What happens if the value of VOq doubles

What Happens If The Value Of VOq Doubles

Answers

Answer 1

If Voq doubles, abN gets multiplied by 16 .

If Voq=3, abN=81 .

Answer 2

If the value of VOq doubles, the magnitude of the restoring force doubles.

The formula for the restoring force of an abductin pad is:

F = k * x

where:

F is the restoring force

k is the spring constant

x is the distance the spring is compressed or stretched

In this case, we are told that VOq doubles. VOq is the spring constant. So, if VOq doubles, k doubles. This means that the restoring force doubles.

The restoring force is the force that pushes the shell open when the muscles relax. If the restoring force doubles, the shell will be pushed open with twice the force. This means that the shell will open more quickly and easily.

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Related Questions

A scientific law is?

Answers

Scientific law is also known as natural law. It  imply a cause and effect between the observed elements and always apply under the same conditions .

Answer:

Scientific law is a statement based on repeated experimental observations that describes some aspect of the Universe.

The term law has diverse usage in many cases (approximate, accurate, broad, or narrow theories) across all fields of natural science (physics, chemistry, biology, geology, astronomy, etc.). Scientific laws summarize and explain a large collection of facts determined by experiment.A scientific law always applies under the same conditions, and implies that there is a causal relationship involving its elements.

The most reactive metals are located at the of the periodic table.

Answers

Answer:

the elements towards the bottom left corner

Explanation:

Metals are the substances which tend to lose their valence electrons in order to attain stability.

For example, metals of group 1 are lithium, sodium, potassium, rubidium and cesium.

And, each of these elements have only 1 valence electron present. So, it is much easier to lose just one electron rather than losing 2 or 3 valence electrons.

Hence, alkali metals are the most reactive substances of the periodic table and they are present at extreme left side of periodic table.

Therefore, we can conclude that the most reactive metals are located at the extreme left of the periodic table.

Why is the law of gravity an example of a universal law?
A) gravity is the attraction of any mass to any other other mass .
B) Gravity is a force that affects everyone on earth
C) gravity is the reason the earth revolves around the sun
D) gravity is a force that exist between any two masses in the universe

Answers

A) gravity is the attraction of any mass to any other other mass .

D) gravity is a force that exist between any two masses in the universe


both are ok ...

Which is an effect of gravity on objects on the surface of Earth? Check all that apply.

• Objects “fall” toward the center of Earth.

• Objects are pulled by Earth but do not pull on Earth.

• Objects accelerate at a rate of 9.8 m/s each second.

• Objects travel at a rate of 9.8 m/s to are the center of Earth.

• Objects are pulled by Earth more strongly than they pull on Earth.

Answers

• Objects “fall” toward the center of Earth.  (TRUE)

Since the gravitational force between earth and any object is always along the line joining the centers of two so all the objects near the surface of earth will always feel force towards the centre of the earth due to gravity.

• Objects are pulled by Earth but do not pull on Earth.  (FALSE)

Since gravitational force will always follow Newton's III law as per which every action has equal and opposite reaction force so object near the surface of earth will also pull the earth as earth is pulling the object towards the center.

• Objects accelerate at a rate of 9.8 m/s each second.  (TRUE)

Since acceleration due to gravity of Earth is 9.8 m/s^2 so here we can say that all objects near the surface of earth will accelerate towards the center of earth at rate of 9.8 m/s^2 due to gravitational pull.

• Objects travel at a rate of 9.8 m/s to are the center of Earth. (FALSE)

Since earth is pulling all objects near its surface with gravitational force so objects can not move at constant speed but it will move with constant acceleration.

• Objects are pulled by Earth more strongly than they pull on Earth. (FALSE)

Since gravitational force will always follow Newton's III law which say every action has equal and opposite reaction so we can say that force due to all objects on earth will be same as the force of earth on the object.

Salmon often jump waterfalls to reach their breeding grounds. Starting 3.15 m from a waterfall 0.45 m in height, at what minimum speed must a salmon jumping at an angle of 33.2 degree leave the water to continue upstream? the acceleration due to gravity is 9.81 m/s2. Answer in units of m/s.

Answers

Let the salmon jump with speed v at an angle of 33.3 degree

So here we can find out the components of his velocity in x and y direction

[tex]v_x = v cos33.2[/tex]

[tex]v_y = v sin33.2[/tex]

now the horizontal displacement of the salmon is 3.15 m so he cover this horizontal distance with constant speed as there is no acceleration in x direction

here we can say

[tex]v_x * t = 3.15[/tex]

[tex]v cos33.2 * t = 3.15[/tex]

[tex]v*t = 3.76[/tex]

now in Y direction it is an accelerated motion as it is accelerated due to gravity

[tex]y = v_y * t + \frac{1}{2}at^2[/tex]

[tex]-0.45 = v sin33.2* t - \frac{1}{2}*9.8* t^2[/tex]

now we will plug in v*t = 3.76

[tex]-0.45 = 3.76 * sin33.2 - 4.9 * t^2[/tex]

[tex]4.9 t^2 = 2.51[/tex]

[tex]t^2 = 0.512[/tex]

[tex]t = 0.72 s[/tex]

now speed v is given by equation above

[tex]v*t = 3.76[/tex]

[tex]v*0.72 = 3.76[/tex]

[tex]v = 5.25 m/s[/tex]

so here he must have to jump with minimum speed of 5.25 m/s

Salmon often jump waterfalls to reach their breeding grounds. Starting 3.15 m from a waterfall 0.45 m in height, at what minimum speed must a salmon jumping at an angle of 33.2 degree leave the water to continue upstream? The acceleration due to gravity is 9.81 m/s2. Answer in units of m/s.

Answers

Let the salmon jump with speed v at an angle of 33.3 degree

So here we can find out the components of his velocity in x and y direction

[tex]v_x = v cos33.2[/tex]

[tex]v_y = v sin33.2[/tex]

now the horizontal displacement of the salmon is 3.15 m so he cover this horizontal distance with constant speed as there is no acceleration in x direction

here we can say

[tex]v_x * t = 3.15[/tex]

[tex]v cos33.2 * t = 3.15[/tex]

[tex]v*t = 3.76[/tex]

now in Y direction it is an accelerated motion as it is accelerated due to gravity

[tex]y = v_y * t + \frac{1}{2}at^2[/tex]

[tex]-0.45 = v sin33.2* t - \frac{1}{2}*9.8* t^2[/tex]

now we will plug in v*t = 3.76

[tex]-0.45 = 3.76 * sin33.2 - 4.9 * t^2[/tex]

[tex]4.9 t^2 = 2.51[/tex]

[tex]t^2 = 0.512[/tex]

[tex]t = 0.72 s[/tex]

now speed v is given by equation above

[tex]v*t = 3.76[/tex]

[tex]v*0.72 = 3.76[/tex]

[tex]v = 5.25 m/s[/tex]

so here he must have to jump with minimum speed of 5.25 m/s

Amy uses 20n of force to push a lawn mower 10 meters. How much work does she do

Answers

the answer would be work=200J

As a country advances from an undeveloped nation to a modern industrialized nation, it changes in many significant ways.
How ever, some parallels will remain. For example ______ was used as an energy source by ancient civilization, and is still being used to produce energy today.
A.) wind
B.) fusión
C.) eléctricity
D.) volcanic ash

Answers

I’m not sure but I’m guessing wind.

Answer:

wind

Explanation:

From powering ships and windmills to wind-farms that generate electricity, wind has proven to be somewhat useful.

State the difference between sensible heat and latent heat

Answers

Latent heat is related to changes in phase between liquids ,gases and solids.

Sensible heat is related to changes in temperature of a gas or object with no change in phase.

sara and tory are out fishing on the lake on a hot summer day when they both decide to go for a swim. sara dives off the front of the boat with a force of 45° N, while Tory dives off the back of the boat with a force of 60° N. Draw a vector diagram of the situation. Find the resultant force on the boat.

Answers

Here it is an application of Newton's III law

as we know by Newton's III law that every action has equal and opposite reaction

So here as we know that two boys jumps off the boat with different forces

from front side of the boat the boy jumps off with force 45 N which means as per Newton's III law if boy has a force of 45 N in forward direction then he must apply a reaction force on the boat in reverse direction of same magnitude

So boat must have an opposite force on front end with magnitude 45 N

Now similar way we can say

from back side of the boat the boy jumps off with force 60 N which means as per Newton's III law if boy has a force of 60 N in backward direction then he must apply a reaction force on the boat in reverse direction of same magnitude

So boat must have an opposite force on front end with magnitude 60 N

So here net force due to both jump on the boat is given by

[tex]F_{net} = F_1 - F_2[/tex]

[tex]F_{net} = 60 - 45[/tex]

[tex]F_{net} = 15 N[/tex]

so boat will have net force F = 15 N in forward direction due to both jumps

Explain the versatility of epithelial tissue

Answers

Epithelial cells are classified by the following three factors : 1. Shape . 2. Stratification. 3.Specialization . It's a main aspect to the mehe family , and plays a huge part in helping the movement of bobbing your head.

Answer:

Explanation:

The epithelial tissues cover the body surfaces, forms a lining over the body cavities and hollow organs. These tissues also forms a protective barrier between the external environment and the body.

The epithelial tissues are the tissues which performs various functions. These tissues are composed of cells that are laid close to each other with the cells that lies in the close association with each other. The structure and function of the epithelial cells vary from both upper and lower surfaces. Due to variety in the functions of the epithelial tissues like protection, secretion, cellular transportation, filtration, selective absorption and sensing, these are called as the versatile tissues.

Type the correct answer in the box. Use numerals instead of words.


On average, how much of their income will a family spend on food?

Income level of a family is one of the factors that affect a food budget. On average, a family will spend ________percent of their income on food.

Answers

Answer:

10% of the income.

Explanation:According to the most recent data from the U.S. Bureau of Labor Statistics, in 2013 the average American household spent about 10% of its total budget on food.For example if you have income of $6000, you will spend $600 on food.

Answer:

20% of their income

Explanation:

I got a five on Plato

You are driving up an inclined road. After 2.4km you notice a roadside sign that indicates that your elevation has increased by 160m. What is the angle of the road above the horizontal?

Answers

The 'slope' of the road is (rise between two points) / (hotizontal distance between the same two points).  Or (rise)/(run).  It's also the tangent of the angle between the horizontal and the incline.

In this problem, your 'run' is 2.4 km, and the 'rise' is 160 m.

The slope of the incline is (160) / (2,400) .

That's 0.0667 .

To answer the question, you need to find the ANGLE whose tangent is that same number.

If your calculator has ANY functions on it, then " tan⁻¹ " is the one you want.  Key in a number, and " tan⁻¹ " will give you the angle whose tangent is that number.

Final answer:

The angle of the road above the horizontal is found using trigonometry, specifically the tangent function, which is the ratio of the elevation gain to the distance traveled along the road. By applying the arctan function to 160m/2400m, we can calculate the angle of inclination in degrees.

Explanation:

The question involves finding the angle of the road above the horizontal when the elevation change and the distance traveled along the road are known. This requires the use of trigonometry to determine the angle, given the rise (elevation change) and run (distance traveled along the road).

To find the angle, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle. In this scenario, the rise is 160 m and the run is 2400 m (2.4 km). We need to convert the run into meters to match the units of the rise, making the run 2400 m.

Now we compute the angle θ:

Rise (opposite side) = 160 mRun (adjacent side) = 2400 mTangent of θ = Rise / Run = 160m / 2400mTan θ = 1/15θ = arctan(1/15)

Once we calculate the arctan(1/15), we will get the angle of inclination of the road in degrees.

if 2 objects have the same momentum which statement is true

A.mass and velocity are the same for both

B.they both have the same mass

C.the product of mass x velocity is the same for both

D.they both have the same velocity

Answers

C is the correct option

As momentum = (mass) (velocity)

P=mv

So the object having greater mass has less velocity and the object having smaller mass will move faster. But product of mass and velocity is same to each other.

A cylindrical block of aluminum has a radius 2.5 cm and
length 20 meters. The center of the cylinder has 20 mm of
aluminum removed radially
(A) What is the resistance of this block of material?
(B) What temperature would the aluminum have to be at to have the
same resisttivity as tungsten of the same size and length?
C) How much power is dissipated when 30 amps of is passed through
the cylindrical block using the resistance from part A.

Answers

(A) The resistance of the block of aluminum is given by:

[tex]R=\frac{\rho L}{A}[/tex]

where

[tex]\rho[/tex] is the aluminum resistivity

L is the length of the cylinder

A is the cross-sectional area of the cylinder

We already know the aluminum resistivity ([tex]\rho=2.65 \cdot 10^{-8} \Omega m[/tex]) and the length of the cylinder (L=20 m), so we must find the cross-sectional area A, which is given by the difference between the area of the larger cylinder and the area of the radial hole:

[tex]A=\pi (R^2 -r^2)[/tex]

where [tex]R=2.5 cm=0.025 m[/tex] and [tex]r=20 mm=0.02 m[/tex] (assuming that the 20 mm removed radially refers to the radius of the hole).

Therefore, the cross-sectional area is

[tex]A=\pi ((0.025 m)^2-(0.020 m)^2)=7.06 \cdot 10^{-4} m^2[/tex]

Substituting into the initial formula of the resistance, we find:

[tex]R=\frac{\rho L}{A}=\frac{(2.65 \cdot 10^{-8} \Omega m)(20 m)}{7.06 \cdot 10^{-4} m^2}=7.51 \cdot 10^{-4} \Omega[/tex]


(B) The resistivity of the tungsten is [tex]\rho=5.6 \cdot 10^{-8} \Omega m[/tex], so a cylinder of tungsten of the same size would have a resistance of

[tex]R=\frac{\rho L}{A}=\frac{(5.6 \cdot 10^{-8} \Omega m)(20 m)}{7.06 \cdot 10^{-4} m^2}= 1.59 \cdot 10^{-3} \Omega[/tex]

The behaviour of the resistance versus temperature is given by:

[tex]R=R_0 (1 + \alpha \Delta T)[/tex]

where [tex]\alpha[/tex] is a coefficient that for aluminum is equal to [tex]\alpha = 0.004308[/tex], R0 is the resistance of the piece of aluminum we found at point (A), and R is the resistance of the tungsten. Re-arranging the formula and substituting, we find

[tex]\Delta T = \frac{R/R_0 -1}{\alpha}=\frac{\frac{1.59 \cdot 10^{-3} \Omega}{7.51 \cdot 10^{-4} \Omega}-1}{0.004308}=259.3^{\circ}C[/tex]

So, the temperature must increase by 259.3 degrees.


(C) The power dissipated is given by:

[tex]P=I^2 R[/tex]

where I=30 A is the current. Substituting the numbers into the formula, we find

[tex]P=(30 A)^2 (7.51 \cdot 10^{-4} \Omega)=0.68 W[/tex]

What is the most important concern when trying to prevent frostbite?

A. Drinking enough fluids
B.wearing cotton next to your skin
C. Dressing to protect hands
D.wearing sunscreen

Answers

answer is C. dressing to protect hands

Hello!

The most important concern when trying to prevent frostbite would be C.) dressing to protect hands. The more coverage you have, the warmer or more protected your skin will be. :)

Hope this helps!!! Good lucky!!

A rock is thrown at an angle of 30 degrees above the horizontal with initial velocity 15m/s what is the displacement when the rock returns to the ground

Answers

The displacement of the rock will be the same as the total horizontal distance traveled. Here the rock's horizontal position is given by

[tex]x=\left(15\,\dfrac{\mathrm m}{\mathrm s}\right)\cos30^\circ\,t[/tex]

so to find the horizontal distance it traversed, we need to know the time it took for the rock to return to the ground. We use the rock's vertical position over time to figure that out:

[tex]y=\left(15\,\dfrac{\mathrm m}{\mathrm s}\right)\sin30^\circ\,t-\dfrac g2t^2=0[/tex]

where [tex]g=9.8\,\dfrac{\mathrm m}{\mathrm s^2}[/tex] is the acceleration due to gravity. Then we find that [tex]t\approx1.5\,\mathrm s[/tex], at which point we find [tex]x\approx20\,\mathrm m[/tex].

At take off, a plane flies 100 km north before turning to fly 200 km east. How far is its destination from where the plane took off?

Question 3 options:

173 km


300 km


224 km


200 km

Save
Question 4 (1 point)
A runner traveled 15 kilometers north then backtracked 11 kilometers south before stopping. His resultant displacement was






Question 4 options:

26 km south


4 km south


26 km north


4 km north

Answers

Answer

224 Km

4 Km


Explanation

Part 1

The plane flies 100 Km north and then 200 Km east. This makes a 90° turn. To get the distance taken by the plane we get the hypotenuse.

c² = a² + b²

c² = 100² + 200²

   = 50,000

c = √50,000

    = 223.606 Km

The answer to the nearest whole number is 224 Km

Part 2

If the runner run 15 Km north then 11 Km south, the resultant distance would be,

15 - 11 = 4 Km

Help? Will give thanks if right (thank you)

Answers

Answer:

1.986 * 100,000 = 1,986,000

in a free body diagram, the force arrows always point what way?

Answers

Forces are presented as straight arrows pointing in the direction they function  on the body.

The force arrows always points straight arrows.

What was the Great Dark Spot of Neptune?

A. an area with a high concentration of methane
B. a shadow cast by a nearby dwarf planet
C. a windy and powerful storm system
D. a pool of water on the planet's surface

Answers

C. a windy and powerful storm system


C. a windy and powerful storm system

If a person is standing still in a moving elevator at 55 mph what is her speed in mph relative to the elevator

Answers

We are standing still inside an elevator

So our speed in the frame of elevator is zero

we can write this relative speed as

[tex]v_{pE} = v_p - v_E[/tex]

also we know that speed of the elevator is 55 mph

[tex]v_E = 55 mph[/tex]

now the velocity in relative frame is zero as he is  still in the moving elevator while in the ground frame or observing from the ground its velocity will be same as velocity of elevator.

So whenever an object is at rest in a moving frame then its relative velocity with respect to that frame must be ZERO

Select the statement that is true regarding scientific theories.
A. Scientific theories are what laws are called before they are proven.
B. Scientific theories attempt to explain why natural events occur.
C. Scientific theories are based on true facts.
D. Scientific theories describe natural events.

Answers

B. Scientific theories attempt to explain why natural events occur.

Answer: B. Scientific theories attempt to explain why natural events occur.

Explanation:

The scientific theories are the detailed explanations which gives reasons for the cause of natural events, processes and phenomena that occur in the natural world. These are supported by the evidences and observations that are obtained through experimental trials. These theories can be changed due to the changing of facts due to further experimental studies conducted by new generation scientists.

Across what potential difference does an electron have to be accelerated in order to reach the speed v=3e7 m/s?

Answers

When an electron is accelerated through potential difference then the speed that it attain will be explained by energy conservation

here by energy conservation we can say that

change in kinetic energy of electron = electrostatic potential energy gained through given potential difference

kinetic energy is given as

[tex]KE = \frac{1}{2}mv^2[/tex]

electrostatic potential energy is given as

[tex]PE = qV[/tex]

now by energy conservation

[tex]qV = \frac{1}{2}mv^2[/tex]

given that for electron

[tex]m = 9.1 * 10^{-31} kg[/tex]

[tex]v = 3 * 10^7 m/s[/tex]

[tex]q = 1.6 * 10^{-19} C[/tex]

now by plug in values

[tex]1.6 * 10^{-19} * V = \frac{1}{2}*9.1* 10^{-31} *(3*10^7)^2[/tex]

[tex]V = \frac{4.095 * 10^{-16}}{1.6 * 10^{-19}}[/tex]

[tex]V = 2559.4 Volts[/tex]

So here it is accelerated through potential difference of 2559.4 Volts

The electric potential is 4100 V or 4.1kV.

We know that the kinetic energy of the moving electron is equal to the 1/2mv^2. On this basis, we can write;

1/2mv^2 = eV

Where;

m = mass of the electron

v = speed of the electron

V = potential of the electron

e = charge on the electron.

Hence;

V = 1/2mv^2 /e

V = 0.5 × 9.11 × 10^-31 × (3 × 10^7)^2/1.6 ×10^-19

V = 4100 V or 4.1kV

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Why is an abseiling rope tested beyond twice the maximum possible weight when in use

Answers

ANSWER:

Abseiling rope is tested beyond twice the maximum possible weight when in use because of safety purposes.

EXPLANATION:

Every rope has its elastic limit.Abseiling rope is used basically for climbing or descending purposes so this type of rope must be of quite good quality and  it must bear maximum possible weight. We test it  just to check the elastic limit of the rope so that the rope shouldnot increase its elastic limit and it doesnot break when we use it.

How do you know that a sealed calorimeter is a closed system? Because the temperature is conserved Because the masses of the sample and water are equal Because the thermal energy is not transferred to the environment Because the work is done on the test sample

Answers

Answer: A sealed calorimeter is a closed system because thermal energy is not transferred to the environment.


A closed system is an isolated system where there is no transfer of energy with its surroundings. Also the system is not subjected to any external force whose source is external to the system.



Answer:C. Because thermal energy has not transferred to the environment.

Explanation:

to improve the acoustics in an auditorium, a sound reflector with a mass of 170kg is suspended by a chain from the ceiling. what is the tension in the chain? assume that the mass of the chain itself is 8.0kg.

Answers

Mass of the sound reflector is given as

[tex]m_1 = 170 kg[/tex]

mass of the chain itself is

[tex]m_2 = 8 kg[/tex]

now here since this system is suspended at rest and no acceleration is given for the system so in order to find the tension in the chain we will just use force balance equation

As per force balance we can say that weight of the chain and reflector downwards will be counter balanced by tension in the string

Now here we will have

[tex]T = m_1g + m_2g[/tex]

since chain is given with some mass so tension at the top end of the chain will be

[tex]T = 170* 9.8 + 8 * 9.8[/tex]

[tex]T = 1744.4 N[/tex]

So here tension in the chain will be 1744.4 N at the top end and this tension will decrease as we move down along the length of the chain.

Help Please!! An object is dropped from a height h meters. From the time the object is h/2 meters above the ground, it takes 1 second until the object strikes the ground. From what height was the object dropped?

Answers

Here object is dropped from height "h"

so we can say its initial speed is zero

and it will accelerate downwards due to gravity

now we can say it will take time T to hit the ground

now we can use

[tex]h = v_i*t + \frac{1}{2}gt^2[/tex]

[tex]h = 0 + \frac{1}{2}*gT^2[/tex]

now it is given that it will take 1 second to drop h/2 height to strike the ground

so here we have can say that in "T - 1" s it will cover the h/2 distance from start

[tex]h/2 = 0 + \frac{1}{2}g(T-1)^2[/tex]

now we can say

[tex]h = g(T-1)^2[/tex]

from above two equations we have

[tex]\frac{1}{2}gT^2 = g(T-1)^2[/tex]

[tex]T^2 = 2(T^2 + 1 -2T)[/tex]

[tex]T^2 - 4T + 2 = 0[/tex]

[tex]T = 3.41 s[/tex]

now we can find total height of the drop by first equation

[tex]h = \frac{1}{2}gT^2[/tex]

[tex]h = \frac{1}{2}*9.81*3.41^2[/tex]

[tex]h = 57.2 m[/tex]

The chart shows data for four heat engines.



Which lists the engines from most efficient to least efficient?

Y, X, W, Z
Z, W, X, Y
Z, X, W, Y
Y, W, X, Z

Answers

efficiency of the heat engine is calculated by the formula

[tex]\eta = 1- \frac{T_c}{T_h}[/tex]

here we know that

[tex]T_c [/tex] = cold temperature

[tex]T_h [/tex] = hot temperature

now we will find the efficiency of all

1) for W

[tex]\eta_1 = 1- \frac{T_c}{T_h}[/tex]

[tex]\eta_1 = 1- \frac{120}{620}[/tex]

[tex]\eta_1 = 0.806[/tex]

2) for X

[tex]\eta_2 = 1- \frac{T_c}{T_h}[/tex]

[tex]\eta_2 = 1- \frac{100}{840}[/tex]

[tex]\eta_2 = 0.88[/tex]

3) For Y

[tex]\eta_3 = 1- \frac{T_c}{T_h}[/tex]

[tex]\eta_3 = 1- \frac{300}{900}[/tex]

[tex]\eta_2 = 0.67[/tex]

4) for Z

[tex]\eta_4 = 1- \frac{T_c}{T_h}[/tex]

[tex]\eta_4 = 1- \frac{25}{500}[/tex]

[tex]\eta_4 = 0.95[/tex]

So here most efficient engine is Z and least is Y

so we can arrange it as

Z > X > W > Y

so 3rd option is correct here

Answer:

C.) Z, X,W, Y

What modifications did Kepler make to Copernicus model

Answers

Planets move in elliptical orbits and this theory was formulated by Johannes Kepler.  Kepler's laws of planetary motion defined a set of rules followed by the planets while revolve around the sun and determines their orbits.  

This modified the earlier theory of circular orbits from Nicholas Copernicus.

Kepler made two key modifications to Copernicus's model:

1. Kepler modified the circular orbits of planets proposed by Copernicus into elliptical orbits.

2. Kepler introduced the concept of varying planetary speeds along their orbits, rather than assuming constant speeds as Copernicus did.

To calculate the modifications Kepler made:

1. Elliptical Orbits:

  - Kepler's first law states that planets move in elliptical orbits with the Sun at one of the foci. The formula for an ellipse is [tex]\( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)[/tex], where [tex]\( a \)[/tex] is the semi-major axis and [tex]\( b \)[/tex] is the semi-minor axis.

  - In contrast, Copernicus's model assumed perfect circular orbits with the Sun at the center.

2. Varying Planetary Speeds:

  - Kepler's second law states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. Mathematically, this is expressed as [tex]\( \frac{dA}{dt} = \text{constant} \),[/tex]where [tex]\( A \)[/tex] is the area swept and [tex]\( t \)[/tex] is time.

  - Copernicus's model assumed uniform orbital speeds for planets.

Kepler's modifications were revolutionary as they better explained observations such as varying planetary brightness and retrograde motion. These changes laid the foundation for modern celestial mechanics and our understanding of planetary motion.

Complete Question:

What modifications did Kepler make to Copernicus model?

Other Questions
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