Assuming air is an incompressible fluid, enter an expression for an estimate of the density of air, in terms of the defined quantities and the acceleration due to gravity, g.

Answers

Answer 1

Answer:

Density of Air = ([tex]P_{1}[/tex]  - [tex]P_{2}[/tex] )/(g x h)

Density of Air =  1.27 Kg/[tex]m^{3}[/tex]

Explanation:

Note: This question is not complete, and lacks its first part in which it contains important data to solve for the density of air. But, I have found the similar question and its data. So. I will be solving the question for the sack of understanding and concept.

Missing part: A weather balloon has an absolute-pressure sensor attached. On the ground the sensor reads [tex]P_{1}[/tex]  = 1.01x [tex]10^{5}[/tex] Pa. At a height of h = 950 m, the sensor reads [tex]P_{2}[/tex]=8.92x[tex]10^{4}[/tex] Pa.

Solution:

Let

[tex]P_{1}[/tex] be the pressure of the balloon at ground.

[tex]P_{2}[/tex] be the pressure of the balloon at height h = 950 m

g = acceleration due to gravity,

In order to derive the expression, we need to find the pressure difference:

Pressure difference = ΔP

ΔP = [tex]P_{1}[/tex]  - [tex]P_{2}[/tex]

As we know that,

Pressure difference = density x acceleration due to gravity x height.

So,

ΔP = [tex]P_{1}[/tex]  - [tex]P_{2}[/tex]  = (Density of Air) x (g) x (h)

We need expression for the density of air, so,

Density of Air = ΔP / (g x h)

Hence, the expression is:

Density of Air = ([tex]P_{1}[/tex]  - [tex]P_{2}[/tex] )/(g x h)

Now, we can calculate the density of air as well, by putting the values given above in the data.

[tex]P_{1}[/tex]  =  1.01 x [tex]10^{5}[/tex]

[tex]P_{2}[/tex] = 8.92 x [tex]10^{4}[/tex]

g = 9.8 m/s

h = 950 m

So,

Density of Air = ((1.01 x [tex]10^{5}[/tex]) - (8.92 x [tex]10^{4}[/tex]) )/ (9.8 x 950)

Density of Air =  1.27 Kg/[tex]m^{3}[/tex]

Answer 2

An expression for an estimate of the density of air is; ρ = ( P₁ - P₂)/gh

According to pascal's principle;

ΔP = ρgh

Where;

ΔP is change in pressure = P₁ - P₂

g is acceleration due to gravity

h is height of pressure change

Now, we want to find an expression for an estimate of the density of air. This means we want to make density the subject of the formula. Thus;

ΔP = ρgh

⇒ divide both sides by gh to get;

ρ = ΔP/(gh)

Recall that ΔP = P₁ - P₂

Thus; ρ = ( P₁ - P₂)/gh

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Related Questions

The most common complaint among patients about their doctors is the time spent waiting in the doctor's office. Patients claim that doctors overbook appointments. Doctors claim that a significant number of patients fail to show or are late for their appointments. Doctors also note that as medical professionals they must tend to anyone who has need of their service. The medical profession is also uncertain because doctors never know when an emergency will occur. Considering the economic concepts of scarcity and economic resources, why must doctors book as many patients as necessary during office hours?

A doctor has the time and resources to choose how many patients to treat

A doctor, by law, must treat every patient who shows up in a medical facility

A doctor must make as much money as possible during normal business hours

A doctor's time is scarce and must be used effectively to see the most patients​

Answers

Answer: B- a doctor, by law, must treat every patient who shows up in a medical facility

Explanation:

1. The volume of a given mass of gas is 20cm when its
pressure is 400mmHg. Calculate its pressure when the
volume becomes 80cm'at constant temperature,​

Answers

Answer:

Explanation:

The way to show a cubed substance is either like this³ or like this x^3. The small three is found at the bottom toolbar at the bottom of the question space marked by the  Ω symbol.

100 mmHg

Givens

V1 = 20 cm^3

V2 = 80 cm^3

P1 = 400 mmHg

P2 = ?

Formula

V1 * P1 = V2 * P2

Solution

20 * 400 = 80 * P2              Divide by 80

20 * 400/80 = P2

P2 = 8000 / 80

P2 = 100 mmHg

There are two different isotopes; X and Y, both contain the same number of radioactive substances. If sample X
has a longer half-life than Y, compare their rate of radioactive decay.
O A. Rate does not depend on half-life
B. Both of their rates are equal
O C. X has a smaller rate than Y
O D. X has a greater rate than Y​

Answers

Answer:

Half life refers to the time for 1/2 of the radioactive atoms to decay.

Suppose that X has a half life of 10 days and Y has a half life of 20 days

If both start out with 1000 radioactive atoms then after 20 days

X would have 250 radioactive atoms and Y would have 500 atoms

The rate of decay is greater for the shorter half life:

In the example given X  must have the smaller rate of decay because it has a longer half life.

True or False do Eclipses, tides, season, and moon phases ALL have to do with the positions of the Earth, Sun, and Mars.

Answers

I think the answer would be false

When a glass rod is rubbed with silk, the silk becomes negatively charged. Which of the following explanations best describes that is happening?

a. Electrons move from silk to glass
b. Electrons move from glass to silk
c. Protons move from silk to glass
d. Protons move from glass to silk

Answers

Answer: b. Electrons move from glass to silk

Explanation:

When the glass rod is rub over against the silk, the glass loses the electrons due to the physical contact with the silk and the friction so produced.  The surface of the glass becomes positively charged and the surface of the silk becomes negatively charged. As the surface of the glass loses electrons which are accepted by the silk surface.

please help thank you

Answers

Answer:

[tex]\theta \approx 59.036^{\circ}[/tex], [tex]T_{2} \approx 23.324\,N[/tex]

Explanation:

First we build the Free Body Diagram (please see first image for further details) associated with the mass, we notice that system consist of a three forces that form a right triangle (please see second image for further details): (i) The weight of the mass, (ii) two tensions.

The requested tension and angle can be found by the following trigonometrical and geometrical expressions:

[tex]\theta = \tan^{-1} \frac{W}{T_{2}}[/tex] (1)

[tex]T_{1} = \sqrt{W^{2}+T_{2}^{2}}[/tex] (2)

Where:

[tex]W[/tex] - Weight of the mass, measured in newtons.

[tex]T_{1}[/tex], [tex]T_{2}[/tex] - Tensions from the mass, measured in newtons.

If we know that [tex]W = 20\,N[/tex] and [tex]T_{2} = 12\,N[/tex], then the requested values are, respectively:

[tex]\theta = \tan^{-1} \frac{20\,N}{12\,N}[/tex]

[tex]\theta \approx 59.036^{\circ}[/tex]

[tex]T_{2} = \sqrt{(20\,N)^{2}+(12\,N)^{2}}[/tex]

[tex]T_{2} \approx 23.324\,N[/tex]

You are standing next to a table and looking down on a record player sitting on the table. Take the spindle (axis of rotation) to be the center of your coordinate system and the y axis to be perpendicular to the side of the player you are standing next to. Long-playing records revolve 33(1/3) times per minute. You put a small blob of clay at the edge of a record that has a radius of 0.15 m, positioning the clay such that it is at its greatest value of y at t = 0.

Equation of motion for the y component of the clay's position: y(t)=Asin(ωt+ϕi)

Required:
a. What is the rotational speed of the clay?
b. Determine the value of A in the equation of motion.
c. Determine the value of ϕi in the equation of motion. Suppose that −π<ϕi≤π

Answers

Answer:

a) the rotational speed of the clay is  3.45 rad/s

b) the value of A in the equation of motion is 0.15 m

c) the value of ϕi is 90° or π/2 rad.

Explanation:

 Given that;

Revolution per minute rpm = 33( 1/3) =  100/3

The frequency f = 100 / 3(60) = 0.55 Hz

a)

Rotational speed W = 2πf

we substitute

W = 2π × 0.55

W = 3.45 rad/s

Therefore, the rotational speed of the clay is  3.45 rad/s

b)

given equation; y(t)=Asin(ωt+ϕi)

given that radius = 0.15 m

y(t)=(0.2)sin(ωt+ϕi)

Therefore, the value of A in the equation of motion is 0.15 m

c)

since y(t) has the maximum value at t =0

so at t=0

y(0) = (0.15)sin(ω(0)+ϕi)

= 0.15sin(ϕi)

this will give maximum value when ϕi = 90°

so

y(0) = (0.15)sin(ω(0)+ϕi)

= 0.15sin(90°)

= 0.15

hence, the value of ϕi is 90° or π/2 rad.

Which is in the Moneran kingdom? A. plants B. bacteria C. animals D. mushrooms

Answers

Answer: b

Explanation:

A teacher places a warm bottles in a cooler filled with ice. Which statement best explains what happened over time?

A) Thermal energy will move from ice to water bottles
B) Coldness will move from the water bottles to the ice.
C) Coldness will move from the ice to the water bottlers
D) Thermal energy will move from the water bottle to the ice.

Answers

Answer:

D) Thermal energy will move from the water bottle to the ice.

Explanation:

Overtime, what happens is that thermal energy will move from the water bottle to the ice.

The water bottle is at a higher temperature compared to the ice. So, thermal energy will move from a place at higher temperature to one with lower temperature.

Thermal energy will stop moving until thermal equilibrium is attained. The water bottle will lose heat to the ice and by so doing it becomes colder. The ice will gain heat and begins to warm up

A truck pushes a mound of dirt 5 meters with a force of 75 newtons. How much
work has been done?

Answers

Answer:

[tex]375\:\mathrm{N}[/tex]

Explanation:

Work is given by the equation [tex]W=F\Delta x[/tex]. Plugging in given values, we get:

[tex]W=75\cdot 5=\fbox{$ 375\:\mathrm{N}$}[/tex].

At a certain instant, a ball is thrown downward with a velocity of 8.0 m/s from a height of 40 m. At the same instant, another ball is thrown upward from ground level directly in line with the first ball with a velocity of 12 m/s. Find (a) the time when the balls collide and (b) the height at which they collide. Take g = 10 m/s2

Answers

Answer:

(a) The two balls collide [tex]2\; \rm s[/tex] after launch.

(b) The height of the collision is [tex]4\; \rm m[/tex].

(Assuming that air resistance is negligible.)

Explanation:

Let vector quantities (displacements, velocities, acceleration, etc.) that point upward be positive. Conversely, let vector quantities that point downward be negative.

The gravitational acceleration of the earth points dowards (towards the ground.) Therefore, the sign of [tex]g[/tex] should be negative. The question states that the magnitude of [tex]g\![/tex] is [tex]10\; \rm m \cdot s^{-2}[/tex]. Hence, the signed value of [tex]\! g[/tex] should be [tex]\left(-10\; \rm m \cdot s^{-2}\right)[/tex].

Similarly, the initial velocity of the ball thrown downwards should also be negative: [tex]\left(-8.0\; \rm m \cdot s^{-1}\right)[/tex].

On the other hand, the initial velocity of the ball thrown upwards should be positive: [tex]\left(12\; \rm m \cdot s^{-1}\right)[/tex].

Let [tex]v_0[/tex] and [tex]h_0[/tex] denote the initial velocity and height of one such ball. The following SUVAT equation gives the height of that ball at time [tex]t[/tex]:

[tex]\displaystyle h(t) = \frac{1}{2}\, g \cdot {t}^{2} + v_0 \cdot t + h_0[/tex].

For both balls, [tex]g = \left(-10\; \rm m \cdot s^{-2}\right)[/tex].

For the ball thrown downwards:

Initial velocity: [tex]v_0 = \left(-8.0\; \rm m \cdot s^{-1}\right)[/tex].Initial height: [tex]h_0 = 40\; \rm m[/tex].

[tex]\displaystyle h(t) = -5\, t^{2} + (-8.0)\, t + 40[/tex] (where [tex]h[/tex] is in meters and [tex]t[/tex] is in seconds.)

Similarly, for the ball thrown upwards:

Initial velocity: [tex]v_0 = \left(12\; \rm m \cdot s^{-1}\right)[/tex].Initial height: [tex]h_0 = 0\; \rm m[/tex].

[tex]\displaystyle h(t) = -5\, t^{2} + 12\, t[/tex] (where [tex]h[/tex] is in meters and [tex]t[/tex] is in seconds.)

Equate the two expressions and solve for [tex]t[/tex]:

[tex]-5\, t^{2} + (-8.0)\, t + 40 = -5\, t^{2} + 12\, t[/tex].

[tex]t = 2[/tex].

Therefore, the collision takes place [tex]2\, \rm s[/tex] after launch.

Substitute [tex]t = 2[/tex] into either of the two original expressions to find the height of collision:

[tex]h = -5\times 2^{2} + 12 \times 2 = 4\; \rm m[/tex].

In other words, the two balls collide when their height was [tex]4\; \rm m[/tex].

The time the two balls collide is 0.4 seconds while the height at which they collide is 4m

The given parameters are :

Initial Velocity U = 8m/s

Height H = 40m

For the second ball, the initial velocity = 12m/s

a.) For the first ball, the height attained at the point of collision will be

h = ut + 1/2gt^2

h = 8t + 1/2 x 10t^2 ........ (1)

For the second ball, the height attained at the point of collision will be

h = 12t - 1/2 x 10t^2 .........(2)

Since the height will be the same for the two balls, equate the two equations

8t + 10t^2 = 12t - 10t^2

Collect the like term

8t - 12t = -5t^2 - 5t^2

-4t = -10^2

10t = 4

t = 4/10

t = 0.4s

b.) Substitute time t in any of the equation to find the height

h = 12(0.4) - 0.5 x 10(0.4)^2

h = 4.8 - 0.8

h = 4m

Therefore, the time the two balls collide is 0.4 seconds while the height at which they collide is 4m

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Plz help this is so confusing

Answers

The correct answer is 5 km/h

Explanation:

The speed at which the duck travels can be found by using the equation that is given (speed= distance/ time). The first step to do this is to replace distance and time using the values given. Here is the process:

speed = distance / time

speed = 10 km / 2 hours

Now, solve this equation

speed = 10 km/ 2 hours

10 / 2 or 10 divided 2 = 5

Finally, use the units, in this case, the correct units are km/h

Plz help this is so confusing

Answers

Answer:

5 Km/h

Explanation:

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

Distance travelled = 10 Km

Time = 2 hours

Speed =?

Speed is simply defined as the distance travelled per unit time. Mathematically, it can be represented as:

Speed = distance travelled /time.

With the above formula, we can obtain the speed at which the duck is travelling as follow:

Distance travelled = 10 Km

Time = 2 hours

Speed =?

Speed = distance travelled /time.

Speed = 10 / 2

Speed = 5 Km/h

Thus, the duck is travelling at a speed of 5 Km/h

a student lift a 25kg mass at vertical distance of 1.6m in a time of 2.0 seconds. a. Find the force needed to lift the mass (in N ). b. Find the work done by the student (in J). c. Find the power exerted by the student (in W)

Answers

Answer:

a. F = 245 Newton.

b. Workdone = 392 Joules.

c. Power = 196 Watts

Explanation:

Given the following data;

Mass = 25kg

Distance = 1.6m

Time = 2secs

a. To find the force needed to lift the mass (in N );

Force = mass * acceleration

We know that acceleration due to gravity is equal to 9.8

F = 25*9.8

F = 245N

b. To find the work done by the student (in J);

Workdone = force * distance

Workdone = 245 * 1.6

Workdone = 392 Joules.

c. To find the power exerted by the student (in W);

Power = workdone/time

Power = 392/2

Power = 196 Watts.

This illustration shows two opposing forces pulling on a wagon. Which description best describes how the wagon will move?
10N
30N
The wagon will slow down
The wagon will move to the left.
The wagon will not move because the forces are opposite
The wagon will move to the right.
4 5 6 7 8
9 10 11 12 13
Next
Type here to search

Answers

Answer:

The wagon will move to the right.

Explanation:

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

Force applied to the left (Fₗ) = 10 N

Force applied to the right (Fᵣ) = 30 N

Direction of the wagon =.?

To determine the direction in which the wagon will move, we shall determine the net force acting on the wagon. This can be obtained as follow:

Force applied to the left (Fₗ) = 10 N

Force applied to the right (Fᵣ) = 30 N

Net force (Fₙ) =?

Fₙ = Fᵣ – Fₗ

Fₙ = 30 – 10

Fₙ = 20 N to the right

From the calculations made above, the net force acting on the wagon is 20 N to the right. Hence the wagon will move to the right.

A girl walks 20.0 m east then 70.0 meters north. What is the girl’s displacement (mag. And direction)? What is the girl’s distance?

Answers

Explanation:

Given that,

A girl walks 20.0 m east then 70.0 meters north.

Displacement is the shortest path covered by an object. Let it is d. It is calculated as :

[tex]d=\sqrt{20^2+70^2} \\\\=72.80\ m[/tex]

For direction,

[tex]\theta=\tan^{-1}(\dfrac{70}{20})\\\\\theta=74.05^{\circ}[/tex]

Girl's distance = 20 m + 70 m

= 90 m

Hence, this is the required solution.

What is the kinetic energy of a disk with a mass of 0.20 g and a speed of 15.8 km/s?

Answers

Answer:

0.025J

Explanation:

Kinetic energy = ½ × Mass × velocity²

0.20÷1000=0.0002

½ × 0.0002 × 15.8²=0.024964J

A racecar makes 24 revolutions around a circular track of radius 2 meters in
162 seconds. Find the racecar's frequency

Answers

Answer:

[tex]0.15\: \mathrm{Hz}[/tex]

Explanation:

The frequency is of an object is given by [tex]f=\frac{1}{T}[/tex], where [tex]T[/tex] is the orbital period of the object.

Since the racecar makes 24 revolutions around a circular track in 162 seconds, it will take the racecar [tex]\frac{162}{24}=6.75\:\mathrm{s}[/tex] per revolution.

Therefore, the frequency of the racecar is [tex]\frac{1}{6.75}=\fbox{$0.15\:\mathrm{Hz}$}[/tex] (two significant figures).

The radius of the track is irrelevant in this problem.

Calculate the extension of a 20cm spring that has a spring contrast of 45000N/m and 1500N of elastic potential energy.

Answers

Answer:

See the answer below

Explanation:

The elastic potential energy can be calculated by means of the following equation:

[tex]E_{el}=\frac{1}{2} *k*x^{2}[/tex]

where:

Eel = elastic energy = 1500 [J]

k = spring constant = 45000 [N/m]

x = extension [m]

[tex]1500=\frac{1}{2} *45000*x^{2} \\3000=45000*x^{2} \\x=\sqrt{0.06666}\\x=0.258[m] = 25.8 [cm][/tex]

a toy car has a 2.0 A current, and its resistance is 1.75 ohms. How much voltage does the car require

Answers

Answer:

the answer will be 24.40 ohms law

Explanation:

What is the correct organization of living things, from smallest to largest?
Cells - Tissues - Organs - Organ Systems - Organism
Organs - Tissues - Cells - Organ Systems - Organism
Cells - Organs - Tissues - Organism - Organ Systems
Cells - Organism - Tissues - Organ Systems - Organs

Answers

The first one A should be your correct answer

What is the strength of an electric field that will put a force of
1.28 x 10-15 N on a proton?

Answers

Answer: E =  7,490.6 N/C

Explanation:

If we have a field E, and a particle with a charge q, the force that the particle experiences is:

F = E*q

In this case, we know that the force is:

F = 1.2*10^(-15) N

And we know that the particle is a proton, where the charge of a proton is:

q = 1.602*10^(-19) C

Then we can replace these two values in the equation to get:

1.2*10^(-15) N = E*1.602*10^(-19) C

We just need to isolate E.

(1.2*10^(-15) N)/(1.602*10^(-19) C) = E

7,490.6 N/C = E

That is the strength of the electric field.

An assessment tool that measures the amount of stress in a person’s life over a one-year period resulting from major life events is called

the Social Readjustment Rating Scale.

the Stress Scale.

the Annual Stress Scale.

the Social Scale.

Answers

Answer:

The correct answer is - the Social Readjustment Rating Scale.

Explanation:

The social readjustment rating scale is developed by Richard Rahe and Thomas Holmes to measure the stress caused by this important and major life event. Stress helps in developing a psychological approach for the particular person.

It is an assessment tool to calculate the impact of the major life events in the time period of one year with the help of units of 0 to 100. 100 is extreme or highest stress caused by the event such as the death of the spouse.

Planet Earth is held in orbit by the sun's gravitational force pulling on the Earth.
Which one of the following statements are true about that gravitational force?
The sun does not have a gravitational force because it is made of gas.
The earth pulls with more force since it is less massive than the sun.
The sun and the earth pull on each other with equal and opposite forces.
The sun pulls with more force since the sun is more massive than the earth.

Answers

Answer:

The sun pulls with more force since the sun is more massive than the earth.

Explanation:

That your answer because the Earth is getting pulled by the gravitational pull from the Sun

A receiver catches a football on the 50.0 yard line and is tackled 5.42 seconds later on the 12 yard line. What
was the runner's average speed?

Answers

Answer:

7.01yard/sec

Explanation:

Given parameters:

Initial position  = 50yard

Final position = 12yard

Time  = 5.42s

Unknown:

Average speed of runner  = ?

Solution:

To solve this problem;

        Speed  = [tex]\frac{distance}{time}[/tex]  

Distance covered  = Initial position  - final position  = 50 - 12  = 38yards

So;

       Speed  = [tex]\frac{38}{5.42}[/tex]   = 7.01yard/sec

at what speed does the kg ball move ?

Answers

Answer:  Choice A) 2 meters per second

=======================================================

Explanation:

The smaller ball has momentum of

p = m*v

p = (1 kg)*(4 m/s)

p = 4 kg*m/s

All of this momentum transfers into the larger ball because the smaller ball comes to a complete stop.

For the larger ball, we have p = 4 and m = 2. Let's find v.

p = m*v

4 = 2*v

4/2 = v

2 = v

v = 2 m/s which is why the answer is choice A

The larger ball moves at a speed of 2 meters per second. The speed is cut in half compared to the smaller ball because the larger ball has more inertia (aka more mass), and therefore it takes more energy to move it. If you apply the same energy to each, then the smaller object moves faster.

we had to drive 150 miles to the hotel we left at 1 p.m. and got there at 4 p.m. what is our average speed

Answers

Answer:

Our average speed was 50 mph

Explanation:

Constant Speed Motion

An object is said to travel at constant speed if the ratio of the distance traveled by the time taken is constant.

Expressed in a simple equation, we have:

[tex]\displaystyle v=\frac{d}{t}[/tex]

The distance we had to drive is d=150 miles. If we left at 1 p.m. and got to the hotel at 4 p.m. This means we took t=3 hours to get there.

The average speed is:

[tex]\displaystyle v=\frac{150\ miles}{3\ h}[/tex]

[tex]v=50\ mi/h[/tex]

Our average speed was 50 mph

Which ray diagram demonstrates the phenomenon of absorption?

An illustration with a vector pointed right going through an opening in a boundary and splitting into 3 vectors. One up and to the right, one straight and one down to the right.

An illustration with a vector pointed right going through an opening in a boundary and turning into a transverse wave on the other side.

An illustration with a vector striking a boundary at an angle and a second vector coming off the boundary at the exact same angle.

Answers

Answer:

B

Explanation:

on edge

The illustration with a vector pointed right going through an opening in a boundary and turning into a transverse wave on the other side demonstrates the phenomenon of absorption, so, option B is correct.

What is absorption?

Absorption, in wave motion, is the process by which a wave's energy is transferred to matter when the wave travels through it. The energy of an electromagnetic, acoustic, or other wave is related to the square of its amplitude, which is the maximum displacement or movement of a point on the wave.

The amplitude of a wave continuously diminishes as it travels through a substance. The medium is described as being transparent to a specific type of radiation if just a tiny portion of the energy is absorbed, whereas it is described as opaque if all the energy is lost.

To know more about absorption:

https://brainly.com/question/19053744

#SPJ2

PLEASEEEEEEEEE HELPPPPPPPPPP

Describe what determines magnetism.

Answers

Answer:

Magnetism is caused by the motion of electric charges. Every substance is made up of tiny units called atoms. Each atom has electrons, particles that carry electric charges. ... Their movement generates an electric current and causes each electron to act like a microscopic magnet.

Explanation:

A student asks the following question:
"If all things with mass have a gravitational field, why doesn't this glue bottle and
stapler, sitting on the counter, stick together because of gravitational forces?"
Which classmate answers correctly?
Ashton says that the gravitational fields between the bottle and the stapler
cancel out because of Newton's 3rd Law.
O Natalie says that all things with mass have a gravitational field, but the force is
very weak and cannot be perceived around small objects.
Xavier says the bottle and the stapler are way too small to have a gravitational
field.
Katherine says the bottle and the stapler have a strong gravitational field, and
would move towards each other quickly if there were no friction on the counter.

Answers

Answer:

  Natalie says that all things with mass have a gravitational field, but the force is very weak and cannot be perceived around small objects.

Explanation:

The force due to gravity is proportional to the mass of the object and inversely proportional to the square of the distance between objects. The Earth is so massive that the force due to its gravity is much greater than the force between objects on the counter.

If there were no friction, the objects might move toward each other, depending on what other masses were near them tending to cause them to move in other directions.

Natalie's explanation is about the best.

__

Additional comment

The universal gravitational constant was determined by Henry Cavendish in the late 18th century using lead balls weighing 1.6 pounds and 348 pounds. His experiment was enclosed in a large wooden box to minimize outside effects. While these masses are somewhat greater than those of a glue bottle and stapler, the experiment shows the force of gravity between "small" objects can be measured.

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