cars race by rolling down a hill. Assume that the track begins with a 51-ft-long (1 m= 3.28 ft) section tilted 14 ∘ below horizontal.



What is the maximum possible acceleration of a car moving down this stretch of track?

If a car starts from rest and undergoes this acceleration for the full l, what is its final speed in m/s ?

Answer:

Object 1 has more surface area than Object 2.

Explanation:

Even if both objects are falling at the same rate due to gravity, air will usually always mess with the 'speed' of an object (I hope that makes sense, I'm not the best at explaining things but Object 1 has more surface area than Object 2 IS correct).

Because of this, regardless of their mass, all objects descend in free fall at the same speed.

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The net charge on the pith ball in coulombs when the number of electrons is specified is calculated to be 2.96 × 10⁻² C.

Given that, number of electrons = 1.85 × 10¹⁷

We know the charge on electron as, e = 1.6 × 10⁻¹⁹ C

The relation between charge and number of electrons is known to be,

Q = n e

where, Q is charge

n is number of electrons

e is charge on electron

After putting the values into the equation above, we have,

Q = 1.85 × 10¹⁷ × 1.6 × 10⁻¹⁹ = 2.96 × 10⁻² C

Thus, the net charge is calculated to be 2.96 × 10⁻² C.

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The output power of the hearing aid is approximately 1.6 micro-watts.

What is the sound level supplied to the ear canal by the hearing aid?

The sound stage furnished to the ear canal by using the hearing resource is ninety dB. This is precise within the trouble assertion, in which it's miles said that the female calls for an amplification of 30 dB to pay attention the tv set at a regular extent of 60 dB. Consequently, the hearing resource materials sound at ninety dB to the ear canal. The sound degree is measured in decibels (dB) and is used to specific the relative loudness of a sound. The higher the decibel degree, the louder the sound is.

A sound stage of 90 dB is considered loud and can reason harm to the ears if uncovered to it for an extended time frame.

Lets find the intensity as follows,:

β = 10log( I / Io) where Io = 10^-12 W/m^2

90dB = 10log( I / 10^-12 W/m^2)

9 = log ( I / 10^-12)

10^9 = I / 10^-12

I = .001 W/m^2

Put this  into the equation of I = P/a

The diameter is .0076m so the radius us .0038m

a = pi(.0038^2) = 4.534x10^-5 m^2

Then we multiply that by the intensity above

(.001 W/m^2)(4.534x10^-5 m^2) = 4.534x10^-8 W

output power of the hearing aid = 4.534x10^-8 W

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The b-k colour of a galaxy is a measure of the difference in brightness between the galaxy at blue (b) wavelengths and infrared (k) wavelengths. If the luminosity of the galaxy at blue wavelengths rises by a factor of 100, without any change in the luminosity at k wavelengths, the new b-k colour will be different.

We can use the following equation to calculate the new b-k colour:

b-k = -2.5 * log(Lb/Lk)

Where Lb and Lk are the luminosity of the galaxy at blue and infrared wavelengths, respectively.

Given that the luminosity at blue wavelengths has increased by a factor of 100 and the luminosity at k wavelengths has remained unchanged, the new b-k colour can be calculated as:

b-k = -2.5 * log(100*Lb/Lk) = -2.5 * log(100) + b-k = -2.5 * 2 + 3.2 = -0.8 + 3.2 = 2.4

Therefore, the new b-k colour of the galaxy is 2.4 magnitudes.

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The time taken by the electron  is [tex]3.33*10^{-8} seconds[/tex] .

Complete question:

An electron traveling at  [tex]3*10^{6} m/s[/tex] enters a 0.1 m region with a uniform electric field. Find the time it takes the electron to travel through the region of the electric field, assuming it does not hit the side walls.

(See the figure attached)

Since, no field and hence no force act on the electron along X-direction.

Hence, [tex]v_{x}[/tex] remains constant.

Now time taken = t = l/[tex]v_{x}[/tex]

Where,

l = length of field = 0.1 m

v = speed of electron = [tex]3*10^{6} m/s[/tex]

Putting this value in above equation, we get t = [tex]3.33*10^{-8} seconds[/tex] .

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When a panther appears and attempts to eat the monkey, the monkey performs 3740 J of work to increase its speed.

Work in physics is the energy transferred to or from an object by applying force along a displacement. In its most basic form, work equals the product of force strength and distance traveled for a constant force aligned with the direction of motion. Work is the transfer of energy caused by a force acting on an object as it moves. The work done by a force on an object is calculated as the product of the magnitude of the force multiplied by the magnitude of the displacement multiplied by the cosine of the angle between them.

Here,

W=1/2mv1²-1/2mv2²

=1/2*40(14²-3²)

=3740 J

The monkey does 3740 J of work of increase its speed when a panther appears and tries to eat the monkey.

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Using the fine focus when trying to put a specimen in sharp focus when using the 40x objective lens ensures that the specimen is brought into focus as accurately and precisely as possible.

This knob is used to adjust the specimen's focus. Additionally, it is used to highlight specific areas of the specimen. The coarse focus knob should often be used to get near before switching to the fine focus knob for fine tweaking.

The fine focus allows for a much finer adjustment of the specimen's position to be made, which is necessary when using a higher magnification objective lens like the 40x.

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The total number of charges moved to power up the light for 20 min is 3.75 x 10¹⁹

The voltage of the battery = 1.50 V
The power supplied by the battery = 0.45 W

The flashlight will glow for 20 min

The total number of charges moved during the flashing of the flashlight can be found using the formula,

              I = P/V
where I is the current

          P is the power

          V is the voltage supplied

We also know that,

            I = Q/t

Let us substitute this equation, with the above equation, and we get

           Q = Pt/V

Now, let us substitute the known values in the above equation, we get

           Q = 0.45 x 20 / 1.50

              = 9 / 1.50

              = 6 C

Then, the number of charges is

            n = Q/e

where e is the charge of an electron

            n = 6 / 1.6 x 10⁻¹⁹

               = 3.75 x 10¹⁹

Therefore, the number of charges moved is 3.75 x 10¹⁹

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The maximum height of the water after coming out of the nozzle is affected is by the initial speed and the value of the

The water level of the tank on the building is 20m. The hose leads from the tank bottom to the ground and leads to the nozzle that is point to the top.

Here, we know, the energy will also be conserved because the there is o external force, so the kinetic energy at the top will be equal to the potential energy at the bottom in the ideal case.

Now, we can write,

1/2mv² = mgh

v = √(2gh)

g is the acceleration due to gravity and the h is the height of the tank.

Putting values,

v = √(2 x 10 x 20)

v = 20 m/s

Now, we can use the equation of motion,

v = √(2hg)

h = v²/2g

v is the speed of the water from the nozzle.

h = 10m.

This is because we have considered the ideal case where there is no energy loss, so water will go till a height of 10m when it comes out of the nozzle. The height rise is affected by the initial speed.

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The magnitude of the acceleration due to gravity near the surface of Mars is[tex]2*d / 4.41s^2[/tex].

To calculate the acceleration due to gravity near the surface of Mars, we can use the equation:

d = 1/2 * a * t^2

Where d is the distance fallen, a is the acceleration due to gravity, and t is the time taken to fall.

We know that on Earth, the marker took 1.3s to fall to the ground and on Mars it took 2.1s. We also know that the distance fallen is the same on both planets, since the marker was dropped from the same height. Therefore, we can set the distance fallen equal on both planets and use the equations above to solve for the acceleration due to gravity on Mars:

d = 1/2 * a_Earth * (1.3s)^2 = 1/2 * a_Mars * (2.1s)^2

a_Mars = 2d / (2.1s)^2

a_Mars = 2d / (4.41s^2)

Where d is the distance fallen and a_Earth = 9.8 m/s^2 is acceleration due to gravity on Earth.

Therefore, the magnitude of the acceleration due to gravity near the surface of Mars is [tex]2*d / 4.41s^2[/tex]

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Mike would rapidly forget most of the material that he read. Dr. Ummel conducts a memory experiment where he shows a fight between two men and describes the contact as "punching" to one group and "tapping" to the other group.

What is meant by memory ?

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In warm air, sound travels more quickly than in cold air. Since the speed of sound is directly inversely proportional to the square root of the air's absolute temperature, the speed of sound rises with temperature.

Additionally, dry air travels faster than humid air for sound. The speed of sound is slightly affected by humidity, with sound traveling slightly slower in more humid air. This is due to the fact that airborne water vapor has the ability to slow down sound waves by absorbing some of their energy.

The amount of water vapor in the air is measured by humidity. At a given temperature, it is typically expressed as a percentage of the maximum amount of water vapor that the air can hold.

It is said that the air has a humidity of 100 percent when it is saturated. Any additional water vapor will condense into liquid or solid form (such as dew, fog, clouds, or precipitation) because the air cannot hold any more water vapor at this point. The air can hold more water vapor and is less likely to reach 100% humidity as the temperature rises.

Specific humidity or mixing ratio, which is the ratio of the mass of water vapor in the air to the mass of the air as a whole, is another way to measure humidity.

The weather and climate can be significantly affected by humidity. High humidity can cause clouds to form and precipitation to fall. It can also make the air feel hotter. Low humidity can make the air feel cooler, make it dry, and make wildfires more likely. The human body is also affected by humidity; low humidity can dry out the skin and nasal passages, while high humidity can make it difficult to cool down and can exacerbate respiratory issues.

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Answer: (D.) It does not include object with different masses

Explanation:

It does not include objects with different masses. Therefore, option D is correct.

The force that pulls items toward the center of a planet or other entity is called gravity. All of the planets are kept in orbit around the sun by gravity. A universal, non-contact force, gravity. The gravitational pull of the Earth keeps everything on its surface.

All objects with mass, including our Earth, really bend and curve spacetime, which is what causes gravity to pull you toward the ground. What you experience as gravity is that curvature. If things of different masses are dropped from the same height, they will still impact the ground at the same time because Earth provides everything with the exact same acceleration.

One thing that is wrong about Marcus' experiment is that it does not include objects with different masses. Therefore, option D is correct.

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The equator is characterized by relatively  low atmospheric pressure aloft.

The equator is a large circle that surrounds Earth and sits on a plane perpendicular to its axis, everywhere being equally far from the geographic poles.

This geographic, or terrestrial, Equator separates Earth's Northern and Southern hemispheres and serves as the fictitious reference line on the planet's surface from which latitude is calculated; in other words, it is the line at latitude 0°.

In hotter equatorial regions, the air above expands, gets less dense, and rises. At this latitude, this causes a low pressure band to form.

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The "Load Capacity" of a jack refers to the greatest weight it can support. Maximum weight of cargo that has been authorised by the country where the vehicle was registered.

We can determine the necessary minimum capacity for a trailer jack by analysing the concentration of loads in a typical trailer.

Thus, the "Load Capacity" of a jack refers to the greatest weight it can support.

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The bullet goes up to the height of 1074.6 m, and its initial velocity was 145.2 m/s,  If the bullet takes 14.8 sec to reach its peak.

Time taken by the bullet to reach its peak, t = 14.8 sec

Velocity after 14.8 sec, v = 0

Let the initial velocity, = u

Acceleration working on the bullet, a = -g = -9.81 m/s²

By the first equation of motion,

v = u + at

0 = u - 9.81 × 14.8

u = 145.2 m/s

Let the highest peak reach by the bullet is h meter, then by using the second equation of motion,

h = ut + 0.5at²

h = (145.2 × 14.8) + 0.5(-9.81)(14.8)²

h = 1074.6 m

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The time spent in the air by the rock is 4.2 seconds.

The range of the of the rock's motion is 88.2 m.

The time spent in the air by the rock is its time of motion and it is calculated as follows;

t = √ ( 2h / g )

where;

t = √ ( 2 x 85 / 9.8 )

t = 4.2 seconds

The range of the of the rock's motion is calculated as follows;

x = vt

x = 21 m/s  x 4.2 s

x = 88.2 m

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The energy of the first sound is 6.81 times bigger than the energy of the second sound, or 6.81 times stronger than the intensity of another sound.

Its intensity is the term used to describe how loud a sound is to an individual. Loudness cannot be quantified objectively since everyone perceives loudness differently. Following is a description of the relative characteristics of the acoustic signal, audio intensity, and sound intensity. The kinetic energy of the mass of air is created by the combination of the source's increasing amplitude and the vibrating surface.

The formula for sound intensity is acoustic power divided by the normal area to the propagation direction.

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The gas can be heated at constant pressure if a piston moves outward to let the gas expand as it's heated. Alternatively, the gas can be heated at constant .

Define constant pressure?

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By disassembling the circuit and connecting a "ammeter" in series (or in-line) with it, all of the electrons that are flowing through the circuit must also pass through the meter in order to measure current in the circuit.

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The charge on the inner surface of the sphere is +2nC because the charge on the interior cavity is 2.0nC.

A law that connects the distribution of electric charge to the resulting electric field is known as Gauss's law, commonly referred to as Gauss' flux theorem.

In its integral form, it asserts that the flux of the electric field out of any closed surface, regardless of how that charge is distributed, is proportional to the electric charge enclosed by the surface. In situations where symmetry requires uniformity of the field, it may be possible to determine the electric field throughout a surface encompassing any charge distribution despite the fact that the law alone is insufficient to do so.

When there is no such symmetry, Gauss's law, which states that the electric field divergence is proportional to the local density of charge, can be applied in its differential version.

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Desalination removes potentially harmful minerals and chemicals in addition to the salt that is present in your water.

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The kinetic energy of this vehicle is 605.835 KJ when its mass is 1687 kg and traveling at speed of 96.6 km/h.

Given,

mass of the car, m = 1687 kg

speed, v = 96.6 km/h

we know that, Kinetic energy

KE = 1/2 mv²

But we need KE in Joule or KJ

so first we convert km/h to m/s

v = 96.6 km/h = 96.6 x (1000/3600) m/s

v = 26.8 m/s

Now,

KE = 1/2 x 1687 x (26.8)²

or KE = 605835.44 Joule = 605835.44 x 10⁻³ Kilojoule

or KE = 605.835 KJ

Therefore, the kinetic energy of this vehicle is 605.835 KJ when its mass is 1687 kg and traveling at speed of 96.6 km/h.

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No, we are unable to estimate the austonian's height using this information.

Its Austonian height makes it the second-tallest structure in Texas, behind The Independent, and the second-tallest all-residential structure in North America, west of the Mississippi River.

The second-tallest structure in Austin is the Austinian, which has a connection to an external site. According to a tale, if you drop a rock from the top of a building on a chilly January morning, you will hear the sound of its hit seconds later.

The 58-story Independent, which is 690 feet (210 m) tall and has 58 stories, is the tallest finished structure in the American city of Austin, Texas. After Houston and Dallas, it is the tallest skyscraper in Texas and the tallest all-residential tower west of the Mississippi River. It was completed in 2019.

height of austonian = 16[tex]t^{2}[/tex].

t = [tex]\sqrt{H}[/tex]/4.

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The work required for the dog to come to a complete stop is -900 J (work = force x distance = (30 kg x 9.8 m/s^2) x (1 m))

The distance over which the force is applied, in this case, would be the distance the dog travels as it slows down to a stop. This distance would depend on the initial velocity of the dog, the force applied to slow it down, and the amount of time it takes for the dog to come to a stop. In this case, the initial velocity is 1 m/s and the force applied is the opposite of the dog's weight, or -30 kg x 9.8 m/s^2. However, without information on the amount of time it takes for the dog to come to a stop or the deceleration of the dog, it is not possible to determine the exact distance over which the force is applied.

It is important to note that the distance over which force is applied is a scalar value and is independent of the direction of motion.

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In a downward direction, the magnitude of the acceleration is negative and velocity is zero.

Here,

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The compression in the spring will be 4.9m

What is spring force?

The force needed to compress or extend a spring attached to an object is known as the spring force. A spring exerts an equal and opposite force on a body when the object exerts a force on it. It always acts to bring mass back to its equilibrium. Spring force exerted by the spring on the body is given by = where k is the spring constant of the spring x is the compression or extension caused in the spring. To find the x we can use this formula.

Now, according to the question we have

Spring constant=2000N/m

Mass attached to the spring=1000Kg

On substituting the values in the above formula, we get the compression as

F=kx

mg=kx

1000×9.8=2000×x

x=4.9m

Therefore, the compression in the spring is 4.9m

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The average density of the Earth in g/cm3 is 5.51 g/cm3 and the density at the stage when the sun will end up as a white dwarf in diameter is  [tex]1.1X10^{6} g/cm^{3}[/tex].

For solving the part (a) of the question, we know that,

Mass of the Earth: 5.97x [tex]10^{24} \\[/tex] kg.

Radius of the Earth: 6.37 x [tex]10^{6}[/tex] m.

The formula of the density is :

Density = Mass/ Volume.

Here, Volume is  4/3 [tex]\pi[/tex][tex]r^{3}[/tex].

Substituting all the values written above in the density equation,

Density is  5.51 g/cm3 .

For solving the part (a) of the question, we know that,

Mass of the Sun: 1.99x [tex]10^{30} \\[/tex] kg.

Radius : 7500 km

The formula of the density is :

Density = Mass/ Volume.

Here, Volume is  4/3 [tex]\pi[/tex][tex]r^{3}[/tex].

Substituting all the values written above in the density equation,

Density is 1.1X10^{6}  g/cm^{3}.

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He travels a distance of 300 m in that time interval.

We know that we can be able to obtain the time that he travelled if we use the formula that applies to the average speed. In this case we are told in  a time of 30 seconds, he increases his speed steadily from 8.3 m/s to 11.7 m/s.

Thus;

distance = Average speed/Time

Distance = (8.3 + 11.7/2) * 30

Distance = 300 m

We can see that he would move through a distance of well about 300m as the velocity is increasing as shown here.

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The radius of a planet is 7.01 times of earth's. The volume of the planet is 344.47 times bigger than the volume of earth.

Let's assume that the shape of both planets are perfect spheres. The volume of a sphere is given by:

V = 4/3 πr³

Where r is the radius.

Hence, the volume is directly proportional to r³, or:

V ∝ r³

Let:

r_p = radius of the planet

r_e = radius of earth

Then,

r_p = 7.01 r_e

Using direct proportionality:

V_p : V_e = r³_p :  r³_e

V_p : V_e = (7.01 r_e)³ :  r³_e

V_p : V_e = 344.47 : 1

V_p = 344.47 V_e

Therefore, the volume of the planet is 344.47 times bigger than earth's.

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