what is the best approximation for the area of this circle? use 3.14 to approximate pi.

Answers

Answer 1

The best approximation is 201.0 [tex]in^{2}[/tex]

we know that

The area of the circle is equal to

[tex]A= \pi r^{2}[/tex]

In this problem we have

r =8 in

[tex]\pi =3.14[/tex]

substitute

A= (3.14) ([tex]8^{2}[/tex]) =201.0 [tex]in^{2}[/tex]

What is Pi ?pi—which is written as the Greek letter for p, or π—is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.Pi is most commonly used in certain computations regarding circles. Pi not only relates circumference and diameter. Amazingly, it also connects the diameter or radius of a circle with the area of that circle by the formula: the area is equal to pi times the radius squared. Additionally, pi shows up often unexpectedly in many mathematical situations. For example, the sum of the infinite series.

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Related Questions

a 40.0-kilogram child exerts a 100.-newton force on a 50.0-kilogram object. the magnitude of the force that the object exerts on the child is

Answers

The child is subjected to a force of 100 N from the object.

Given,

Mass of the child, m = 40 kgThe force exerted by the child, F = 100 NMass of the object, M = 50 kg

There is an equal and opposite reaction to every action, according to Newton's third law of motion.

The amount of force the item applied to the child was equal to the force the child applied to the object.These forces are acting in the opposite direction.

Thus, the child is subjected to a force of 100 N as a result of the object.

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suppose the wavelength of the light is 500 nm . how much farther is it from the dot on the screen in the center of fringe e to the left slit than it is from the dot to the right slit?

Answers

The difference for the nth maxima is 500n  farther is it from the dot on the screen in the center of fringe e to the left slit than it is from the dot to the right slit

The maximum intensity occurs at this location in a single-slit diffraction pattern as a result of secondary waves reinforcing one another there.

Distance from the screen's center dot

The difference is (500)(0) = 0 when viewed from the center (zeroth) fringe.

The difference for the first maximum is 500 nm.

It is equal to 500 x 2 1000 nm for the second.

As a result, we can say that the difference for the nth maxima is 500n.

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Rank the following areas in order of largest to the smallest change in average temperature since 1880.a. Northern Canadab. Western Europec. Southern Africad. Australiae. Eastern Pacific Oceanf. Antarctic Ocean

Answers

The geographical regions in different parts of the world are always characterized by different average temperatures during different given periods of time. Moreover, these average temperatures may increase or decrease, which depends on a lot of external geographical factors. The data representing the same has been mentioned above.

Since in 1880, the oceans can be sorted from largest to smallest based on their average temperature change. The order can be kept as-

1. Northern Canada

2. Western Europe

3. Australia

4. Southern Africa

5. Eastern Pacific Ocean

6. Antarctic Ocean

Therefore, the above order is the descending order of the area based on change in the temperature.

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An ostrich with a mass of 163 kg is running to
the right with a velocity of 14 m/s.
Find the momentum of the ostrich
Answer in units of kg · m/s.

Answers

The momentum of the ostrich is determined as 2,282 kg m/s.

What is momentum?

The momentum of an object is defined as the product of mass and velocity of the object.

The momentum of the ostrich running at the given velocity is calculated by applying the following formula as shown below.

P = m v

where;

m is the mass of the ostrichv is the velocity of the ostrich

P = 163 kg  x  14 m/s

P = 2,282 kg m/s

Thus, the momentum of the ostrich is a function of mass of the ostrich and velocity of the ostrich.

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Which of the following is not important when shopping for a credit card?
a. the costs of the card
b. the features of the card
c. what the card looks like
d. how you plan to use the card

Answers

Answer:

C

Explanation:

You don't want to buy a 1000 dollar credit card.

The features are useful, like the little sync feature to automatically pay is awesome.

The plan of use for the card is important

the card aesthetic doesn't affect the card in any way, just your personal preference

calculate the potential energy of a 40 gram sparrow resting on a branch 30 feet above the ground

Answers

Answer:

1.43 J

Explanation:

PE = mgh = (0.04 kg)(9.80 m/s2)(3.6576 m) = 1.43 J

You have to convert g to kg, and feet to m

PE = mgh

PE = (0.04) (9.8) (9.144)
= (0.392) (9.144)
= 3.584448 J

Approximately = 3.6 Joules

what fraction of ice is submerged when it floats in freshwater, given the density of water at 0 c is very close to 1000 kg / m3

Answers

The fraction of ice submerged when it floats in freshwater is 0.9.

Given that,

The density of water is 1000 kg/m³

The density of ice is 0.917 gm/cm³

Converting gm/cm³ to kg/m³

We get, 0.917 gm/cm³ = 917 kg/m³

Let ρ₁ = 1000 kg/m³, ρ₂ = 917 kg/m³

V₁ = Volume of water displaced = x V₂

V₂ = Volume of ice submerged

Archimedes principle states that buoyant force on the ice will be equal to the weight of the water displaced. It can be written as an equation as:

ρ₁ V₁ = ρ₂ V₂

V₁ = ρ₂ V₂/ ρ₁

x V₂ = 917 *V₂/ 1000

x = 0.9

Thus, the fraction of ice submerged in water is 0.9.

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If the acceleration of the body is towards the center what is the direction of the unbalanced force.

Answers

If  the acceleration of the body is towards the center, the direction of the unbalanced force is also toward the center.

According to the Newton's 2nd law of motion, the direction of the acceleration is the same as the direction of the net force.

Hence, if  the acceleration of the body is towards the center, the direction of the unbalanced force is also toward the center.

This is called a centripetal force and its direction is always toward the center. The magnitude of the force is given by:

F = mv²/r

Where:

F = centripetal force

m = mass of the object

v = tangential velocity

r = radius of the circle trajectory

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(01. 03 MC)
An object i moving 10 m/ to the outh. After one minute, it moving at a rate of 15 m/. Explain what type of motion thi i decribing. Then explain
whether thi repreent a calar or vector quantity

Answers

The motion being described is linear motion, and since it has direction, it is a vector quantity.

What type of motion is linear?

A linear motion is a style of motion in which the object's movement is inversely proportional to its speed and duration of motion.

This type of motion also happens in a straight line.

The following is the formula for final velocity in a linear type of motion:

v = u + at

where;

V is the object's final speed or moving rate.

u is an object's initial speed, and a represents its acceleration.

t is the object's motion in time.

Our equation is formed by the supplied statement as follows:

v = u + at

15 m/s = 10 m/s + 60a

Thus, the final velocity formula, which is a vector quantity, is shown by the equation above.

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Solomon arrives at his first day of work at a nuclear power plant. when putting on safety gear for the first time, he notices that everyone else is tucking their gloves into their sleeves, and he decides to do the same because he assumes this is part of the safety protocol. what kind of influence is solomon experiencing in this scenario?

Answers

The kind of influence which Solomon is experiencing in this scenario is generally referred to as informational social influence.

What is an informational social influence?

In Psychology, an informational social influence can be defined as a situation in which a person (individual) conforms to new information or arguments because he or she has a desire to be right (good and just), especially by looking to others who are believed to have more information.

This ultimately implies that, an informational social influence is a type of conformity which is associated with internalization and it typically occurs when a person (individual) is either unsure and skeptical about a situation or lacks knowledge.

In this context, we can reasonably infer that Solomon is experiencing informational social influence in this scenario.

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imagine that the source is to the right of the listener, so that the positive reference direction (from the listener to the source) is in the x direction. if the listener is stationary, what value does fl approach as the source's speed approaches the speed of sound moving to the right?\

Answers

The cost of method because the source's pace procedures the velocity of sound transferring to the proper will be 1/2fs.

When each movements withinside the same route with same velocity n' = n, i.e. there can be no Doppler impact because of the truth relative motion amongst deliver and listener is zero.

The motion of the observer will adjust the frequency of the measured sound from a table certain deliver: An observer moving in the direction of the deliver measures a higher frequency. An observer moving a ways from the deliver measures a lower frequency.

The Doppler impact is an alteration withinside the determined frequency of a legitimate due to motion of each the deliver or the observer. The actual trade in frequency is called the Doppler shift.

It will cause an increase in frequency heard thru an observer at the same time as the deliver is moving withinside the direction of the observer and a decrease in frequency heard thru an observer at the same time as the deliver is moving a ways from the observer. The doppler impact can be determined at the same time as an ambulance with a siren on procedures and passes an observer.

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How much energy is in the elastic potential energy store of a spring?

Answers

The elastic potential energy of a spring is the product of one-half of its spring constant and the square of its deformation.

The potential energy of the spring is defined as the potential energy stored as a result of the change in the shape of a particular elastic object or a spring.

The energy is stored before the force is removed, and the spring comes back to its original shape. It does work in the process. The deformation could involve compressing, stretching, or twisting the object.

It is calculated as the work done in stretching the spring, and it depends on the spring constant k, and the distance stretched.

The potential energy formula of a spring is given as

P.E = ½ k x2

Where,

k = the spring constant

x = the spring displacement

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provide a procedure how to solve the related rate problem: a l foot ladder is resting in a wall and start slipping along the wall at a rate of k m/sec. how fast is the based of the ladder moving away from the wall when the ladder is at the high h meters?

Answers

There are two methods:

Pythagorean Theorem

Take the Derivative with Respect to Time

Pythagorean theorem:

Let's name the horizontal distance from the wall to the bottom of ladder h, and the vertical distance from the ground to the top of ladder y. Then, because the ladder is l feet long, we may know at any time

This statement expresses the connection between

h² + y² = l²

the quantity you want (something about the vertical position of the ladder's top, y), and the quantity you've been given (something about the horizontal location of the ladder's bottom, x).

Take the Derivative with Respect to Time

h² + y² = l²

d/dt [h² + y²] = d/dt[l²]

2x dh/dt + 2y dy/dt = 0[*]

The last statement provides the necessary relationship between the unknown dy/dt and the known dh/dt.

So, once again, the problem is virtually solved.

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objects that radiate relatively well group of answer choices absorb radiation relatively well. reflect radiation relatively well. absorb and reflect radiation well.

Answers

They absorb radiation relatively well.

All bodies continuously emit and absorb radiation.

The rate of loss of heat from an warm object is proportional to temperature.

The perfect example of good emitter and absorber is black body, whereas a very shiny surface will be a poor emitter and absorber.

The intensity of radiation increases as body gets hotter and radiation is released.

Stars are also considered the best example of black body radiation.

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sealed beam headlights are being discussed. technician a say the lens of a sealed beam headlight has convex prisms molded into its inner surface to concentrate the light into a narrow beam. technician b says a sealed beam is an airtight assembly containing a filament, reflector, and lens. who is correct?

Answers

Technician A says the lens of a sealed beam headlight has convex prisms molded to the inner surface. Technician B says it’s an airtight assembly containing a filament, reflector, and lens. The correct statement is told by: both technicians.

What is a sealed beam component?

A sealed beam lamp is an enclosed bulb in front of a glass lens we can find in a headlamp. Each part of the sealed beam cannot be replaced separately. The sealed beam headlights have parabolic aluminized reflectors in the form of convex prisms molded to inner surface. It also contains a filame, reflector, and lense. Hence, both statement from the technicians are true.

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A piano tuner stretches a steel piano wire with a tension of 765 n. the steel wire has a length of 0.900 m and a mass of 6.75 g. What is the frequency fi of the string's fundamental mode of vibration?

Answers

Fundamental Frequency of the String is 177.42 Hz.

What does "frequency of a wave" mean?

The quantity of waves emitted by a source per second is known as a wave's frequency. Additionally, it is the quantity of waves per second that pass a specific spot. The hertz is a measure of frequency (Hz).

How can you determine a wave's frequency?

The equation f=v f = v, where is the wavelength in meters and v is the wave speed in m/s, can be used to determine the frequency of a wave if the wavelength and speed of the wave are known. This also provides the wave's frequency in Hertz.

The Tension in the String is 765 N.

Steel wire length L is 0.900 m

Mass of the string m is 6.75 g = 6.75 * 10^-3 kg.

Frequency of the string = n *(Velocity of the wave on the String/(2L) )

v = 319.37 m/sec

For Fundamental Frequency n = 1

Frequency = V / 2L

f = 319.37 / (2*0.9)

f = 177.42 Hz

How do frequency and wavelength differ?

The wavelength, which will also apply to troughs, is the separation between two wave crests. The frequency is measured in cycles per second (Hz), which is the quantity of vibrations that cross a specific area in a second (Hertz).

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What is the wavelength of 20 Hz?

Answers

The wavelength of wave is 0.15×10⁸m if its frequency is 20Hz.Waves need  medium to travel from one place to another.

Expecting a sinusoidal wave moving at a proper wave speed, frequency is conversely corresponding to recurrence of the wave: waves with higher frequencies have more limited frequencies, and lower frequencies have longer wavelengths.

Frequency relies upon the mode (for instance, vacuum, air, or water) that a wave goes through. Instances of waves are sound waves, light, water waves and occasional electrical signs in a conduit.

For electromagnetic wave ,we know an expression

c=ν × λ

where c is the defined as the speed of wave in any medium,

ν is  defined as the frequency of the wave and

λ is defined as the  wavelength of the wave.

We know that value of c=3×10⁸m/sec and we have v=20Hz

Therefore,3×10⁸=20×λ

=>λ=(3×10⁸)/20

=>λ=0.15×10⁸m

Hence, wavelength of wave is 0.15×10⁸m.

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Two forces act concurrently on an object. Their resultant force has the largest magnitude when the angle between the forces is.

Answers

Answer:

If the two forces are acting simultaneously on the body, then vector addition will supply us with the resultant force. Note that when the two forces are acting directly opposite each other, we expect the resultant to be smallest, and conversely, when they are acting in exactly the same direction, they will exert the greatest resultant force (simply the sum of the two force magnitudes).

The velocity of a proton in an accelerator is known to an accuracy of 0.250% of the speed of light. (This could be small compared with its velocity.) What is the smallest possible uncertainty in its position?

Answers

The smallest possible uncertainty in the position of the proton is 4.211×1/10¹⁴m.

The velocity of a proton in an accelerator is known to an accuracy of 0.250% of the speed of light.

∆x∆v = h/4πm

uncertainty in velocity, ∆v = 0.25×3×10⁸/100 = 4.211×1/10¹⁴m

What is a proton?

The number of protons in the nexus of an element is called the infinitesimal number. In the titles of any particular element, the number of protons in the capitals is always the same. A snippet of simple hydrogen has a nexus conforming of a single proton. The capitals of all other rudiments nearly always contain neutrons in addition to protons. Protons need not be confined to the capitals of titles. When protons are set up outside infinitesimal capitals, they acquire fascinating, crazy and potentially dangerous parcels, analogous to those of neutrons under analogous circumstances.

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A mass is connected to a spring and is allowed to move horizontally. The mass is at a position L when the spring is unstretched. The mass is then moved, stretching the spring, and released from rest. It then moves with simple harmonic motion. At the instant that the mass passes through the position where the spring is unstretched, what can be said about its instantaneous acceleration?

Answers

Maximum instantaneous speed occurs when the mass moves through the region where the spring is compressed.

Explain about the acceleration?

The rate at which the speed and direction of a moving object alter over time is known as acceleration. An item or point is said to be accelerated when it moves more quickly or more slowly in a straight path. Because the direction is always changing, travel on a circle accelerates even while the speed is constant.

The rate at which an object's velocity alters in relation to time is referred to as acceleration in physics. The acceleration of an object is the result of all the forces acting on it, according to Newton's Second Law. The meter per second squared is the unit of acceleration in the SI system (m s2).

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A car goes around a circular track at 30 m/s. If the radius of the curve is 90 m, what is the centripetal acceleration of the car in m/s2 ?.

Answers

The centripetal acceleration of the car on the circular track is found to be 10m/s².

The car is running on a circular track at a speed of 30m/s. The radius of the circular curve is 90 m.

The centripetal acceleration of the car is given by the relation,

a = v²/r

Where is the centripetal acceleration we is the speed of the car and R is the circular radius of the curve,

Putting values,

a = (30)²/90

a = 10m/s²

So, the centripetal  acceleration of the car is 10m/s².

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During most of its lifetime, a star maintains an equilibrium size in which the inward force of gravity on each atom is balanced by an outward pressure force due to the heat of the nuclear reactions in the core. But after all the hydrogen "fuel" is consumed by nuclear fusion, the pressure force drops and the star undergoes a gravitational collapse until it becomes a neutron star. In a neutron star, the electrons and protons of the atoms are squeezed together by gravity until they fuse into neutrons. Neutron stars spin very rapidly and emit intense pulses of radio and light waves, one pulse per rotation. These "pulsing stars" were discovered in the 1960s and are called pulsars.
Part A. A star with the mass (M=2.0×1030kg) and size (R=3.5×108m) of our sun rotates once every 35.0 days. After undergoing gravitational collapse, the star forms a pulsar that is observed by astronomers to emit radio pulses every 0.200 s . By treating the neutron star as a solid sphere, deduce its radius.
Part B. What is the speed of a point on the equator of the neutron star? Your answer will be somewhat too large because a star cannot be accurately modeled as a solid sphere.

Answers

The radius of star is [tex]97.22*10^{3} m[/tex].

Using the angular  formulas can determine the radius using both values neutron star and the the knowing star. So,

L=I*w

[tex]L_{1}=I_{1}*w_{1}=L_{2}=I_{2}*w_{2}[/tex]

[tex]I_{1}*w_{1}=I_{2}*w_{2}[/tex]

where,

           I=Inertia of the star

          w=angular velocity

[tex]I=\frac{2*m*r^{2}}{5}\\w=\frac{2\pi}{t}[/tex]

Notice the angular velocity determinate by the time and the Inertia have the radius value. So,

[tex]\frac{2}{5}*m*r_{sn}^{2}*\frac{2\pi }{t_{1}}=\frac{2}{5}*m*r_{s}^{2}*\frac{2\pi }{t_{2}}r_{sn}^{2}*\frac{1}{t_{1}}=r_{s}^{2}*\frac{1}{t_{2}}r_{sn}^{2}=r_{s}^{2}*\frac{t_{1}}{t_{2}}\\t_{1}=0.2s\\t_{2}=30day*\frac{24hr}{1day}*\frac{60minute}{1hr}*\frac{60seg}{1minute}=2.592*10^{6}s\\r_{sn}=3.5*10^{8}m*\sqrt{\frac{0.2s}{2.592*^{6}s}}\\r_{sn}=97.22*10^{3} m[/tex]

So the radius of the star is [tex]97.22*10^{3} m[/tex].

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the sun delivers an average power of 1.529 w/m2 to the top of neptune's atmosphere. find the magnitudes of max and max for the electromagnetic waves at the top of the atmosphere.

Answers

The magnitudes of Emax and  Bmax for the electromagnetic waves at the top of the Neptune's atmosphere are 33.95 N / C and 11.31 * 10⁻⁸ T respectively.

I = ( Emax )² / ( 2 μo c )

I = Intensity

Emax = Maximum Electric field

μo = Absolute permeability of free space

c = Speed of light

μo = 4π * 10⁻⁷ H / m

c = 3 * 10⁸ m / s

I = 1.529 W / m²

Emax² = I * 2 μo c

Emax² = 1.529 * 2 * 4π * 10⁻⁷ * 3 * 10⁸

Emax² = 1152.25

Emax = 33.95 N / C

I = c Bmax² / ( 2 μo )

Bmax² = 2 μo I / c

Bmax² = ( 2 * 4π * 10⁻⁷ * 1.529 ) / ( 3 * 10⁸ )

Bmax² = 128 * 10⁻¹⁶

Bmax = 11.31 * 10⁻⁸ T

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What is the frequency of a sound wave with a period of 2 seconds?

Answers

The frequency of a sound wave with a period of 2 seconds is 0.5Hz..Frequency is said to be inversely proportional to time period.

Frequency suggests the amount of cycles in a particular unit of time. The avocation for why the sky is blue or anything contains assortment can be really figured out by it. In addition, it can similarly get a handle on why the voice of specific individuals is significant while for others it isn't significant. Moreover, recurrence plays a significant impact on the notes of a piano or different instruments.

This number of occasions is obviously a major property of a wave. The waves incorporate people reliably. Besides, light is an electromagnetic wave and the fan is a sound wave. A wave is certainly a vibration and conveys energy with it. By and large objective, the amount of waves passing by each second suggests the repeat of the wave. Additionally, its assessment occurs in Hertz (Hz).

So, we know a formula

Frequency=1/Time period

which states that frequency is just converse of time period.

=>v=1/2

=>v=0.5/sec

or v=0.5Hertz.

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Which electromagnetic radiation wavelength is efficiently observed using ground based telescopes?

Answers

The majority of electromagnetic energy from space cannot reach the Earth's surface. The only light that reaches sea level is radio waves, visible light, and some ultraviolet light.

Some infrared wavelengths can be observed by astronomers by mounting telescopes on mountain peaks. The majority of space-derived electromagnetic radiation cannot reach the surface of the Earth due to the atmosphere. This diagram demonstrates how deep into the atmosphere various EM spectrum wavelengths can go before being absorbed. Radio and visible light only partially make it to the surface.A typical natural eye can detect frequencies between 380 and 750 nanometers. This contrasts with a band nearby 400-790 terahertz in terms of repetition. These restrictions are not specifically stated and may vary from person to person. These limits of human insight can extend to wavelengths of 310 nm (bright) and 1100 nm under perfect conditions (close to infrared).

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A moving car has 40,000 \mathrm{J}40,000J of kinetic energy while moving at a speed of 7.0 \mathrm{m} / \mathrm{s}7.0m/s. A spring-loaded automobile bumper compresses 0.30 \mathrm{m}0.30m when the car hits a wall and stops. What can you learn about the bumper’s spring using this information? Answer quantitatively and list the assumptions that you made.

Answers

Assuming the car stops instantaneously and that the spring is the only force acting against the car's kinetic energy:

When the car hits the wall, the spring-loaded bumper compresses 0.30 m. This means that the spring must have exerted a force on the car in the opposite direction of its motion.

The spring must have stored a minimum of 286,000 J (40,000 J of kinetic energy + 0.3 m of potential energy) of energy to bring the car to a stop.

Assumptions:

- The car stops instantaneously

- The spring is the only force acting against the car's kinetic energy

- The spring is linear (i.e. Hooke's Law applies)

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a 0.140-kg baseball is dropped and reaches a velocity of -1.20 m/s just before it hits the ground and bounces. it rebounds with an upward velocity of 1.00 m/s. if the interaction time between the baseball and the ground is 0.02 s, what is the average force during the bounce?

Answers

The average force during the bounce of a 0.140-kg baseball that is dropped and reaches a velocity of -1.20 m/s just before it hits the ground and bounces with an upward velocity of 1.00 m/s is 15.5 N

J = m Δv

J = Impulse

m = Mass

m = 0.14 kg

Δv = Change in velocity

Δv = vf - vi

vf = Final velocity

vi = Initial velocity

vf = 1 m / s

vi = - 1.2 m / s

Δv = 1 - ( - 1.2 )

Δv = 2.2 m / s

J = 0.14 * 2.2

J = 0.31 kg m / s

J = F Δt

F = Force

Δt = Change in time

Δt = 0.02 s

F = J / Δt

F = 0.31 / 0.02

F = 15.5 N

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You have a galaxy that is too far away to see individual stars, but you can see a little smudge of light from the galaxy.What would be the best way to find the distance to this galaxy?Group of answer choices- Red shift- Radar ranging- Triangulation- Cepheid variables- H-r diagram, brightness-distance- Type 1A supernova, brightness-distance

Answers

Using a high-resolution telescope like the Hubble space telescope is the most effective approach to determining the distance to a galaxy.

The most distant star ever observed is Icarus, a huge blue star that covers more than half the universe. Even with the biggest telescopes in the world, they are typically too faint to be seen.

However, scientists were able to find this far-off star and achieve new distance records because of a natural variation that considerably intensifies the star's feeble shine. Icarus was also used to test the dark matter hypothesis and investigate the makeup of nearby galaxy clusters.

This star is so far away, hidden in a very vast spiral galaxy, that it took nine billion years for its light to reach Earth. The cosmos seems to have existed when it was around 30% older than it is now.

This star can be seen because of gravitational lensing, a cosmic phenomenon. Light is bent and amplified by the gravity of large foreground galaxy clusters, which functions like a natural lens in the cosmos. A single backdrop object's light can produce several images. Light is bright enough to see extremely faint and far-off objects and is substantially intensified.

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how can an emperor penguin on the outer edge of a huddle conserve heat as efficiently as a penguin in the middle of the huddle?

Answers

The penguin that is currently on the outside of the group will eventually be in the middle. Because huddles are dynamic structures, no penguin can stay on the edge for very long.

While swimming in the ocean, a penguin's fat coat shields them from the cold. However, on land, their feathers serve as a means of heat retention. Instead of being long and flat like those of flying birds, penguin feathers are short and contain an underlayer of soft, woolly down. When a penguin comes out of the water, its feathers are excellent at shedding water. They cross each other, creating a good streamlined effect in the water and excellent wind-shedding properties on land. Penguins can puff their feathers out when it's extremely cold to capture more air and provide better insulation.

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A 12-kg block on a horizontal frictionle urface i attached to a light pring (force contant = 0. 80 kN/m). The block i initially at ret at it equilibrium poition when a force (magnitude P = 80 N) acting parallel to the urface i applied to the block, a hown. What i the peed of the block when it i 13 cm from it equilibrium poition?

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The speed of a 12 kg block on a frictionless horizontal surface attached to a light spring (force constant = 0.80 kN/m) when it is 13 cm from its equilibrium position is 1.32 m/s.

Law of conservation energy

The law of the conservation of energy states: “The total energy is constant in any process. It may change form or be transferred from one system to another, but the total is the same.”

Energy can be changed from one form to another (potential energy can be converted to kinetic energy) but the total energy in the domain remains the same.

The equation is:

Total energy = KE + PE

In a spring, the applied force is stored as potential energy which is given by

PE = ½ kx²

And kinetic energy:

KE =  ½ mv²

Remember that energy is the ability to do work and the work done is the force applied to an object and the resulting displacement.

So,

E = Fx

We have,

m = 12 kg

k = 0.8 kN/m

F = 80 N

x = 13 cm ⇒ 0.13 m

To determine the speed, use the equation:

Fx = ½ kx² + ½ mv²

80 (0.13) = ½ (0.8) (0.13)² + ½ (12)v²

10.4 = 0.00676 + 6v²

6v² = 10.39

v² = 1.73

v = [tex]\sqrt{1.73}[/tex]

= 1.315 ≈ 1.32 m/s

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Answer:

The answer should be about 0.77 m/s.

Explanation:

This is because there is a rightward force of 80 N (the applied parallel force that’s stated)
BUT, there’s also the leftward force which is the potential energy produced by the pulling of the spring,
which equals to: (0.5)*(k, or spring constant, or in this case 800N)*(x, or distance from equilibrium point, or in this case 0.13m)^2 = 0.5*800*0.13*0.13 = 6.76J
This is the work done by the spring, and since work equals Force times Distance(in this case 0.13m) we get 6.76=0.13F, solve for F, F=52N
NOTE: since this is a leftward force, it is a negative force.
This means that there’s a net force of 28N
Since: F=ma, 28=12a
Which is about: 2.33=a
Now, as we know, a equals change in velocity over change in time, so substitute into the equation above:
2.33 = deltaVelocity / deltaTime
deltaVelocity = finalVelocity(at 0.13m) - initialVelocity(in this case 0) = finalVelocity
deltaTime = finalTime(at 0.13m) - initialTime(in this case 0) = finalTime
And so: 2.33 = finalVelocity / finalTime
Rewrite: 2.33*(finalTime) = finalVelocity
As we know: (displacement) = (intialVelocity)*(time) + (0.5)*(acceleration)(time)^2
If we plug in everything we know: 0.13 = 0*t + 0.5*2.33*t^2
Simplify: 0.13 = 1.17*t^2
Solve for t: 0.11 = t^2
0.33 = t
Back to our previous equation: 2.33*(finalTime) = finalVelocity
Plug in 0.33 for time: 2.33*0.33 = finalVelocity = 0.7689
Round off: 0.77 m/s

*I apologize for not including units throughout all of my explanation, but it’s hard to write this much on my phone, and it’s currently 2am.
Also, some of my terms might probably not be the most commonly used, but it’s how i feel i can explain it best.
Also, judging by the wording of the question from the poster(which by the way has a bunch of misspellings), where they write “acting parallel to the surface is applied to the block, as shown” I’m led to believe it is the same problem I saw in my class, as a picture is displayed below with the parallel force pulling on the string, and the right answer was marked as 0.77 m/s.

**Please correct me if I’m wrong in any part of my explanation, as I’m still learning, but as I got this problem marked as correct, I’m led to believe I got this right ;-;

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