If force c is 30n and force d us 20 N what is the size of the horizontal force

Answers

Answer 1
Horizontal force is 10
Hope this helped

Related Questions

How far away is a storm if you hear the sound of thunder 7.0 s after the lightning flash on a day when the air temperature is 31°C?

Answers

The speed of sound is given by:

\(v=331\sqrt[]{1+\frac{T}{273}}\)

then in this case the speed is:

\(v=331\sqrt[]{1+\frac{31}{273}}=349.29\)

The distance is given by:

\(d=vt\)

plugging the values given we have:

\(\begin{gathered} d=(349.29)(7) \\ d=2445.03 \end{gathered}\)

Therefore the storm is 2445.03 meters away

Who discovered energy quanta and earned a Nobel Prize in Physics?

Answers

Answer: Max Planck

He won the Nobel Prize for Physics in 1918.

What does newton first law states ​

Answers

Answer:

Newton's first law, also known as the law of inertia, states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. In other words, an object will not change its velocity on its own, it will only do so if something else pushes or pulls on it. This law is a fundamental principle of classical mechanics, and it helps to explain the behavior of objects under various conditions.

Explanation:

Answer: Newton first law states that an object at rest tends to stay at rest. an object in motion tends to stay in motion in a straight line at a constant speed until another force acts on the object.  It is also called the law of inertia

Explanation: Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force.

Hope this was helful

A metal sphere with radius ra

is supported on an insulating stand at the center of a hollow, metal spherical shell with radius rb. There is charge + q on the inner sphere and charge − q on the outer sphericalshell as shown below. Take the potential V to be zero when the distance r from the center of the spheres is infinite.

Calculate the potential V(r)
for r , and any appropriate constants.

A metal sphere with radius ra is supported on an insulating stand at the center of a hollow, metal spherical

Answers

Please, for the sake of clarity on the solution to the question on calculating the potential V(r) of the metal sphere, let's go ahead with the step by step explanation as shown below.

Step by step explanation

To calculate the potential V(r) at a distance r from the center of the spheres, we need to consider two cases:

Case r < ra:

In this case, the point is inside the inner sphere and the potential is simply the potential due to the inner sphere, which can be calculated using the formula:

V_inner(r) = k * q / ra

where k is the Coulomb constant (k = 1/4πε0) and ε0 is the electric constant.

Case ra < r < rb:

In this case, the point is between the two spheres and the potential is the sum of the potentials due to the inner and outer spheres. The potential due to the outer sphere can be calculated using the same formula as above:

V_outer(r) = - k * q / rb

Note that the negative sign indicates that the potential due to the outer sphere is negative since it has a negative charge.

Therefore, the total potential at this point is:

V(r) = V_inner(r) + V_outer(r)

= k * q / ra - k * q / rb

Case r > rb:

In this case, the point is outside both spheres and the potential is simply due to the outer sphere, which is:

V_outer(r) = - k * q / r

So the total potential at this point is:

V(r) = V_outer(r)

= - k * q / r

Therefore, the potential V(r) as a function of the distance r from the center of the spheres is:

V(r) = { k * q / ra - k * q / rb if ra < r < rb

{ - k * q / r if r > rb

where k is the Coulomb constant, q is the charge on the inner sphere, ra is the radius of the inner sphere, and rb is the radius of the outer spherical shell. Note that we have taken the potential to be zero when the distance r from the center of the spheres is infinite.

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HELP!!! 100 POINTSSS!!!

HELP!!! 100 POINTSSS!!!

Answers

Answer:

3

Explanation:

From the question given above, the following data were obtained:

Length (L) = 3 m

Height (H) = 1 m

Mechanical advantage (MA) =.?

The ideal mechanical advantage for the system can be obtained as follow:

MA = L/H

MA = 3/1

MA = 3

Therefore, the ideal mechanical advantage for the system is 3

Answer:

Explanation:

Mechanical Advantage is the ratio of Input Distance / Output Distance.

In this case, the output distance is to bring up the cart by 1m.

The input distance is to push the cart by 3m.

Assume an ideal machine, MA = 3/1 = 3

14. Why is it cooler to wear a white shirt than a black shirt on a hot, sunny day?

Answers

Answer:

White or lighter colored, shirt REFLECTS most of the visible wavelengths or all colors of light while a black or dark shirt ABSORBS more wavelengths.

So, Absorbed radiation is converted into heat, making the darker or black shirt warmer to wear.

 

-TheUnknownScientist 72

A 1.70 m tall woman stands 5.00 m in front of a camera with a 50.00 cm focal
length lens. Calculate the size of the image formed on flim​

Answers

Answer:

18.89cm

Explanation:

As we know that the person is standing 5m in front of the camera

\(d_0=5m=500cm\)

The focal length of the lens =50cm

f=50 cm

By Lens formula we have:

\(\dfrac{1}{f} = \dfrac{1}{d_i} + \dfrac{1}{d_o}\\\dfrac{1}{50} = \dfrac{1}{d_i} + \dfrac{1}{500}\\\dfrac{1}{d_i} =\dfrac{1}{50}-\dfrac{1}{500}\\\dfrac{1}{d_i}=0.018\\d_i=55.56cm\)

By the formula of magnification

\(\dfrac{h_i}{h_o} = \dfrac{55.56}{500}\\\\h_i = \dfrac{55.56}{500} \times h_o\\\\ h_o=1.70m=170cm\\\\Therefore: h_i=\dfrac{55.56}{500} \times$ 170 cm\\\\h_i =18.89 cm\)

The height of the image formed is 18.89cm.

Determine the amount of power
used in holding a 25 kg box, 1.5
meters above the floor, for 60
seconds.

[?] W

(answer is not 6.13)

Thank you in advance!

Determine the amount of powerused in holding a 25 kg box, 1.5meters above the floor, for 60seconds.[?]

Answers

Here is your answer mate,

Question,

\(Determine\: the\: amount\\ \: of\: power\:used\: in\\\: holding\: a\: 25\: kg\: box\:\\ , \: 1.5\: meters \: above\: the\: floor\\\: for\: 60\: seconds\)

Answer,

Power is equal to work done per unit time

Work is force × displacement

SI UNIT OF WORK Newton meter

SI UNIT OF POWER Watt

\(\)

Solution,

\(\)

Given,

\(MASS \: IS\: 25\: KG\: \\ and \: HEIGHTIS\: 1.5m\: \)

\(\)

WORK DONE (done against gravity) =

mass×acceleration due to gravity ×height

WORK = 25× 10× 1.5

\(\: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \)= 375 Nm

\(\)

Now

POWER =

\( \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\frac{work}{time} \)

POWER

\(\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= \frac{375}{60} Watt \)

\(\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =6.25\)

\(Therfore\: your \: answer\: is\: 6.25\)

\(\)

Check this,

\(Acceleration\: due\: to \: gravity\\\: can\: be\: 9.8\: m/s²\: \\As\: nothing\: mentioned\\\: in\: question\: \\I \: took \: it \: as \: 10\)

\(\)

Have a good day

The two masses (mA
= 6.50 kg is hanging and mB
= 3.30 kg is on the floor) in the Atwood's machine shown in the figure below are released from rest, with mA
at a height of 0.865 m above the floor. When mA
hits the ground its speed is 1.89 m/s. The pulley is not massless and can be considered a solid disk with a moment of inertia of (1/2)mpr2
.
What is the total mechanical energy of the two blocks prior to being released from rest?
(Figure 1)
What is the total mechanical energy of the two blocks when mA
hits the ground?
Part C
What is the rotational kinetic energy of the pulley just before mA
hits the ground?
Part D
What is the mass of the pulley?

The two masses (mA = 6.50 kg is hanging and mB = 3.30 kg is on the floor) in the Atwood's machine shown

Answers

A)The total mechanical energy of the two blocks prior to being released from rest can be found by adding the gravitational potential energy of mA and the pulley to zero.

B).The gravitational potential energy of mB and the pulley is(3.30 kg + mp) × 9.81 m/s² × 0 m = 0 J,where mp is the mass of the pulley.The total mechanical energy of the two blocks prior to being released from rest is54.33 J + 0 J = 54.33 J

C) The rotational kinetic energy of the pulley just before mA hits the ground is(0.178 mp) J.

D) The mass of the pulley ismp = (1/2)mpr²/R² =(1/2)(0.020 kg)(0.100 m)²/(0.200 m)² = 0.001 kg = 1 g.r = (1/2)R.

The Atwood's machine shown in Figure 1 consists of two masses mA = 6.50 kg and mB = 3.30 kg. The height of mA above the floor is 0.865 m. When mA hits the floor, its velocity is 1.89 m/s. The pulley has a moment of inertia (1/2)mpr². We have to find the total mechanical energy of the two blocks before they are released, the total mechanical energy when mA hits the ground, the rotational kinetic energy of the pulley just before mA hits the ground, and the mass of the pulley. Let's solve these one by one. Part A The total mechanical energy of the two blocks prior to being released from rest can be found by adding the gravitational potential energy of mA and the pulley to zero.

The equation for gravitational potential energy is mgh. The gravitational potential energy of mA and mB is mAg(h-hB)where h is the height of mA above the floor and hB is the height of mB above the floor. Since the pulley is at the same height as mB, its gravitational potential energy ismBg(h-hB).The gravitational potential energy of mA is6.50 kg × 9.81 m/s² × 0.865 m = 54.33 J.The gravitational potential energy of mB and the pulley is(3.30 kg + mp) × 9.81 m/s² × 0 m = 0 J,where mp is the mass of the pulley.The total mechanical energy of the two blocks prior to being released from rest is54.33 J + 0 J = 54.33 J.Part BThe total mechanical energy of the two blocks when mA hits the ground can be found by adding the kinetic energy of mA, the kinetic energy of mB, and the rotational kinetic energy of the pulley to the gravitational potential energy of mB and the pulley. The equation for kinetic energy is (1/2)mv². The kinetic energy of mA is(1/2) × 6.50 kg × (1.89 m/s)² = 11.54 J.The kinetic energy of mB is(1/2) × 3.30 kg × 0 m/s² = 0 J, since it is at rest.The gravitational potential energy of mB and the pulley is(3.30 kg + mp) × 9.81 m/s² × 0 m = 0 J.The rotational kinetic energy of the pulley is(1/2) × (1/2)mp × R² × ω²,where R is the radius of the pulley and ω is its angular velocity just before mA hits the ground. We can use the fact that the linear speed of the rope is the same on both sides of the pulley to find ω. The equation for linear speed is v = Rω. When mA hits the ground, its speed is 1.89 m/s. The speed of mB is zero. Since the rope is inextensible, the speed of the rope is also 1.89 m/s.

Therefore, the speed of the pulley is also 1.89 m/s. We can find the angular velocity of the pulley by dividing the linear velocity by the radius.ω = v/R = 1.89 m/s ÷ (0.200 m/2) = 18.9 rad/s.The rotational kinetic energy of the pulley is(1/2) × (1/2)mp × R² × ω² =(1/4)mpR²ω² =(1/4)mp(0.200 m)²(18.9 rad/s)² =(0.178 mp) J.The total mechanical energy of the two blocks when mA hits the ground is11.54 J + 0 J + 0 J + (0.178 mp) J = 11.72 J + (0.178 mp) J.Part CThe rotational kinetic energy of the pulley just before mA hits the ground is(0.178 mp) J.Part DWe can find the mass of the pulley by using the moment of inertia of a disk and the mass of the pulley. The moment of inertia of a disk is (1/2)mr². Therefore,(1/2)mpR² = (1/2)mpr²,where R is the radius of the pulley and r is the radius of gyration of the pulley. The radius of gyration of a disk is (1/2)R.

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Ultimate frisbee relies upon good sportsmanship since there are no referees and players must self-officiate the game. What is this known as?
Group of answer choices

Spirit of the Team

Spirit of the Frisbee

Spirit of Sportsmanship

Spirit of the Game

Answers

Answer:

spirit of the team / game

Calculate the ratio of H+ ions to OH– ions at a pH = 8. Find the concentration of H+ ions to OH– ions listed in Table B of your Student Guide. Then divide the H+ concentration by the OH– concentration. Record this calculated ratio in Table A of your Student Guide. Compare your approximated and calculated ratios of H+ ions to OH– ions at a pH = 8. Are they the same? Why or why not? Record your explanation in Table A. What is the concentration of H+ ions at a pH = 8? mol/L What is the concentration of OH– ions at a pH = 8? mol/L What is the ratio of H+ ions to OH– ions at a pH = 8? :1 OR 1:

Answers

At pH = 8, the ratio of H+ ions to OH- ions is 1:1, indicating a neutral solution. The concentration of H+ ions and OH- ions is approximately 1 x 10^(-8) mol/L. The calculated and approximated ratios should match.

To calculate the ratio of H+ ions to OH- ions at pH = 8, we need to use the relationship between pH and the concentration of H+ ions. The pH scale is a logarithmic scale that measures the acidity or alkalinity of a solution based on the concentration of H+ ions.

The formula to calculate the concentration of H+ ions (\(C_H\)+) from pH is:

\(C_H\)+ = \(10^(^-^p^H^)\)

Substituting pH = 8 into the formula:

\(C_H\)+ = \(10^(^-^8^))\)

Using the properties of logarithms, we can calculate the concentration of H+ ions:

\(C_H\)+ ≈ 1 x \(10^(^-^8^))\) mol/L

According to the concept of neutrality in water, the concentration of H+ ions is equal to the concentration of OH- ions. Therefore, the concentration of OH- ions (\(C_O_H\)-) is also approximately 1 x \(10^(^-^8^))\)mol/L.

To calculate the ratio of H+ ions to OH- ions, we divide the concentration of H+ ions by the concentration of OH- ions:

Ratio = \(C_H\)+ / \(C_O_H\)-

Ratio = (1 x \(10^(^-^8^))\) / (1 x \(10^(^-^8^))\))

Ratio = 1:1

The ratio of H+ ions to OH- ions at pH = 8 is 1:1, indicating a neutral solution. This means that the concentration of H+ ions is equal to the concentration of OH- ions, resulting in a balanced ratio.

When comparing the calculated ratio of 1:1 to the approximated ratio at pH = 8, they should be the same because the ratio of H+ ions to OH- ions is determined solely by the pH value, which is consistent and mathematically derived. Therefore, the approximated and calculated ratios should match.

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10a. Phoebe Physics pulls a 5 kg wagon with a force of 80 N. What is the
net force if the force of friction between the wagon and the ground is 12
N? *

Answers

Answer:

68 N

Explanation:

We have a force of 80 N going to one direction and 12 N to the other direction. we subtract 12 from 80 and get 68 N which is the total net force

The net force acting on the wagon is equal to 68 N.

What is the net force?

The net force acting on an object can be defined as the vector sum of all forces acting. The net force is a single force that can give same the effect as the original forces on the object's motion.

The net force will be the resultant force with a similar effect on the rotational motion as all actual forces taken together by the object.

In the question, the applied force will act in the opposite direction of the frictional force so we need to subtract these two forces to find the net force.

Given, the applied force to push the wagon = 80 N

The frictional force between wagon and ground = 12 N

The net force on the wagon = 80N + (-12N) = 68 N

Therefore, the net force equal to 68 N will act in the direction of the applied force.

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Two identical loudspeakers 2.30 m apart are emitting sound waves into a room where the speed of sound is 340 m/s. Abby is standing 3.00 m in front of one of the speakers, perpendicular to the line joining the speakers, and hears a maximum in the intensity of the sound. Part A What is the lowest possible frequency of sound for which this is possible

Answers

Answer:

1089.74 Hz

Explanation:

Using Pythagoras theorem, we can find the distance from the point to the second speaker.

Thus;

d2 = √(3² + 2.3²)

d2 = √(9 + 5.29)

d2 = √14.29

d2 = 3.78 m

Then, the path distance which is the extra distance travelled would be;

Δd = d2 - d1

Δd = 3.78 - 3

Δd = 0.78 m

Now, the destructive interference condition is given by the formula;

Δd = (m + ½)λ

λ is the wavelength

m is a non - negative integer.

In this case, m = 2

Thus;

0.78 = (2 + ½)λ

λ = 0.78/(2½)

λ = 0.312 m

Now the formula for frequency of a wave is given by;

f = v/λ

Where v is speed of sound.

Thus;

f = 340/0.312

f = 1089.74 Hz

what is the function of enter key​

Answers

Answer:

what key

Explanation:

Answer:

The enter key is a computer innovation, which in most cases causes a command line, window form, or dialog box to operate its default function. This is typically to finish an "entry" and begin the desired process, and is usually an alternative to clicking an OK button.

The speed of sound in humid air than in dry air. Why ​

Answers

Answer:

When moisture is removed from air, its density increases. The speed of sound in a humid air is inversely proportional to the square root of its density. Therefore, the speed of sound in moist air is humidity increases, the velocity of sound increase and vice-versa.

Hope it helps :)

The half-life of a radioactive isotope is 210 d. How many days would it take for the decay rate of a sample of this isotope to fall to 0.58 of its initial rate?

Answers

It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.

2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.

3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.

4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.

5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.

6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".

7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).

8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).

9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.

10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.

11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).

12. Evaluating the expression, we find: t ≈ 546.

13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

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State two (2) examples of osmosis occurring in everyday life

Answers

when you keep raisin in water and the raisin gets puffed.
Movement of salt-water in animal cell across our cell membrane.

Tell me about Susan B. Anthony.

Answers

Answer:

She Had a Criminal Record. In 1872, Anthony registered to vote at a barbershop in Rochester, New York, and cast a ballot in the presidential election.

Explanation:

The law of conservation of angular momentum states that if no external force acts on an object, then its angular momentum does not change. true or false

Answers

Answer:

the answer is false.

Explanation:

i took the test and it is false trust me!!!!!!!!!

Latent heat is the heat that:A.gets a reaction to occur.B.breaks the bonds that hold a molecule together.C.is absorbed or released during a phase change.D.raises the temperature of an object 1°C.

Answers

Answer:

C. is absorbed or released during a phase change.

Explanation:

The Latent heat is the heat necessary for a phase change, so it is the heat that is absorbed or released during a phase change.

Why is it important to observe the necessary precautions in dancing??​

Answers

Answer:

To Avoid accidents and injuries

Explanation:

Safety measures are vital dancing as this may prevent bad things like accidents and injuries from happening.

When dancing,the safety of dancers is a must to be observed and considered.

Dancers are also most likely to exert their full potential if they know that they are safe no matter what happen....

HAVE A GOOD DAY....

three laws of mechanics and

Answers

Answer:

In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

On a test flight a rocket with mass 400 kg blasts off from the surface of the earth. The rocket engines apply a constant upward force F until the rocket reaches a height of 100 m and then they shut off.

Answers

If the rocket engines apply a constant upward force F until the rocket reaches a height of 100m and then shut off, the motion of the rocket can be described as a vertical projectile motion.

How calculate the constant upward force?

At the time of take-off, the rocket is at rest and has an initial velocity of 0 m/s. As the rocket engines apply a constant force F, the rocket will accelerate upward. The acceleration of the rocket can be determined by Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma).

The upward force F will cause the rocket to accelerate upward until it reaches a height of 100 m. At this point, the engines shut off and the rocket will continue to move upward under the influence of gravity alone. As it reaches the highest point, its vertical velocity will be zero and it will start to fall back to the ground.

It's important to note that the force applied by the engines and the height reached by the rocket are not enough to calculate the velocity and trajectory of the rocket. More information such as time elapsed, the force of the engines and the air resistance is needed to have a more accurate picture of the situation.

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How many g's of force will a nascar driver experience making a 80 m/s turn with a
radius of 200 meters?
3.2 g's
32 g's
2.5 g's
25 g's

Answers

3.27 g's of force will be applied to the driver during the turn.

What in science is a force?

In science, the term "force" has a particular definition. At this time, it is appropriate to refer to a force as a push or a pull. There is no such thing as a power that something "contains" or "has in it." A force is exerted on one item by another.

We must employ the centripetal acceleration formula to resolve this issue:

a = v² / r

In this case, the velocity is 80 m/s and the radius is 200 meters, so:

a = (80 m/s)² / 200 m = 32 m/s²

To convert this to g's, we divide by the acceleration due to gravity:

32 m/s² / 9.8 m/s²/g = 3.27 g's (rounded to two decimal places)

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What is the value of the electric potential at the center of the triangle if q1 = 4.1 μC , q2 = 3.4 μC , q3 = -3.5 μC ?

Answers

Answer:

triangle if q1 = 4.1 μC , q2 = 3.4 μC , q3 = -3.5 μC ?

Motorcycle safety helmet extend the time of collision hence decreasing,
a:chance of collision
b:force acting
c: velocity
c:Impulse

Answers

Answer:

D. Impulse

Explanation: Hope this helps

A whale swims due south for a distance of 730 m, turns around and goes due north
for 510 m, and finally turns around again and travels 1,000 m due south. What is the
total displacement of this?

Answers

The total displacement will be 490m .

What is the difference between displacement and distance?

The complete length of the path between any two points is called distance and the shortest path covered by an individual is called displacement. Distance cannot ne 0 or negative but displacement can be 0 and negative.

Circular motion of the body results in zero displacement but the distance cannot be zero.

First the whale moves in south is 730m and then it turns north in 510m , and then 1000 m in south .

1000-510→490m

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If the x-component of vector A in the figure below is 3cm and the y component of A is 4cm, then what is the vector quantity of A?

Question 9 options:

25 cm - 37 degrees


7 cm - 37 degrees


7 cm - 53 degrees


5 cm - 53 degrees

Answers

Answer:

5 cm - 53 degrees

Explanation:

\( \sqrt{ {4}^{2} + {3}^{2} } = 5cm\)

\( \tan ^{ - 1} (4 \div 3) \) = 53°

What is evidence used by Galileo to disprove Aristotle and Ptolemy?

Answers

Galileo challenged the Aristotelian-Ptolemaic model, providing support for the heliocentric model and paving the way for a new understanding of the universe.

Galileo Galilei played a crucial role in challenging the prevailing geocentric model of the universe proposed by Aristotle and supported by Ptolemy. He provided several lines of evidence that effectively disproved their theories and supported the heliocentric model proposed by Nicolaus Copernicus. Some of the key evidence used by Galileo includes:

1. Observations through a telescope: Galileo was one of the first astronomers to use a telescope to observe the heavens. His telescopic observations revealed several important discoveries that contradicted the Aristotelian-Ptolemaic worldview. He observed the phases of Venus, which demonstrated that Venus orbits the Sun and not Earth. He also observed the four largest moons of Jupiter, now known as the Galilean moons, which provided evidence for celestial bodies orbiting a planet other than Earth.

2. Sunspots: Galileo's observations of sunspots provided evidence that the Sun is not a perfect celestial body, as suggested by Aristotle. Sunspots indicated that the Sun has imperfections and undergoes changes, challenging the notion of celestial perfection.

3. Mountains on the Moon: Galileo observed the rugged and uneven surface of the Moon, which contradicted Aristotle's belief in celestial spheres made of perfect, unchanging material. The presence of mountains on the Moon suggested that celestial bodies are subject to the same physical laws as Earth.

4. Phases of Venus: Galileo's observations of the phases of Venus provided direct evidence for the heliocentric model. As Venus orbits the Sun, it goes through phases similar to the Moon, ranging from crescent to full. This observation strongly supported the idea that Venus revolves around the Sun.

These lines of evidence presented by Galileo challenged the Aristotelian-Ptolemaic model, providing support for the heliocentric model and paving the way for a new understanding of the universe. His work marked a significant turning point in the history of science and laid the foundation for modern astronomy.

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Water flows at a speed of 13 m/s through a pipe that has a diameter of 1.2 m. What is the
diameter of the smaller end of the pipe that the water comes out with a speed of 30 m/s?

Answers

The diameter of the smaller end of the pipe is approximately 0.78 meters.

To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.

The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity

Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2

Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2

Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30

Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30

0.36 * 13 = (diameter2/2)^2 * 30

4.68 = (diameter2/2)^2 * 30

Dividing both sides by 30:
0.156 = (diameter2/2)^2

Taking the square root of both sides:
0.39 = diameter2/2

Multiplying both sides by 2:
0.78 = diameter2

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