An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T. The spaceship enters a geosynchronous orbit at a distance of R.

Answers

Answer 1

(a) Radius's general expression is  R = ∛T²GM/4π²

(b)The planet's mass during its geosynchronous orbit is 4.9 × 10²⁵ kg.

We are given that,

T = period of the orbit = 26hours

r = radius of the orbit = = 2.1 × 10⁸ m.

G = gravitational constant = 6.674×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²

M = mass of the planet

Putting the value in radius equation we get,

R = ∛T²GM/4π²

8.98 ×10⁷ m = ∛ (26 × 60 × 60)² ×( 6.67 ×10⁻¹¹) M/ 4×(3.142)²

M = (8.98 ×10⁷ m ×39.49 )/ (∛2.86 × 10¹⁸)

M = 4.9 ×10²⁵

As a result, the planet has a mass of  4.9 ×10²⁵kg throughout its geosynchronous orbital period.

The complete question is given below,

An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T. The spaceship enters a geosynchronous orbit at a distance of R. a) From the given information, write a general expression for the mass of the planet in terms of G and the variables from the problem statement. b) Calculate the mass of the planet in kilograms if T = 26 hours and R = 2.1 × 108 m.

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Related Questions

What is the momentum of a car with a mass of 1200 kg moving at 25 m s?

Answers

The momentum of the moving car is 30000 kg m/s.

The momentum of a moving body is calculated as the product of mass and velocity. It is a vector quantity. In simple terms, it is the strength or force gained by a moving object.

Newton's second law is related to momentum. According to newton's second law, " The time rate of change of momentum is equal to force".

We have the formula for finding the momentum,

Momentum = Mass× Velocity

P = M × V

Put the value in the formula,

P = 1200 × 25 kg m/s

= 30000 kg m/s

So, the car is moving with a momentum of 30000 kg m/s.

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Where is IR on the electromagnetic spectrum?

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Infrared Radiation lies on third place of electromagnetic spectrum in the increasing order of frequency.

In his experiments to measure temperature differences between colors in the visible spectrum, he placed a thermometer in the path of light within each color in the visible spectrum. He noticed that the temperature rose from blue to red, and found that just beyond the red end of the visible spectrum showed even higher temperatures. Within the electromagnetic spectrum, infrared waves occur at frequencies higher than those of microwaves and slightly lower than those of red visible light, hence the name "infrared".

Infrared radiation is an integral part of the electromagnetic spectrum.

It has wavelength of 700nm and has good application for earth sciences.

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how much work is required to push a crate at constant velocity with a force of 210 n across a floor a distance of 5 m?

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Work done is calculated as the scalar product of force and displacement along the force's direction, so it should be zero because there is no net force acting on the object (hence the constant velocity). Thus, W is equal to 0.

How do you figure out an object's force with constant velocity?

Newton's first law of motion states that any object moving at a constant speed experiences no net external forces, so the total amount of forces acting on the object must be zero. The mathematical expression for an object being under no net external force is Fnet=0 or F=0.

Acceleration equals zero when velocity stays the same. Therefore, an object moving at a constant speed does not require any force.

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Does dilation change the vertices?

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Dilation doesn't always change the vertices.

In mathematics, dilation is a type of transformation that changes the size of a shape or geometric figure, but keeps the relative proportions and shape the same. Magnification is defined as the ratio of the size of the new image to the size of the old image. The center of expansion is a fixed point in the plane. A dilation transform is defined based on the scale factor and dilation center.If the scale factor is greater than 1, the image will be stretched.If the scale factor is between 0 and 1, the image will be scaled down.If the scale factor is 1, the original image and the generated image are congruent.

Some of the shape features that are not changed during the stretch deformation are:All angles of the shape are the same.The center of the sides of the shape remains the same as the center of the unfolded shape.Parallel and vertical lines of the shape Enlargement The parallel and vertical lines of remain the same. The image remains the same.

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A 61. 7 kg carpenter at a construction site plans to swing in a circular arc from one roof top to an adjacent roof at the end of a 11. 5 meter rope suspended from a crane boom. If her wiry arms, toughened by years of driving spikes with a no. 22 framing hammer, are capable of exerting 1229 n of force on the rope, what is the maximum speed that she can tolerate at the low point of her swing?

Answers

The maximum speed she can tolerate at the low point of her swing is 10.78 m/s.

Given that,

Mass of the carpenter = 61.7 kg

Length of the rope = 11.5 m

Capable force = 1229 N

Centripetal force acting on the body, F = mv²/r = 61.7* v²/11.5 = 5.37 v²

Gravitational force acting on her is

F = mg = 61.7* 9.81 = 605.28 N

Equating the summation of centripetal force and gravitational force with total capable force,

5.37 v² + 605.28 = 1229

5.37 v² = 623.72

v² = 116.15

v = 10.78 m/s

Thus, the maximum speed she can tolerate at the low point of her swing is 10.78 m/s.

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Two coherent sources of radio waves, A and B, are 5.00 meters apart. Each source emits waves with wavelength 6.00 meters. Consider points along the line connecting the two sources.1) At what distance from source A is there constructive interference between points A and B?2) At what distances from source A is there destructive interference between points A and B? Note that there will be two separate interference fringes between point A and point B. Enter your answers in ascending order separated by a comma.I know 1) is 2.5m but for b i need more than 1 answer

Answers

Constructive interference between points A and B will occur at 2.5m from source A. Destructive interference between points A and B will occur 4m and 1m from source A.

Interference refers to a phenomenon where two waves are combined by adding their displacement together at every single point in space and time, to form a resultant wave of greater, lower, or the same amplitude. Constructive interference occurs when two waves overlap in a way to create a larger wave. Destructive interference occurs when two waves overlap in a way to cancel each other out.

The condition for constructive interference to occur is |dA-dB|=mλ

Where dA is the distance of the point from source A, dB is the distance of the point from source B, m is an integer number, and λ is the wavelength = 6m.

Based on the condition, there can be one solution when m = 0 otherwise the difference between dA and dB would be at least 6m which is impossible as the sources are at a distance of 5m. Hence,

dA – dB = 0

dA = dB = 5/2 = 2.5m

The condition for constructive interference to occur is |dA-dB|=(m+1/2)λ

Based on the condition, the solution will occur when m = 0 otherwise the point will not be between source A and B.

Hence, when m = 0

|dA-dB|=(0+1/2)λ=λ/2=3

Using dB = 5 – dA to find the possible solutions.

dA = dB + 3

dA = 5 - dA + 3

2dA = 8

dA = 4m

and

dB – dA = 3

5 – dA – dA = 3

2dA = 2

dA = 1m

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Which is the internal energy of an object due to the kinetic energy of its atoms and or molecules?

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Internal energy of equipartition energy is due to kinetic energy of molecules.

Some thermodynamic confusion. For simplicity we will assume an ideal gas.dU = n Cv dtIf a gas does some work adiabatically, heat change dQ = 0

There are now two possible cases:

1) Expansion occurs at the expense of the gas's internal energy, so the gas temperature decreases as it expands. Therefore U decreases.

2) As the temperature decreases, so does the velocity of the gas molecules and the K of the gas decreases continuously.

This concept often takes into account what considers heat as internal energy. Molecular kinetic energy, vibrations, rotations, electron "shell" positions, molecular bending, crystal lattice vibrations, etc.

Generally, pressure should be considered part of the internal energy. Theoretically, matter can be expanded or heat can be transferred to do work.

At absolute zero temperature and pressure we can see that there is still internal energy. This can be seen as a result of the blurring principle. Particles cannot be confined to too small a volume and velocity.

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a cart starting from a speed of 3 m/s moves down a slope and at the bottom has a speed of 7 m/s. what is the height of the slope?

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A cart speed will often increase on a downhill slope while decreasing on an uphill section. A steeper gradient portion has a more pronounced impact on the acceleration or slowdown of a vehicle's speed.

What effect of slope on speed of car?

The cart speed/velocity will progressively rise by the same amount each second. The rate of acceleration of the car increases with the slope's steepness (or the ramp's greater angle of inclination). This is so because the slope's angle determines how much gravity is felt.

Therefore, the more gravitational potential energy that can be turned into kinetic energy, the higher the ramp will be, and the more kinetic energy there is, the faster the car will move.

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A simple pendulum consisting of a bob of mass m attached to a string of length L swings with a period T. If the bob's mass is doubled, approximately what will the pendulum's new period be?

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The pendulum's new time period is T.

A bob suspended at the end of a thread that is so light as to be regarded massless makes up a simple pendulum. It serves as an example of a conservative oscillatory system. A point mass m anchored to one end of a massless rod of length L makes up this idealized representation of a pendulum.

The time period of a simple pendulum is calculated by the formula, [tex]T=2\pi\sqrt{\frac{L}{g}}[/tex] where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity. Since this formula is independent of mass, the change in the mass of the bob doesn't affect the time period. Therefore, the new time period will still be T. There is no change.

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a carnot engine operates between reservoirs at 500 k and 300k, discarding 1800 j of heat in each cycle. how much heat is supplied to the engine by the hot reservoir in each cycle? give your answer in j but do not include the units in the answer box.

Answers

The Carnot engine is 40% efficient.

It's far a super reversible thermodynamic manner that includes the subsequent 4 tactics, Isothermal growth, No different heating is more efficient than this one, as there may be no finite temperature distinction between the warmth supply and warmth receiver. Therefore, it's miles the most efficient reversible system.

A Carnot engine can be notion of to include a cylinder with adiabatic lateral partitions packed with a substance which can take in and supply warmness. The cylinder is closed by way of an adiabatic piston which could move out and deliver work. The cylinder can acquire paintings by means of shifting the piston inward.

The Carnot engine is a theoretical thermodynamic cycle proposed by means of Leonard Carnot. It estimates the maximum feasible performance that a heat engine all through the conversion manner of warmth into paintings and, conversely, operating among two reservoirs can own.

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an astronaut on the moon has a 110 kg crate and a 230 kg crate. how do the forces required to lift the crates straight up on the moon compare with the forces required to lift them on earth? (assume that the astronaut lifts with constant velocity in both cases.)

Answers

A lunar astronaut carries a 110 kg box and a 230 kg load. The forces required to move the containers straight up on the moon are enormous compared to the forces required to hoist them on Earth.

A forces is an influence with the capacity to change the motion of an object. When an object with mass moves away from rest, for example, a force can cause it to accelerate as its velocity increases. A push or a pull are two straightforward ways to demonstrate force. Since a force has both magnitude and direction, it is a vector quantity. It is computed using the SI unit of newton (N). The letter F stands for force (formerly P). The original wording of Newton's second law states that the net force acting on an item is equal to the rate of change of its momentum over time. This law states that if an object's mass stays constant, its acceleration should be directly proportional to the net force exerted on it and inversely proportional to the object's mass. Thrust, which increases an object's velocity; drag, which decreases an object's velocity; and torque, which modifies an object's rotational speed, are all ideas connected to force. Internal mechanical stress describes how these forces are distributed within the body. The adjacent regions are frequently put under stress by each expanded body part.

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calculate the wavelength for an electron moving at 3.00x103 m/s in nanometers. (mass of an electron

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The wavelength for an electron moving at 3.00x103 m/s is 244 nm

Given, Mass of electron = 9.1093 * [tex]10^{-31}[/tex]

velocity = 3.00 * [tex]10^{3}[/tex] m/s

wavelength λ = h / mv

λ = 6.626 * [tex]10^{-34}[/tex] / [tex]9.1093 * 10^{-31}[/tex] * [tex]3.00 * 10^{3}[/tex]

λ = 244 nm

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a car traveling 25 m/s begins to decelerate at a constant rate of 4 m/s^2. after how many seconds does the car come to a stop and how far will the car have travaled before stopping?

Answers

6.25 s does the car come to a stop and 78.125 m distance travelled before stopping.

Solution:

Given:

Initial velocity, v0 = 25 m/s

Acceleration, a = -4m/s2

Final velocity, vf = 0

Put these values in the formula,

To find time,

vf = v0 + a*t

0 = 25 - 4t

t = 25/4

t = 6.25 s

To find distance travelled,

d = ((vf + v0)/2)*t

d = 25/2 * 6.25

d = 12.5 * 6.25

d = 78.125 m

Hence,  6.25 s does the car come to a stop and 78.125 m distance travelled before stopping.

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the index of refraction of water and diamond are 1.33 and 2.42, respectively. in which medium does light travel faster? a. water b. diamond c. same speed in both water and diamond d. not enough information

Answers

The light travels faster in water medium with a density of 1.33 when compared to diamond medium with a density of 2.42.

A denser medium will have more matter compared to rarer medium. So, the scattering of light is higher in a denser medium resulting in lesser travel speed. Slower the speed higher will be the index of refraction. So light will travel more slowly in a dense medium.

Refractive index of Diamond = 2.42

Refractive index of water = 1.33

Since, refractive index is inversely proportional to speed of the wave, speed of light in water is higher than the speed of light in diamond.

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A blue car travels at a constant velocity of 24 m/s on a hot 100 degree summer day and has a momentum of 28,800 kg-m/s. What is the mass of the car? Data Formula Work

Answers

Answer:

the mass of the car is very big

Explanation:

its heavy

a block is placed on a spring, compressing it 0.30m. what height does the block reach when launched by the spring?

Answers

The height the block reachs when launched by the spring 0.917 m.

What is a box-spring system?

Simply said, a spring-mass system is a spring system with a block hanging or fastened to the free end of the spring. The period of any item moving in a simple harmonic motion may often be determined using the spring-mass system. There are several other uses for the spring-mass system. For instance, the spring-mass system may be used to replicate foot skin deformation and the action of human tendons using computer images. There are two ways to arrange spring mass systems. These consist of: The parallel arrangement of springs , a series of springs combined.

m = 0.5 kg , K = 100 N/m , ∆x = 0.3 m

By conservation of energy :-

KEi + PEg + PEelastic = KEf + PEg + PEelastic

0 + 0 + 0.5*K*∆x^2 = 0 + mgh + 0

0.5*100*(0.3)^2 = 0.5*9.81*h

h = 0.917 m

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a high or low tide that is more extreme than usual is a(n) tide; a weaker than usual tide is a(n) tide.

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A high or low tide that is more extreme than usual is a(n) tide, it is stronger than usual tide.

The moon is the primary cause of high and low tides. The tidal force is produced by the moon's gravitational pull. Earth and its water protrude outward on both the side that is closest to and farthest from the moon as a result of the tidal force. These watery peaks are high tides.

Your part of the Earth spins around both of these bulges every day. You encounter a high tide while you're inside one of the bulges. The tide is low when you are not in one of the bulges. On the majority of the world's coastlines, this cycle of two high tides and two low tides occurs every day.

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how much friction force must the brake apply to the rim to bring the he 3.40 kg , 32.0-cm-diameter disk to a halt in 2.50 s

Answers

We need to know angular acceleration α to  give answer to this question. For completing the question, suppose the disc is spinning at 300 RPM.

Angular acceleration α = (300× 2/ 60)/2.50 = 4 m/square second

The required torque L is given by

L = I*alpha,

where,

I = the moment of inertia of the disc,

I = (1/2) M R^2

Therefore

L = (1/2) M R^2 *4 rad/s^2

The units will be Newton-meters

Once you have determined L, use

F = L/R for the required friction force, in Newtons.

Friction is the force that always resists motion of a moving object on the surface of other object.

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When a weight W is hanging from a light vertical string, the speed of pulses on the string is V. If a second weight W is added without stretching the string, the speed of pulses on this string will now become Select one: a_ V/ V2 b. V/2 C V: d. 2V. e_ V V.

Answers

The pulse rate on a light straight string is V sqrt when a weight W is suspended from it (2V)

The correct answer is D

What the is physics' definition of speed, and how do you quantify it?

A distance's rate of change over time is used to calculate speed. It has a dimension of distance via time. The Vernier scales of speed is made up of the fundamental units of distance and time. The unit of speed in the metric system is meters per second.

Exactly what is speed?

What is considered speed? the rate at which an object's location changes in any direction. Speed is defined as the relationship between length and the time required to travel a distance. Speed is a scalar number because it has no magnitude and only a direction.

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how far from the lens should an object be held so that its image is seen at the near-point distance of 25 cm ? assume that your eye is immediately behind the lens.

Answers

The distance of lens from the object is 4.16 cm, so that its image is seen at the near-point distance of 25 cm.

The near-point distance of a human eye, described to be s = 25 cm, is the shortest item distance that a typical or "normal" eye is capable of accommodate, or to photo onto the retina. The some distance point of a human eye is the farthest object distance that a standard eye is able to photo onto the retina.

The human eye can see objects genuinely with none pressure on the attention while an item is placed at the least 25 cm away. This distance of 25 cm is called the close to point of the eye. while the object is positioned at a distance between 25 cm and infinity, the photo of the object is fashioned on the retina and interpreted surely.

Calculation:-

for magnifier

magnification m = 25 cm /f

5 = 25/f

f = 25/5 = 5 cm

ten using lens equation

1/f = 1/do + 1/di

1/5 = (1/do)-(1/25)

1/do = (1/5)+(1/25)

do = 4.16 cm

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The temperature at a point in a ball with conductivity is inversely proportional to the distance from the center of the ball. find the rate of heat flow across a sphere of radius with center at the center of the ball.

Answers

The heat flow of the thermal resistance is (r2 - r1) / 4πkr1r2).

Consider the diagram below, the heat flow will be

Fourier's law in radial coordinates

qr = -k.AdT/dr

Substituting the values of the area of sphere,

qr = -k (4πr²) dT/dr

Integrating we get

qr/4π∫dr/r^2 = ∫kdt

qr/4π ∫dr/r^2 = ∫kdt

qr/4π (1/r1 - 1/r2) = k(t2-t1)

qr = 4πkr1r2(t1-t2) / (r2 - r1)

The thermal resistance is expressed as

R = (r2 - r1) / 4πkr1r2)

Therefore, the heat flow of the thermal resistance is (r2 - r1) / 4πkr1r2).

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The specific gravity of an material is defined as the ratio of the density of the material to the density of water. the specific gravity of ice is 0.917, whereas that of seawater is 1.025. What fraction of an iceberg is above the surface of the water?

Answers

The specific gravity of an material is defined as the ratio of the density of the material to the density of water then the fraction of ice berg above the surface of water is 1.11ppm.

Specific gravity is defined by ASTM D4439 as the ratio of the density of the material in question to that of the reference material at the specified temperature and pressure conditions.

In practice, this is accomplished by measuring the mass of a unit volume of geosynthetics in a standard laboratory atmosphere and measuring again with the geosynthetics immersed in water. Substances with a specific gravity less than 1 float in water.

Geotextile specific gravity is actually the specific gravity of the polymeric raw material used to make the geotextile. Polyethylene and polypropylene float in the specific gravity range of 0.90 to 0.96, so be careful when working in water.

Fraction of iceberg = 1.025/0.917=1.11ppm

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Why did the team choose to measure the parallax of nearby stars, whose distances are already well known?

Answers

By utilizing the idea of parallax, we can decide how cosmologists decide distances to stars.

Presently, we perceive how parallax estimations can be utilized to decide the distances, one of the realities we know is that if we have any desire to gauge the distance of divine bodies, we are familiar with the parallax, first and foremost, point. That's what it intends assuming we can quantify tiny parallax points, we can gauge enormous distances moreover.

The purpose for why we can not make precise estimations of parallax past a specific distance is that as the distance of the star from earth builds the parallax point turns out to be tiny.

Subsequently, presently we comprehend how parallax estimations are utilized.

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What is the band gap energy in kilojoules per mole if blue diamonds absorb orange light with a wavelength of 675 nm?

Answers

The band gap energy in kilojoules per mole is 1.73×105 J.

The band gap is the distance between the valence band and the conduction band of an electron. Essentially, the bandgap represents the minimum energy required to excite an electron to a state in the conduction band where it can participate in conduction. Higher frequencies and lower wavelengths of light are absorbed.

In physics, especially for solids, the band gap is also called the energy gap. It is the range of energies that exist in solids where no other electronic state can exist. In the diagram of the electronic band structure of solids, the band gap is commonly called the energy difference.

Therefore, the band gap energy of wavelength 675 nm is 1.73×105 J.

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calculate the drift velocity of electrons in a 12-gauge copper wire (which has a diameter of 2.053 mm) carrying a 20.0-a current, given that there is one free electron per copper atom. (household wiring often contains 12-gauge copper wire, and the maximum current allowed in such wire is usually 20 a.)

Answers

The drift velocity of electron is 4.54 * 10⁻⁴ m/s.

Given that, Density of copper is 8.8* 10³ kg/m³

Charge of an electron is 1.6* 10⁻¹⁹ C

For the density of copper, the number of free electrons n can be calculated by

n = number of electrons per kg * ρ

⇒ (9.4776* 10²⁴ ) (8.8 * 10³ kg/ 1 m³) = 8.314 * 10²⁸ electrons per m³

Diameter of the wire is given as 2.053 mm

Let us calculate A for the provided diameter of wire

A = π * (d/2)² = π * (2.053 /2)² = 3.310* 10⁻⁶ m²

Given, I = 20 A

We know the expression for drift velocity as

Vd = I /(n* A* e) = 20 / (8.314 * 10²⁸ * 3.310* 10⁻⁶ * 1.6* 10⁻¹⁹) = 20 / (4.403 * 10⁴) = 4.54 * 10⁻⁴ m/s

Thus, the drift velocity of electron is 4.54 * 10⁻⁴ m/s.

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how does a sprinter sprint what is the forward force on a sprinter as she accelerates. where does that force come from

Answers

On the starting blocks, sprinters use their feet to push backward. The blocks respond by pressing forward with a force equal to this with their feet.

What drives the sprinter forward?

Vertical forces must be larger than the pull of gravity in order to assist the sprinter in moving forward as gravity is pushing him or her downward. The propulsive force is the force that propelled the runner forward.

Basketball players must jump straight up into the air, but how?

An interaction diagram and a free-body diagram should be included in your explanation. The player pushes down on the ground, which pushes up against him in return. As a result of his push being stronger than gravity, the player accelerates upward.

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if io is the intensity of the light incident on the first polarizer, what is the intensity of the light that passes through the second polarizer whose axis is oriented at an angle of 90 degrees with respect to the axis of the first polarizer?

Answers

Thus, light with an intensity of 2I will be incident on the second polarizer. The intensity will fall by a factor of cos2 across the second polarizer. As a result, the intensity is 2Icos2=2Icos2(450)=4I after going through the second polarizer.

How can you measure the brightness of light passing through a polarizer?

I = Io cos2, where Io is the original intensity and is the angle formed by the polarization direction and the filter's axis, gives the intensity of polarized light after it has passed through a polarizing filter.

What is the right way to calculate intensity?

I = P > A is the formula for intensity in physics. Power is measured in Watts while researching light waves, and since light is so large, area is typically measured in meters.

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a fish is 10.8 cm from the front surface of a fish bowl of radius 40 cm. where does the fish appear to be to someone in air viewing it from in front of the bowl? do not forget the proper sign.

Answers

The fish seems to be -12.96 cm when viewed from above, directly in front of the bowl. the point at which a fish is 10.8 cm from the front surface of a fish bowl with a 40 cm radius.

A surface is the outermost or highest layer of a physical object or place, to use the term in its most common usage. It is the area or piece of the thing where an observer can first perceive it through touch and sight and where other materials first come into contact with it. Any line segment that connects a circle's centre to its perimeter is considered a circle's or sphere's radius in classical geometry.

n1/do+n2/di = n2-n1/R

1/10.8 + 1.3/di = -.3/39

di = -12.96 cm  12.96 cm from the front surface of bowl.

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When viewed directly in front of the bowl from above, the fish seems to be 12.96 cm long. the spot where a fish is 10.8 cm from the front surface of a fish bowl with a 40 cm radius.

To use the word in its most common sense, a surface is the outermost or uppermost layer of a physical item or location. It is the region or portion of the object where an observer can first experience it through touch and sight and where other materials first come into contact with it. In classical geometry, a circle's or sphere's radius is any line segment that connects the center to the edge of the object.

n1/do + n2/di = n2/n1/R

1/10.8 + 1.3/di = -.3/39

di = -12.96 cm 12.96 cm away from the front surface of bowl.

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Question 11
Drop a ball off of a roof that is 12.2 m above the ground.
How much time will it take for the ball to reach the ground?
1.58s
O-2.49s
O 1.6s
O2.49s
5

Answers

2.49 seconds this is because of the amount of time it takes the ball to travel down

as you stand near a railroad track, a train passes by at a speed of 31.7 m/s while sounding its horn at a frequency of 218 hz. what frequency do you hear as the train approaches you? what frequency do you hear while it recedes? use 343 m/s for the speed of sound in air.

Answers

When the train approaches you, the Doppler's effect gives the frequency  240.12 Hz

When the train moves away from you, the Doppler's effect gives the frequency  199.6 Hz

Given that,

Frequency of train horn, f = 218 Hz

Speed of train, Vt = 31.7 m/s

The speed of the sound , V = 344 m/s

When the train approaches you, the Doppler's effect gives the frequency as follows :

[tex]f^{'} = f (V/ V-V_{0} )[/tex]

[tex]f^{'}[/tex] = 218 * ( 344/ 344 - 31.7)

   = 240.12 Hz

When the train moves away from you, the Doppler's effect gives the frequency as follows :

[tex]f^{'} = f ( V / V+ Vt)[/tex]

   = 218 * ( 344/ 344 + 31.7)

   = 199.6 Hz

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