Collisions in Saturn’s Rings : Each of the particles in the densest part of Saturn’s rings collides with another particle about every 5 hours. If a ring particle survived for the age of the solar system, how many collisions would it undergo ?

Answers

Answer 1

The ring particle would undergo roughly 8.3 trillion collisions over that period of time.

The age of the solar system is estimated to be 4.6 billion years. This means that a ring particle would undergo roughly 8.3 trillion collisions over that period of time. To calculate this number, we can use the following formula:

Number of collisions = Time (in hours) / Time between collisions (in hours) x Number of years

Number of collisions = 4.6 x 109 (years) x 24 (hours/day) x 365.25 (days/year) / 5 (hours)

Number of collisions = [tex]8.3 * 10^{12}[/tex] (collisions)

Therefore, the number of collisions in the ring are

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Related Questions

base your answers to the fololwing questions on the informetaion and disgram below. a golf ball leavea a golf club with n nitial velocity of 40.0 mtersp er second at an angle of 40 degrees. with the horrziontal what is the vertical component of the g9lf balls initial velocity

Answers

The ball's parabolic motion causes it to move at a speed of 26.3 m/s right before it strikes the ground, which is faster than its straight-downfall velocity of 17.1 m/s.

How do you determine a golf ball's flight?

The vertical velocity of the ball traveling up the club head face is calculated using the equation 5/7 f v sin 0 where f is the fraction of speed left after the ball is compressed, 0 is the angle of the clubface at impact, and v is the velocity of the club head.

How will the ball's speed change as it descends to the ground?

The ball descends faster and faster. In other words, the ball is moving faster the entire time it is in the air, both during its ascent and at the moment it reaches its peak, as well as throughout its descent. Gravity is what causes the ball to accelerate.

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what is the angular velocity of this microwave in radians per second?

Answers

Angular velocity of the microwave in radians per second = 0.6492 rad/s

What is angular velocity ?

The rate at which something rotates or revolves around an axis is known as its angular velocity. The Greek letter omega (ω) stands for angular velocity. Because it is expressed as an angle per unit of time, angular velocity in the SI is measured in radians per second.

According to the given information

We need to find the Angular velocity of the microwave in radians per second

For that ,Firstly we will find the frequency

Microwave rotate at the rate of = 6.2 rev/min

                                                    = 6.2/60 rev/s

                                                    = 0.10333 rev/s

Now , we know that

Angular velocity = 2[tex]\pi[/tex]f

                      ω  = 2×3.14×0.10333

                      ω = 0.6492 rad/s

Angular velocity of the microwave in radians per second = 0.6492 rad/s

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Pls I need help, Select all of the essential conditioning skills for a skier. (Check all that apply)

flexibility

strength

walking

balance

Answers

Answer:

Explanation:

I think its all of the above

have a good day :)

A 0.5âkg block B slides without friction inside a slot cut in arm OA that rotates in a vertical plane. The rod has a constant angular acceleration Ëθ=10rad/s2. Knowing that when θ=45â and r=0.8m the velocity of the block is zero, determine at this instant, (a) the force exerted on the block by the arm, (b) the relative acceleration of the block with respect to the arm.

Answers

a) Force exerted on the block by the arm is  4N.

b)  The relative acceleration of the block with respect to the arm is  10rad/s2.

(a) The force exerted on the block B by the arm OA is given by:

F = m × a = 0.5 kg × (10 rad/s2) × 0.8 m = 4 N

The force exerted on the block by the arm is equal to the product of the mass of the block and the relative acceleration of the block with respect to the arm. Since the velocity of the block is zero at the given instant, the relative acceleration of the block with respect to the arm is equal to the angular acceleration of the arm, i.e., 10rad/s2. Hence, the force exerted on the block by the arm is  

                               0.5kg×10rad/s2 =5N.

(b) The relative acceleration of the block with respect to the arm is given by:

a_rel = a + θ2 × r = 10 rad/s2 + (45 rad/s2)2 × 0.8 m = 15.6 m/s2

The relative acceleration of the block with respect to the arm is equal to the angular acceleration of the arm, i.e., 10rad/s2.

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true or false: the quantities di and do are measured from the lens (or mirror).

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The quantities di and do are measured from the lens (or mirror): False.

True statement: The quantities of di and do are not measured from the lens (or mirror).

What is lens?

A lens is a piece of transparent material that is typically round in form with two polished surfaces that are either convex (bulging) or concave on one or both sides (depressed). In other words, the radius of curvature is constant since the curves are virtually always spherical.

Lenses are a common component of telescopes, binoculars, and cameras, among other image equipment. Additionally, they are utilized as visual aids in spectacles to treat vision problems including myopia and hypermetropia.

The statement is false.

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When the velocity of a moving body decreae by equal amount in equal time,the body i aid to have??

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If the velocity of moving body decreases by equal amounts in equal interval of time, it is said to have negative acceleration.

What is velocity?

The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity. The standard unit of velocity magnitude is the meter per second (m/s).

What is acceleration?

Acceleration is the rate at which an object's velocity with respect to time changes. Negative acceleration is the acceleration that results when a moving object's velocity decreases. When a body's velocity is decreasing, it typically experiences negative acceleration. Given that the velocity is rising in that direction, its direction is the inverse of the body's motion.

If the velocity of moving body decreases by equal amounts in equal interval of time, it is said to have negative acceleration.

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Matter can undergo chemical reactions and nuclear reactions. Which
statement is true for both types of reactions?
O A. Atoms are rearranged.
B. New types of compounds are formed.
C. The products are different from the reactants.
OD. New types of atoms are formed.
SU

Answers

The statement that is true if matter undergoes both chemical and nuclear reaction is that atoms are rearranged (option A).

What is a chemical reaction?

A chemical reaction is a process, typically involving the breaking or making of interatomic bonds, in which one or more atoms or substances are changed into others.

Also, a nuclear reaction is a process such as the fission of an atomic nucleus, or the fusion of one or more atomic nuclei and/or subatomic particles in which the number of protons and/or neutrons in a nucleus changes.

In a nuclear reaction, the products may contain a different element or a different isotope of the same element.

This suggests that are atoms are rearranged in both chemical and nuclear reactions.

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the cosmic microwave background radiation was produced when the temperature of the universe was around 3,000 k. by what factor has the universe expanded between then and now?

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When the universe's temperature fell below 3000 K and a plasma of protons and electrons came together in the early cosmos, the CMBR was created.

Why do we see a 3k cosmic microwave background?

The blackbody radiation is seen as a remnant of the transparency point at  the expanding universe dropped below about 3000K so that radiation could escape.

What happened after the cosmic microwave background?

Matter then became neutral, and allowed the light to travel freely: the Universe became transparent. The relic of that 'first light' is the CMB. Since the time when that radiation was released, the Universe has expanded, becoming at the same time cooler and cooler.

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why are electrical insulators important? they help the flow of electricity they provide power for electric circuits they are used to protect us from electricity they help conduct heat they are not important

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Electrical insulators are important because they are used to protect us from electricity.

Why are we use Electrical insulator?As they don't carry electricity, insulators are used in circuits to insulate wire, switches, plugs, and other electrical components. So that circuit may be made safe to touch and shock-free.An insulator prevents electricity from moving. Insulators are crucial for protecting humans from electricity. A rubber-like insulator covers the wire carrying electricity to your computer or television to prevent you from being electrocuted. Glass, the air, and paper are all effective insulators.Electrical equipment uses insulators to hold and separate electrical conductors without allowing current to flow through them. Insulation is an insulating substance that is wrapped in large quantities over electrical lines or other equipment.

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Find the electrical energy consumed by an electric geyser of power rating 2000 watt when it is used for 1 h

Answers

The electrical energy consumed is 2KWh

How do we calculate electrical energy consumption?

Electrical energy or electricity consumption represents the amount of electrical energy that has been consumed over a specific time, in units of Wh (or kWh), electricity demand represents that rate at which electrical energy is consumed for a needed output rating, in units of W (or kW).

Energy is given as :

Energy = power ×time

power = 2000w = 2kw

time = 1hr

therefore electrical energy consumed over 1hr

= 2kw× 1hr

= 2kwhr

therefore the electrical energy consumed is 2KWh

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a boxer rides with a punch so as to reduce__

which one?

force; speed; impulse; or momentum

Answers

A boxer rides with a punch so as to reduce force.

Force is an external influence that can change the velocity or motion of an object.

It can also be defined as the product of mass and acceleration.Mathematically, force F = m*a

Force is also the amount of impact the object suffers due to another body's action.

Speed is the rate of change of distance w.r.t time, which cannot affects the boxer in any format

Impulse is force times the time interval which does not defines the impact.

Momentum is the product of mass and velocity which does not satisfies the boxer's condition while punching.

Therefore only force is the suitable answer, i.e. a boxer rides with a punch so as to reduce force.

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in 1923, the united states army (there was no united states air force at that time) set a record for in-flight refueling of airplanes. using two refueling planes, an airco dh-4b biplane was able to remain in flight for 38 h . during the flight, the refueling planes were able to air-transfer a total of 687 gallons of fuel to the plane in 9 refueling transfers. assume that the refueling nozzle had a diameter of 1.35 in and each refueling took 2.51 min to perform. calculate the velocity of the fuel through the nozzle. assume that the fuel filled the entire cross-sectional area of the nozzle.

Answers

The velocity of the fuel through the nozzle. assume that the fuel filled the entire cross-sectional area of the nozzle. 6.45ft/sq

Velocity is a vector expression of the displacement that an item or particle undergoes with appreciate to time . the usual unit of pace importance (additionally referred to as speed ) is the meter according to 2nd (m/s).

calculation:-

Volume of the fuel pump is V = Avt

V = 687 gallons = 2.6 m³

t = (2.31) 60 × 9

= 1247.4 sec

A = πr²

= 3.141 × (0.0368/2)²

= 0.00106 m³

V = Avt

2.6 m³ = 0.00106 m³ v × 1247.4

V = 1.966 m/s

V = 6.45 ft/sec

Nozzles are used within the rocket and plane engineering to provide jet propulsion, in intensive shattering and spraying technology, in jet gadgets and ejectors and in fuel dynamic lasers and gasoline mills (see gasoline turbine).

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A bow wave is produced when a speed boat moves fast as the waves it produces_ faster than the waves it produces. nearly as fast as the waves it produces none of the above

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A Bow wave is produced when a speed boat moves faster than the waves it produces.

A Bow wave is a progressive disturbance that propagates through a fluid, such as water or air, as a result of a displacement of the anterior point of an object passing through the fluid that is greater than the speed of the wave travelling across the fluid, produced by the same object. If the speed of the object is slower than the waves it produces, then no Bow waves will be generated. In the above scenario, when the speed boat moves faster than the waves it generates, it produces the Bow wave in the water.

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Using the CER format (claims, evidence and reasoning), answer the following question: Three resistors are connected in series: (14 Ohms, 2.5 Ohms and 22 Ohms). If all these resistors were light bulbs, which would be the brightest? (CLEARLY IDENTIFY YOUR CLAIM, EVIDENCE AND REASONING.)

Answers

According to Ohm's law  the the bulb which experience the greater resistance will be brightest in the series.

What is Ohm's law?

Ohm's law states that the voltage across a circuit is the product of the current and resistance through it.

Thus, V = IR.

As per this relation, the current and resistance through a circuit are in inverse relation whereas voltage with current and resistance are in direct proportionality.

As the resistance increases, the voltage drop increases, making the more light electrical energy is converted to light energy in bulbs make it brighter. Therefore, the bulb with higher resistance i. e 22 ohms would be the brightest.

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ASAP HELP 80 POINTS !!!!!!!! Answer the questions in this lab, fill in data tables, and provide the two scatter plot graphs requested and submit.

Determine the reaction time for an individual in multiple trials using kinematics.
Calculate an experimental value for the acceleration due to gravity.

Record the distance the ruler falls. Then use the distance to determine the reaction time.

Trial one. [The ruler is caught at 48 centimeters]

Trial two. [The ruler is caught at 41 centimeters]

Trial three. [The ruler is caught at 29 centimeters]

Trial four. [Trial four] [The ruler is caught at 41 centimeters]

Trial five. [Trial five] [The ruler is caught at 40 centimeters]

Trial six. [Trial six] [The ruler is caught at 42 centimeters]

Answers

To determine the reaction time for an individual using kinematics, we need to first collect data on the distance that the ruler falls and the time it takes for the individual to catch it. We can then use this data to calculate the reaction time for each trial.

Here is a data table that includes the distance the ruler falls and the corresponding reaction time for each trial:

Trial Distance (cm) Reaction Time (s)

1 48 0.80

2 41 0.68

3 29 0.48

4 41 0.68

5 40 0.67

6 42 0.70

To calculate the reaction time for each trial, we need to use the formula:

Reaction Time = √(2 * Distance / Acceleration Due to Gravity)

We can use this formula to calculate the experimental value for the acceleration due to gravity. We can then use this value to calculate the reaction time for each trial.

To calculate the experimental value for the acceleration due to gravity, we can use the following formula:

Acceleration Due to Gravity = (Distance / Reaction Time^2) / 2

Using this formula, we can calculate the experimental value for the acceleration due to gravity as follows:

Acceleration Due to Gravity = (48 / 0.80^2) / 2 = 9.60 m/s^2

Using this value for the acceleration due to gravity, we can then calculate the reaction time for each trial as follows:

Trial Distance (cm) Reaction Time (s)

1 48 0.80

2 41 0.68

3 29 0.48

4 41 0.68

5 40 0.67

6 42

what is true of spiral galaxies? what is true of spiral galaxies? they evolve from giant ellipticals. they have never been seen to have large redshifts. they are only found in the center of rich galaxy clusters. they are much less common at larger redshifts. they are relatively rare in regions of high galaxy density.

Answers

The true statement about spiral galaxies is, that they are relatively rare in regions of high galaxy density.

What are Spiral galaxies?

The twisted clusters of stars and gas known as spiral galaxies, which are frequently formed of hot, young stars, have striking shapes. As opposed to the other two major groups of galaxy forms, elliptical and irregular, spiral galaxies make up the majority of the galaxies that astronomers have so far discovered.

What is Density?

The density of a substance reveals how dense it is in a given region. Mass per unit volume is the definition of a substance's density. In essence, density is a measurement of how closely together matter is packed. It is a special physical trait of a specific thing. Greek scientist Archimedes made the discovery of the density principle. If you are familiar with the formula and the corresponding units, calculating density is simple. Density can be symbolized by the letter D or by the symbol.

Hence, the true statement about spiral galaxies is, that they are relatively rare in regions of high galaxy density.

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what is the force on a 1000 kg elevator that is falling freely at 9.8 m/sec/sec?

Answers

Answer:

9.8 m/ssr=2322

Explanation:

find the transfer function g(s)=vo(s)/vi(s)

Answers

Transfer function g(s)=vo(s)/vi(s) is G(s) = s/2s +1

In frequency domain Inductor L transforms to sL and Capacitor C transforms to 1/sC using this ,the output voltage in frequency i.e s domain using voltage division rule is

Vo (s) = Vi(s) * sL ║1 / 1 + sL║1 = Vi (s) * s║1 / 1+ s║1

assume L = 1H

Vo (s) = Vi (s) * s*1/s+1 / 1+ s*1/s+1

G(s) = Vo (s) /Vi (s) = s / s + 1+ s = s/2s + 1

G(s) = s/2s + 1

A mathematical function known as a system function or network function of a system, sub-system, or component theoretically simulates the output of the system for each potential input. Electronics and control systems use them extensively. This function, which is sometimes called a transfer curve or characteristic curve, is a two-dimensional graph of an independent scalar input vs a dependent scalar output. In electronics and control theory, transfer functions for components are used to build and analyze systems that are constructed from components, particularly when utilizing the block diagram technique.

The transfer function's parameters and units simulate the output response of the device for a variety of potential inputs.

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on planet x, an object weighs 19.8 n. on planet b where the magnitude of the free-fall acceleration is 2.46 g (where g = 9.8 m/s2 is the gravitational acceleration on earth), the object weighs 39.6 n. a) what is the mass of the object on planet x? answer in units of kg

Answers

Weight of the object on planet X is 19.8 N, then the mass of the object on planet x  is calculated to be 2.02 kg.

What is gravitational acceleration?

In physics, gravitational acceleration is the acceleration of an object in ab free fall within a vacuum, without experiencing drag.

When objects fall on the ground, gravity causes them to accelerate. Acceleration is the change in velocity, and velocity is a measure of the speed and direction of motion. Gravity causes an object to fall to the ground much fast and faster is velocity, longer the object takes to fall.

On planet X;

Given, W= 19.8 N ; a= 9.8 m/s^2

W = m a

m= W/a= 19.8/9.8

Mass of the object on planet x = 2.02 kg

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a 100 mh inductor whose windings have a resistance of 4.0 ω is connected across a 15 v battery having an internal resistance of 2.0 ω

Answers

The amount of Energy stored in the inductor is calculated as;  0.3125 J

What is the energy stored in the inductor?

We are given;

Inductance; L = 100 mH

Resistance; R = 4.0 Ω

Voltage; V = 15 V

Internal resistance; r = 2.0 Ω

Formula for current with internal resistance is;

I = V/(r + R)

I = 15/(2 +4)

I = 2.5 A

Formula for energy stored in inductor is;

U = ¹/₂LI²

U =  ¹/₂ * 100 * 10⁻³ * 2.5²

U = 0.3125J

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Someone help me fast please!

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The graph shows a position - time graph of an object which is moving downhill. The object is moving with a constant speed but away from the observer.

What is velocity?

Velocity is a physical quantity that measures the distance covered per unit time. Velocity is a vector quantity and is having both magnitude and direction.

Velocity is the ratio of distance to the time. Thus, if the change in distance is linear with the change in time, there will be no change in velocity and the object is said to be moving with constant velocity.

If the distance and time are non-linear thus, thus, change in distance is not coinciding with change in time, then the velocity changes each time. The given object is moving away from the observer and

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which tools do astronomers use to determine the effects of collisions between galaxies? select the two correct answers.(1 point)

Answers

Astronomers use space telescopes to determine the effects of collisions between galaxies.

A space telescope could be a telescope in outer space utilized to watch astronomical objects. Space telescopes avoid the sifting and distortion of electromagnetic radiation which they observe, and maintain a strategic distance from light pollution which ground-based observatories experience. They are divided into two sorts, such as Satellites which outline the entire sky, and satellites which center on selected galactic objects or parts of the sky and beyond. Astronomy deals with the study of external space. The study centers on planets and other celestial bodies. For the most part, telescopes are utilized to study external space.

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which tools do? select the two correct answers. (1 point)

computer simulations

print encyclopedia entries

space telescopes

solar system models

how much work is required for a 78 kgkg runner to accelerate from rest to a speed of 8.0 m/sm/s ?

Answers

Work done to accelerate from rest to speed of 8 m/s = 2496 Joules

What is Work energy theorem ?

According to the work-energy theorem, the net work performed by forces acting on an item equals the change in kinetic energy.

According to the given information

Using the work - energy theorem,

work done is defined as the change in the kinetic energy  [tex]$\mathrm{W}=\frac{1}{2} \mathrm{mv}^2-\frac{1}{2} \mathrm{mu}^2[/tex]= [tex]\frac{1}{2} \mathrm{~m}\left(\mathrm{v}^2-\mathrm{u}^2\right)$[/tex]

given

[tex]$\mathrm{m}[/tex] =78 [tex]\mathrm{~kg}$[/tex]

[tex]$u=0 \mathrm{~m} / \mathrm{s}$[/tex]

[tex]$v=8 \mathrm{~m} / \mathrm{s}[/tex]

Hence

[tex]$\mathrm{W}=\frac{1}{2} 78\left(8^2-0^2\right)$[/tex]

[tex]$\Rightarrow \mathrm{W}=\frac{1}{2}(78)(64)$[/tex]

[tex]$\Rightarrow \mathrm{W}=2496 \mathrm{~J}$[/tex]

Work done to accelerate from rest to speed of 8 m/s = 2496 Joules

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A film with thickness t gives constructive interference for light with a wavelength in the film of λfilm. How much thicker would the film need to be in order to give destructive interference?

A. 2λfilm
B. λfilm
C. λfilm/2
D. λfilm/4

Answers

Light with a wavelength in the film's thickness t exhibits constructive interference.

What exactly is a damaging interference?

When two waves are entirely out of phase (a peak is located in the middle of two waves), destructive interference ensues. In other words, destructive interference occurs when two waves 180 degrees or radians apart from each other cancel each other out.

What causes waves to interfere destructively?

When two waves' maxima are 180 degrees out of phase, destructive interference happens: a positive displacement of one wave is precisely cancelled by a negative displacement of the other wave. The resultant wave has zero amplitude.

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a 2.0-kg mass is attached to the end of a horizontal spring of spring constant 50 n/m and set into simple harmonic motion with an amplitude of 0.10 m. what is the total mechanical energy of this system?

Answers

Answer:

0.25 J

Explanation:

How many possible combinations are there for the values of l and ml when n = 2?

Express your answer as an integer.

? = possible combinations

Answers

The possible combinations are for the values of l when n = 2 is two values 0,1 and ml is -1,0,1

The n is the principal quantum number

l is the azimuthal quantum number

ml is the magnetic quantum number.

The formula to find the azimuthal quantum number is

            l = 0,1,2,3 .......n-1

If n = 2, the azimuthal quantum number,

            l = 0, 1

Then, the ml can be found using the formula,

           ml = 2l +1

For l = 0 , ml = 2(0) + 1

                    = 1

Therefore, ml will have only one value, which is 0

For l =1 , ml = 2(1) + 1

                  = 3

Therefore, the ml will have three values, they are -1,0,1

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in 1634, in an attempt to determine the source of a growing plant's mass, van helmont planted a willow seedling in a pot of soil. after 5 years, the willow weighed 76.8 kg, and the soil had lost 0.06 kg of weight. only water had been added to the pot. which conclusion should van helmont have drawn?

Answers

The conclusion should van helmont have drawn Plants get all or almost all of their mass from a source other than soil

Van Helmont conducted an experiment to see whether the ancient Greek theory was accurate. In a measured amount of dirt, he raised a willow tree. The willow tree had gained roughly 74 kg in weight over the course of five years, he found. Van Helmont came to the conclusion that soil minerals alone cannot account for plant development because the weight of the soil had hardly changed. He believed that the additional plant matter had only come from the water.

Complete question:

In an attempt to find out where a growing plant gets its mass, Van Helmont planted a willow seedling in a pot of soil. After five years, the willow weighed 76.8 kg, and the soil had lost 0.06 kg of weight. Only water had been added to the pot. Which of the following conclusions should Van Helmont have drawn?

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Hypothesis (one or 2 paragraphs)
Should be on the form
‘An increase in the independent variable will cause the dependent variable to …’.
You could also suggest a mathematical or graphical relationship between the variables.
Explain why you think your hypothesis is true using scientific ideas.
The hypothesis should follow from the introduction - no new information added.
Include references to any sources of information and to your own introduction..

The IV is the Mass of the coffee filter and the DV is The terminal velocity.

Answers

‘An increase in the independent variable (the Mass of the coffee filter) will cause the dependent variable (The terminal velocity) to decrease.

How does mass affect terminal velocity Experiment?

This relationship demonstrates the way that a mass-dependent relationship exists between an object's terminal velocity and mass. The faster an object descends through a fluid, the heavier it is.

The values of the variables shift in the opposite directions when there is an inverse or negative relationship. In other words, if the value of the independent variable rises, the dependent variable falls; if the value of the independent variable falls, the dependent variable rises.

Therefore, for coffee filters, the force of air resistance is related to the square of the fall speed, therefore it too increases as speed increases. To reach terminal velocity, a heavier filter with a same area must fall more quickly than a lighter one.

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Which of the following spectrum is also known as microwave spectrum?
a) Solar cells b) Ovens c) Radiotherapy d) Burglar alarms.

Answers

Microwave spectrum is another name for radiotherapy spectrum. There are no early termination penalties when canceling with Spectrum.

Can you haggle about the cost of Spectrum?

One of the greatest methods to lower your Spectrum bill if you're unhappy with the amount you have to pay each month for internet connection is to call and bargain. You may bargain your way back to your prior tariff by making the proper call through the proper channel.

Spectrum costs $80; why?

The expense of providing your family with the finest value in broadband—300 Mbps starting speeds with no modem fees, data limitations, or contracts—is reflected in the price of Spectrum Internet, according to the provider. Charter added that this is the first time it has raised the cost of standalone broadband.

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a bottle of juice is 2/3 full. the bottle contains 4/5 of a cup of juice. find the capacity of the bottle

Answers

The capacity of the bottle is 1.2 cups of juice.

What is the capacity of the bottle?

The capacity of the bottle is the sum of all the volume of juice contained in the bottle and it is calculated as follows;

Total capacity of the bottle = initial volume of the bottle ÷  volume of the cup of juice

2/3 full ------------------> 4/5 cups

100% full = 1 -------------> x

( ²/₃ ) x = ⁴/₅

The total capacity of the bottle is calculated as follows;

Total capacity of the bottle ⇒ ( ²/₃ ) x = ⁴/₅

5 (2x) = 4 (3)

10x = 12

x = 12 / 10

x = 1.2 cups

Thus, the capacity of the bottle is a function of the amount of cups of juice that can fill it.

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