A ball with a mass of 2000 g is floating on the surface of a pool of water. What is the minimum volume that the ball could have without sinking below the surface of the water? (Note that water has a density of 1.00 g/cm³.)

Answers

Answer 1

Answer:

[tex]2000\; {\rm cm^{3}}[/tex].

Explanation:

When the ball is placed in this pool of water, part of the ball would be beneath the surface of the pool. The volume of the water that this ball displaced is equal to the volume of the ball that is beneath the water surface.

The buoyancy force on this ball would be equal in magnitude to the weight of water that this ball has displaced.

Let [tex]m(\text{ball})[/tex] denote the mass of this ball. Let [tex]m(\text{water})[/tex] denote the mass of water that this ball has displaced.

Let [tex]g[/tex] denote the gravitational field strength. The weight of this ball would be [tex]m(\text{ball}) \, g[/tex]. Likewise, the weight of water displaced would be [tex]m(\text{water})\, g[/tex].

For this ball to stay afloat, the buoyancy force on this ball should be greater than or equal to the weight of this ball. In other words:

[tex]\text{buoyancy} \ge m(\text{ball})\, g[/tex].

At the same time, buoyancy is equal in magnitude the the weight of water displaced. Thus:

[tex]\text{buoyancy} = m(\text{water}) \, g[/tex].

Therefore:

[tex]m(\text{water})\, g = \text{buoyancy} \ge m(\text{ball})\, g[/tex].

[tex]m(\text{water}) \ge m(\text{ball})[/tex].

In other words, the mass of water that this ball displaced should be greater than or equal to the mass of of the ball. Let [tex]\rho(\text{water})[/tex] denote the density of water. The volume of water that this ball should displace would be:

[tex]\begin{aligned}V(\text{water}) &= \frac{m(\text{water})}{\rho(\text{water})} \\ &\ge \frac{m(\text{ball}))}{\rho(\text{water})} \end{aligned}[/tex].

Given that [tex]m(\text{ball}) = 2000\; {\rm g}[/tex] while [tex]\rho = 1.00\; {\rm g\cdot cm^{-3}}[/tex]:

[tex]\begin{aligned}V(\text{water}) &\ge \frac{m(\text{ball}))}{\rho(\text{water})} \\ &= \frac{2000\; {\rm g}}{1.00\; {\rm g\cdot cm^{-3}}} \\ &= 2000\; {\rm cm^{3}}\end{aligned}[/tex].

In other words, for this ball to stay afloat, at least [tex]2000\; {\rm cm^{3}}[/tex] of the volume of this ball should be under water. Therefore, the volume of this ball should be at least [tex]2000\; {\rm cm^{3}}\![/tex].


Related Questions

Q1.
(a) Some students have designed and built an electric-powered go-kart. After testing, the
students decided to make changes to the design of their go-kart.
First design X
Final design Y
The go-kart always had the same mass and used the same motor.
The change in shape from the first design (X) to the final design (Y) will affect the top
speed of the go-kart.
Explain why.

Answers

Answer:Because if the shape gets changed it will move faster without to much weight

Explanation:

The reason galaxies that are distant from our galaxy move away from our galaxy more rapidly than those that are near is:

Answers

The reason galaxies that are distant from our galaxy move away from our galaxy more rapidly is more space expands between us and distant galaxies.

What is a galaxy?

A galaxy is a group of millions of stars and their systems that are grouped due to gravitational forces.

According to the Big Bang theory, galaxies are expanding and separate among them.

In conclusion, the reason galaxies that are distant from our galaxy move away from our galaxy more rapidly is more space expands between us and distant galaxies.

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Answer:

the galaxies are moving as the universe keep expanding .

Explanation:

Avery sees a UFO out her bedroom window and calls to report it to the police. She says, "The UFO moved 20.0 m east, 10.0 m north, and 30.0 m west before it disappeared." What was the displacement of the UFO while Avery was watching?

Answers

Answer:

10^2 + 10^2 = x^2

x = 14.2 m NW

An object has a mass of 8.0 kilograms. a 2.0-newton force moves the object a distance of 3.0 meters to the east, and then 4.0 meters to the north. what is the total work done on the object

Answers

Answer:

1. An object has a mass of 8.0 kilograms. A 2.-newton force displaces the object a distance of 3.0 meters to the east, and then 4.0 meters to the north. What is the total work done on the object? 1)10 J 2) 14 J 3) 28 J 4) 56 J I found the resultant of the two distances, which is 5 m, I used 5 m * 2 N=10 J, but it’s not the answer. 2. A 20-newton block is at rest at the bottom of a frictionless incline, since I can’t show you the diagram, I will describe it. Supposed a right triangle, the vertical height is 3 m, and the base is 4.0 m. Then the hypotenuse is the incline and the block is at the bottom. The question is: How much work must be done against gravity to move the block to the top of the incline? I know that conservative forces are forces for which the work done does not depend on the path taken but only on the initial and final positions. But here I Know I should use 3 m * 20N=60 J. but the thing is it starts from the bottom which is the bottom of the incline, and ends at the top, then it should be the length of the hypotenuse? But if it’s 3 m, then it should have started from left end of the base, not the right end of the base which is the bottom of the incline.

Reference: https://www.physicsforums.com/threads/what-is-the-total-work-done-on-the-object.241750/

A jar contains 100 marbles. There are 20 white marbles, 20 green marbles, 20
blue marbles, 20 red marbles, and 20 yellow marbles. Which of the following
represents the highest entropy for the jar of marbles?
A. The marbles are arranged in horizontal layers by color.
B. The marbles are arranged in a repeating pattern.
O C. The marbles are arranged in a random order.
O D. The marbles are arranged in vertical columns by color.

Answers

The highest entropy for the jar of marbles is represented by the marbles are arranged in a random order.

What is entropy?

Entropy is the measure of the degree of disorderliness of a system or degree of randomness of a system.

Entropy of a system increases with increase in randomness of the system or disorderliness of the system.

Thus, the highest entropy for the jar of marbles is represented by the marbles are arranged in a random order.

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does anyone know this whole distance and displacement concept it makes zero sense

Answers

Answer:

Distance is the total length travelled, or in other words, it is a measure of how far apart two objects are.


Displacement, on the other hand, the difference between the starting and and ending positions of an object.

For example, if a person walks 10m forwards, then 7m backwards, thereby ending up where he started, he will have travelled a distance of

10 + 7 = 17m .

But the difference between his starting and finishing positions is

10 - 7 = 3m.

If, however, the man walked 10m forwards and then 10m backwards, the distance he covered would be 10 + 10 = 20m, but the displacement would've been 0 as there would be no difference between his starting and ending positions.

Let me know if you still don't understand.

The force exerted on the tires of a car that directly accelerate it along a road is exerted by the

Answers

The force exerted on the tires of a car that directly accelerate it along a road is exerted by the road friction.

What is force?

Force is defined as the product of mass and acceleration of an object.

Friction is defined as the force that resists the movement of an object over another.

Therefore, the force exerted on the tires of a car that directly accelerate it along a road is exerted by the road friction.

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The James Webb Space Telescope (JWST) will allow us to look back in time and observe the early universe. You are a scientist trying to observe an object that emitted its light a long time ago.
(a) Explain why the light you receive from the object is red-shifted.

The object has a redshift of 7.6 and the JWST observes the object at a wavelength of 2 microme- tres (mid-infrared light).

(b) What is the wavelength of the light emitted by the object?
(c) What type of radiation was originally emitted by the object?



i will mark you as brainiest please help me sooner​

Answers

#a

This is because red color has higher wavelength and it can clear universe and our atmosphere better,

This has the same reason as how we can see only red color during sunset.

#b

[tex]\boxed{\sf z=\dfrac{ \lambda-\lambda_o}{\lambda_o}}[/tex]

lambda_o be x

Put values

[tex]\\ \rm\Rrightarrow 7.6=\dfrac{2\times10^{-6}-x}{x}[/tex]

[tex]\\ \rm\Rrightarrow 7.6=\dfrac{2\times 10^{-6}}{x}-1[/tex]

[tex]\\ \rm\Rrightarrow 8.6=\dfrac{2\times 10^{-6}}{x}[/tex]

[tex]\\ \rm\Rrightarrow x=0.23\times 10^{-6}m[/tex]

[tex]\\ \rm\Rrightarrow x=0.23\mu m[/tex]

spurs"" are probably the result of ____.

Answers

Spurs are probably the result of self-sustaining star formation.

What is the formation of gaseous spurs in spiral galaxies?

The gigantic form of the magnificent doppelganger spiral patterns that spiral outward from the galactic cores gave spiral galaxies their name. These light arms of spiral galaxies are frequently seen in optical pictures to be speckled with bright star-forming areas at regular intervals.

Smaller structures spread forth and rearward into the interarm area from each major spiral arm. Spiral-arm also known as spurs are the name given to these substructures. Sometimes the spurs are also filled with star-forming clusters. As a consequence, we may draw the conclusion that spurs most likely emerge from self-sustaining star formation.

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ons: READ each question below and ANSWER each part of the question.
Questions:
1. Ms. Woodard walks 1 m between each desk in her classroom. She walks
from desk 1 to desk 3, from desk 3 to desk 4, and finally from desk 4 back to
desk 2.
a. DRAW Ms. Woodard's path to all the desks here:
a.
a.
What DISTANCE has Ms. Woodard traveled? CONVERT (change) your answer to
millimeters.
What is Ms. Woodard's DISPLACEMENT?

Answers

Ms. Woodard has traveled a distance of 5 m.

Ms. Woodard's displacement is 1 m.

1.) Identify one component of the visible spectra
2.) identify the component of the electromagnetic spectra that has the shortest wavelength​

Answers

Answer:

1.) color

2.) Gamma Rays

Explanation:

Q2

the ultraviolet or UV portion of the spectrum has the shortest wavelengths which are practical for remote sensing. This radiation is just beyond the violet portion of the visible wavelengths.

im
Complete the sentence to describe what a wave is and what it does.

A wave is a
that carries
from one place to another.

Answers

A wave is a ( DISTURBANCE) that carries (ENERGY) from one place to another.

Hope this helps.

Good luck ✅.

Now, let's look at how the distance from the charge affects the magnitude of the electric field. Select Values on the menu, and then click and drag one of the yellow E-Field Sensors. You will see the magnitude of the electric field given in units of V/m (volts per meter, which is the same as newtons per coulomb). Place the E-Field Sensor 1 m away from the positive charge (1 m is two bold grid lines away if going in a horizontal or vertical direction), and look at the resulting field strength. Consider the locations to the right, left, above, and below the positive charge, all 1 m away. For these four locations, the magnitude of the electric field is________________. the same. greatest to the left of the charge. greatest below the charge. greatest to the right of the charge. greatest above the charge.

Answers

Electric field strength decreases as the distance from the source increases.

How the distance from the charge affects the magnitude of the electric field?

The strength of an electric field is inversely related to square of the distance from the source. This means that the electric field strength decreases when the distance from the source increases.

So we can conclude that Electric field strength decreases as the distance from the source increases.

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The chart lists four different kinds of atoms.

A chart titled Different Kinds of Atoms with the entries calcium, gold, argon, iodine.

What is true about all of these atoms?

They cannot be solids.
They are the largest units of matter.
They are the only types of atoms that exist.
They cannot be divided and still keep the properties of the element.

Answers

They cannot be divided and still keep the properties of the element true about all of these atoms. Option D is corect.

What is an atom?

The atom consists of matter that may be split without releasing electrical charges.

It's also the smallest unit of matter with chemical element features. As a result, the atom is the fundamental unit of science.

In the nucleus proton and the neutron is exists. The condition of the atom to be electrically neutral is that the number of the proton and electron should be the same.

They cannot be separated while still maintaining the element's characteristics for each and every one of these atoms.

Hence, option D is corect.

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Answer:

The correct answer is d, they cannot be divided and still keep the properties of the element.

Explanation:

You're welcome :)

what type of modulation does the omni-directional antenna transmit?

Answers

AM and FM are the two types of modulation that an omnidirectional antenna transmit.

What is an omnidirectional antenna?

An omnidirectional antenna is also referred to as an isotropic antenna and it can be defined as a type of antenna that is designed and developed to radiate equal radio power or intercept radio-frequency (RF), especially in all directions perpendicular to an axis.

In Science, there are two types of modulation that an omnidirectional antenna transmit and this include the following:

Frequency modulation (FM).Amplitude modulation (AM).

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View the graph of sun hours in a city.
Average Monthly Sun Hours in Addis Ababa, Ethiopia
300 hrs
150 hrs
0 hrs
Jan
Feb
Mar Apr May
Jul Aug Sep
Oct Nov
Dec
Jun
Month
It can be predicted that in the following year, this city can expect the hours of sunshine to significantly increase after
which month?
January
May
July
September

Answers

It can be expected in this city that the hours of sunshine will significantly increase after the month of July

What is the trend in the hours of monthly sunshine in Addis Ababa?

The monthly hours of sunshine in the city is the average of daily sunshine in a month.

The trend as seen on th graph shows that monthly hours of sunshine is maximum between the months of December and January. Afterwards the monthly sunshine hours decreases.

Therefore, it can be expected in this city that the hours of sunshine will significantly increase after the month of July.

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please answer this fast
I 'll marks them brainliest answer

Answers

answer

64 is C (c) 1-Bromo-3-methylbutane

63 is D

i is secondary ii is primary

which factors can change the size of the shadow of an opaque object

a)the color of the object b)the material the object is made from

c)how far the object is from the light source d)the size of the screen

Answers

Answer:

it have two answers a and c

Explanation:

please mark me as brainlyst

Answer: c)how far the object is from the light source
              d)the size of the screen

The size of the shadow depends on the distance of the source of light and on the angle at which the light rays fall on the object. If the source of light is closer to the object, a larger shadow is formed than when the source of light is far from the object.

The angle at which a light strikes an object affects the size and shape of its shadow. Shadows are longer when the light source is at a low angle (side on) and shorter when the light source is at a higher angle (overhead).

The position of the light source can change the size and shape of a shadow. A good example would be, when we are outside on a sunny day, we can see how our shadows change throughout the day. The Sun's position in the sky affects the length of the shadow.

∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
  hope it helped
┗━━━━━━━┛

If your mass is 63.7 kg, and you are standing 7.5 m away from a boulder with
a mass of 9,750.6 kg, what is the gravitational force between you and the
boulder? Newton's law of gravitation is F
Gm m₂. The gravitational
=
gravity
constant G is 6.67 x 10-11 N-m²/kg².

A. 1.10 x 104 N

B. 7.37 x 10-7 N

C. 9.82 x 10-8 N

D. 5.52 x 10-6 N

Please help me!

Answers

Answer:

B

Explanation:

F=[tex]\frac{Gm1m2}{r^2}[/tex]

F=(6.67 x 10^-11)[tex]\frac{63.7X9,750.6}{7.5^2}[/tex]

F=7.36502254e-7

as time passes the sound wave ​

Answers

Answer:

Loud to soft while pitch increases

Explanation:

Sound waves shown graphically display their amplitude (height of the graph) and their wavelength (the horizontal distance from peak to peak, or valley to valley... one full cycle).

Instead of wavelength, alternatively, one can observe the frequency of the wave (how many cycles are completed for a given unit of horizontal distance) which is in an inverse relationship with the wavelength (as a wavelength gets shorter, the frequency gets higher, and as the wavelength gets longer, the frequency gets lower).

The amplitude of a wave corresponds to how loud the sound is.

The frequency of a wave corresponds to the pitch of the sound.


Notice that on the graph, the height of the graph decreases over time (the peaks get shorter and shorter).  So, the sound volume will get quieter and quieter.  Using terminology that matches the answer choices, the sound will start loud and get soft.

Notice that on the graph, the wavelength decreases over time (starts with a pretty long distance between peaks, and then the distance between peaks gets shorter and shorter).  Alternatively, looking at frequency, notice that the frequency gets higher and higher (on the left, one finger-width doesn't is less than one full cycle, but on the right, the same finger-width is wider than multiple cycles).  So, the pitch of the sound will get higher and higher.

Thus, for this graph, the sound goes from loud to soft, and the pitch increases.

Discuss the path that light takes through the human eye

Answers

The cornea is shaped like a dome and bends light to help the eye focus. Some of this light enters the eye through an opening called the pupil (PYOO-pul). The iris (the colored part of the eye) controls how much light the pupil lets in. Next, light passes through the lens (a clear inner part of the eye).

From the cornea, the light passes through the pupil. The iris, or the colored part of your eye, controls the amount of light passing through. From there, it then hits the lens. This is the clear structure inside the eye that focuses light rays onto the retina.

1) Two students are making their way to school. One has a bike and the other
is on foot. If the student on foot is going at a speed of 3 m/s and they make
it to school in 30 s, how far away was the school?

Answers

To find how far away the school is:

3m/s * 30 s = 90m

Hope it helps!

Describe how the speed of a moving object can be measured using a tape measure and stopwatch

Answers

Answer:

See below

Explanation:

Measure the distance and the amount of time to cover that distance

 then speed   =    distance / time

Answer:

s=d/t

Explanation:

s=speed

d=distance

t=time

Just basic formula stuff

A particle moves along a straight line such that its acceleration is a=(4t^2-2)

Answers

The velocity of the particle moving along the straight line at any time, t is determined as v = 4t³/3 - 2t + C.

What is the velocity of the particle?

The velocity of an object is the rate of change of displacement with time. It is also the integral of acceleration of the object.

a = 4t² - 2

v = ∫a

v = 4t³/3 - 2t + C

Thus, the velocity of the particle moving along the straight line at any time, t is determined as v = 4t³/3 - 2t + C.

Complete question:

A particle moves along a straight line such that its acceleration is a=(4t^2-2). Find its velocity at any time, t.

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which of the numbers on this figure indicates typical continental conditions (regional metamorphism)?

Answers

The number that indicates typical continental conditions (regional metamorphism) is that showing schist and gneiss rocks.

What is regional metamorphism?

Regional metamorphism occurs when rocks undergoes changes as a result of high temperatures and pressure deep within the earth's crust.

Regional metamorphic rocks are usually foliated or squashed in appearance.

Examples of regional metamorphism rocks are schist and gneiss rocks.

Therefore, the figure that indicates typical continental conditions (regional metamorphism) is that showing schist and gneiss rocks.

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what evidence would you expect to find on the moon if it had been subjected to plate tectonics? (select all that apply.)

Answers

Volcanoes and mountains are the evidences that show plate tectonics.

What evidence would you expect to find on the Moon if the Moon had been subjected to plate tectonics?

The presence of volcanos and mountains are the evidences that provides information that the moon has plate tectonic. If there is no volcanoes and mountains on the moon then we can say that there is no plate tectonic on the moon.

So we can conclude that volcanoes and mountains are the evidences that show plate tectonics.

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One point charge has a magnitude 5.4x10-7 C. A second charge 0.25 meters away has a magnitude of 1.1x10-17 C. What is the electric force magnitude of one charge on the other?

Answers

The electric force on the charges will be equal and opposite in nature and the magnitude will be 8.5536 × 10⁻¹³ Newton.

Formula for electrostatic force is F = ( K q1 q2 )/ r²

where q1 and q2 represent the charges and r represents the distance between them and the value of K is 9 × 10⁹.

In question we have given

value of q1 = 5.4 x 10⁻⁷ C

value of q2 = 1.1 x 10⁻¹⁷ C

distance between the (r) = 0.25 m

Applying the formula

F = ( K x (5.4 x 10-7) x (1.1x10-17) )/ 0.25²

F = ( (9 × 10⁹ ) x (5.4 x 10-7) x (1.1x10-17) )/ 0.25²

F = ( (9 × 5.4 × 1.1) × ( 10⁹ × 10⁻⁷ x 10⁻¹⁷) )/ ( 6.25 × 10⁻² )

F = ( 53.46 × 10⁻¹⁵) / ( 6.25 × 10⁻² )

F = 8.5536 × 10⁻¹³ Newton

Electrostatic force = 8.5536 × 10⁻¹³ Newton

So, The point charges are possessing equal and opposite electrostatic force of magnitude 8.5536 × 10⁻¹³ Newton.

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How to add two on/off switches that can change the brightness of the light in circuit a without turning it off

Answers

Answer:

ressistor

Explanation:

help in solving this question please
(question is on the picture )

Answers

Answer:

Jesus

Explanation:

he is the way

how can scientists account for the fact that extrasolar planets seem to come in a wider range of types than the planets of our solar system?

Answers

Extrasolar planets come in a wider range of types than the planets of our solar system due to migration of the extrasolar planets and delay in clearing of the solar nebula.

What are extrasolar planets?

Extrasolar planets are planets which exists outside our solar system.

Ours solar system consists of the Sun and its planets.

The extrasolar planets come in a wider range of types than the planets of our solar system.

This is due to migration of the extrasolar planets and delay in clearing of the solar nebula.

Also, there are differences in nebula types.

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