Find the magnitude of the gravitational force (in N) between a planet with mass 6.00 X 10^24 kg and its moon, with mass 2.50 X 10^22 kg, if the average distance between their centers is 2.70 X 10^8 m. What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.)

Answers

Answer 1

Answer:

Magnitude of gravitational force between this planet and its moon: approximately [tex]1.37 \times 10^{20}\; \rm N[/tex].

Acceleration of this moon towards the planet: approximately [tex]5.49 \times 10^{-3}\; \rm m \cdot s^{-2}[/tex].

Acceleration of this planet towards its moon: approximately [tex]2.29 \times 10^{-5}\; \rm m \cdot s^{-2}[/tex].

Explanation:

Look up the gravitational constant, [tex]G[/tex]:

[tex]G \approx 6.67 \times 10^{-11}\; \rm m^3\cdot kg^{-1} \cdot s^{-2}[/tex].

Assume that both this planet and its moon are spheres of uniform density. When studying the gravitational interaction between this planet and its moon, this assumption allows them to be considered as two point masses.

The formula for the size of gravitational force between two point masses [tex]m_1[/tex] and [tex]m_2[/tex] with a distance of [tex]r[/tex] in between is:

[tex]\displaystyle F = \frac{G \cdot m_1 \cdot m_2}{r^2}[/tex],

where [tex]G[/tex] is the gravitational constant.

Let [tex]m_1[/tex] and [tex]m_2[/tex] denote the mass of this planet and its moon, respectively.

Calculate the size of gravitational force between this planet and its moon:

[tex]\begin{aligned} F &= \frac{G \cdot m_1 \cdot m_2}{r^2} \\ &\approx \frac{6.67 \times 10^{-11}\; \rm m^3 \cdot kg^{-1} \cdot s^{-2} \times 6.00 \times 10^{24}\; \rm kg \times 2.50 \times 10^{22}\; \rm kg}{{\left(2.70 \times 10^{8}\; \rm m\right)}^2} \\ &\approx 1.37 \times 10^{20}\; \rm N\end{aligned}[/tex].

Assume that other than the gravitational force between this planet and its moon, all other forces (e.g., gravitational force between this planet and the star) are negligible. The magnitude of the net force on the planet and on the moon should both be approximately [tex]1.37 \times 10^{20}\; \rm N[/tex].

Apply Newton's Second Law of motion to find the acceleration of this planet and its moon:

[tex]\displaystyle \text{acceleration} = \frac{\text{net force}}{\text{mass}}[/tex].

For this moon:

[tex]\displaystyle \frac{1.37 \times 10^{20}\; \rm N}{2.50 \times 10^{22}\; \rm kg} \approx 5.49\times 10^{-3}\; \rm m \cdot s^{-2}[/tex].

For this planet:

[tex]\displaystyle \frac{1.37 \times 10^{20}\; \rm N}{6.00 \times 10^{24}\; \rm kg} \approx 2.29 \times 10^{-5}\; \rm m \cdot s^{-2}[/tex].


Related Questions

A 4.80 g bullet moves with a speed of 170 m/s perpendicular to the Earth's magnetic field of 5.00×10−5T.

Part A
If the bullet possesses a net charge of 1.06×10−8 C , by what distance will it be deflected from its path due to the Earth's magnetic field after it has traveled 1.00 km ?

Answers

Answer:

[tex]3.24\times 10^{-7}\ \text{m}[/tex]

Explanation:

m = Mass of bullet = 4.8 g

v = Velocity of bullet = 170 m/s

B = Magnetic field of Earth = [tex]5\times 10^{-5}\ \text{T}[/tex]

q = Charge of bullet = [tex]1.06\times 10^{-8}\ \text{C}[/tex]

a = Acceleration

Time the bullet will be in the air for is [tex]t=\dfrac{1000}{170}=5.88\ \text{s}[/tex]

Force is given by

[tex]F=ma[/tex]

Magnetic force is given by

[tex]F=qvB[/tex]

So

[tex]ma=qvB\\\Rightarrow a=\dfrac{qvB}{m}\\\Rightarrow a=\dfrac{1.06\times 10^{-8}\times 170\times 5\times 10^{-5}}{4.8\times 10^{-3}}\ \text{m/s}^2[/tex]

From the linear equations of motion we have

[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow s=0+\dfrac{1}{2}\times \dfrac{1.06\times 10^{-8}\times 170\times 5\times 10^{-5}}{4.8\times 10^{-3}}\times 5.88^2\\\Rightarrow s=3.24\times 10^{-7}\ \text{m}[/tex]

The defelection of the bullet is [tex]3.24\times 10^{-7}\ \text{m}[/tex]

Hmmm... Who can answer this question?

How did life begin?

Just a practice

Answers

Answer:

The earliest known life-forms are putative fossilized microorganisms, found in hydrothermal vent precipitates, that may have lived as early as 4.28 Gya (billion years ago), relatively soon after the oceans formed 4.41 Gya, and not long after the formation of the Earth 4.54 Gya.

Explanation:

Is this what your looking for?

significance of practicals in the discipline of geography​

Answers

Geographic information provides context for understanding spatial relationships and human-environment interaction. Geography is considered a science and thus also uses the scientific method for data collection, analysis, and interpretation.

Why Geography is a discipline?
Geography as a discipline is related to space and takes note of spatial characteristics and attributes. It studies the patterns of distribution, location and concentration of phenomena over space and interprets them providing explanations for these patterns.

When you turn off your bedroom lights, the kitchen lights can stay on. This is because your home is wired using which of the following? (AKS 10b / DOK 1)

A.
Fuses

B.
Series circuits

C.
Batteries

D.
Parallel circuits

Answers

The answer is b I think

When you turn off your bedroom lights, the kitchen lights can stay on. This is because your home is wired by using the series circuit. Hence, option B is correct.

What is a Series circuit?

The amount of current in the flow circuits of each element in a series circuit is the same. This is due to the recent flow having a single path. The flow rate (marble speed) at any point in a circuit (tube) at any given moment in time has to be equal because electric current moves through a conductor like marble in a duct.

The requirement that all values (voltage, current, resistance, and power) relate to one another in terms of the identical two places in a circuit is a significant exception to Ohm's law.

Therefore, the wiring of the home is in series combination. So, option B is correct.

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2. Heather and Matthew walk with an average velocity of +0.87 m/s eastward.
If it takes them 27 minutes to walk to the store, what is their
displacement? (include direction)
(5 points)

Answers

The answer is 27 minuets

Zookeepers carry a stretcher that holds a sleeping lion. The total mass of the stretcher and lion is 175 kg. The lion's forward acceleration is 2 m/s2. What is the force necessary to produce this acceleration?

Answers

Answer:

350 N

Explanation:

Newton's second law:

∑F = ma

∑F = (175 kg) (2 m/s²)

∑F = 350 N

1.) There was an earthquake in Salt Lake City, Utah, on March 18, 2020, in the morning at  9 hours, 9 minutes, and 45 seconds Mountain Standard Time (9:9:45 MST).  If the velocity of the p-wave is 7.3 km/sec and the velocity of the s-wave is 5.1 km/sec and the s-p time lag is 16 seconds, what is the distance in kilometers from Salt Lake City to the focus of the earthquake?  Explain how you calculated the answer.


Answers

Answer:

7 because salt lake and Southis weat

If you jump upward with a speed of 1.70 m/s how high will you be when you stop rising?

Answers

Answer:

How long do you jump (sec) ?

Explanation:

Help me guys please with this question

Answers

Answer:

[tex]\mid \vec C\mid=31.9[/tex]

Explanation:

Consider the vectors:

[tex]\vec A=9.4\mathbf{\hat{i}}-3.6\mathbf{\hat{j}}[/tex]

[tex]\vec B=-9.5\mathbf{\hat{i}}-13.4\mathbf{\hat{j}}[/tex]

Calculate the magnitude of

[tex]\vec C=-2\vec B-\vec A[/tex]

Substitute the values of the vectors:

[tex]\vec C=-2(-9.5\mathbf{\hat{i}}-13.4\mathbf{\hat{j}})-(9.4\mathbf{\hat{i}}-3.6\mathbf{\hat{j}})[/tex]

Operate and remove parentheses:

[tex]\vec C=19\mathbf{\hat{i}}+26.8\mathbf{\hat{j}}-9.4\mathbf{\hat{i}}+3.6\mathbf {\hat{j}}[/tex]

Operating both components separately:

[tex]\vec C=9.6\mathbf{\hat{i}}+30.4\mathbf{\hat{j}}[/tex]

Now find the magnitude of C:

[tex]\mid \vec C\mid=\sqrt{9.6^2+30.4^2}[/tex]

[tex]\mid \vec C\mid=\sqrt{1016.32}[/tex]

[tex]\mathbf{\mid \vec C\mid=31.9}[/tex]

A force of 1.50 N acts on a 0.20 kg trolley so as to accelerate it along an air track.
The track and force are horizontal and in line. How fast is the trolley going after acceleration from rest through 30 cm, if friction is negligible?

Answers

Answer: The trolley is moving at 2.12m/s

Explanation:

Given from the question that the track and force are horizontal and inline, we have that

F= ma

where F= force= 1.50 N

m= mass = 0.2kg

therefore Acceleration , a = F/ m= 1.50/0.2 =7.5 m/s^2

To find how fast the trolley  is going ie the Velocity, v

Having that

initial velocity at rest , u = 0,

acceleration a = 7.5 and

and distance, s = 30 cm =  30/100 = 0.30 m

we use motion equation that

v² = u² + 2 a s

v² = 0² + 2 x 7.5  x 0.30

v² = 4.5

v = [tex]\sqrt{4.5}[/tex]

v = 2.12 m/s

The second-order dark fringe in a single-slit diffraction pattern is 1.40 mm from the center of the central maximum. Assuming the screen is 89.0 cm from a slit of width 0.710 mm and assuming monochromatic incident light, calculate the wavelength of the incident light.

Answers

We know, for single slit :

[tex]y =\dfrac{ n\lambda L}{a}\\\\\lambda = \dfrac{ya}{nL}[/tex]       ...1)

[tex]y = 1.4\ mm = 1.4 \times 10^{-3}\ m[/tex]

n = 2

L = 89 cm = 0.89 m

[tex]a=7.1\times 10^{-4}\ m[/tex]

Putting all these in equation 1), we get :

[tex]\lambda = \dfrac{ya}{nL}\\\\\lambda = \dfrac{1.4\times 10^{-3}\times 7.1\times 10^{-4}}{2\times 0.89 }\\\\\lambda = 5.584 \times 10^{-7}\ m[/tex]

Therefore, wavelength of the incident light is [tex]5.584 \times 10^{-7}\ m[/tex] or 558.4 nm.

Hence, this is the required solution.

Why does a watched pot never boil?

Answers

This phrase means that time seems to slow down when one is waiting for something to happen desperately

How many stars are in the universe (approximately)? O 40 sixtillion 0 365 billion O 86.4 million O one​

Answers

Answer:

a i belive

Explanation:

the univerce is VERY large so a, if im wrong i apologise :(

Calculate the average induced voltage between the tips of the wings of a Boeing 747 flying at 970 km/hr above East Lansing. The downward component of the earth's magnetic field at this place is

Answers

This question is incomplete, the complete question is;

Calculate the average induced voltage between the tips of the wings of a Boeing 747 flying at 970 km/hr above East Lansing. The downward component of the earth's magnetic field at this place is 0.7 × 10⁻⁴ T. (DATA: Assume that the wingspan is 60 meters.)

Answer:

the average induced voltage between the tips of the wings of a Boeing 747 flying is 1.132 Volts

Explanation:

Given that;

Speed S = 970 KM/hr

downward component of the earth's magnetic field B = 0.7 × 10⁻⁴

wingspan 1 = 60min

Velocity V = (970 × 10³) / 3600 = 269.44 m/s

So Average Induced Voltage E = VBI

we substitute

E = 269.44 × (0.7 × 10⁻⁴) × 60

E = 1.132 Volts

Therefore the average induced voltage between the tips of the wings of a Boeing 747 flying is 1.132 Volts

Morgan does 50 J of work with a lever
that has an efficiency of 92%. What is
the output work of the lever?

Answers

Answer:

46 J

Explanation:

Simply calculate the 92% of 50 Joules as:

0.92 * 50 J = 46 J

The metric unit of power is _____.

Answers

Answer:

Watt

Explanation:

Power is defined as the work done by an object per unit time. Its mathematical form is given by :

[tex]P=\dfrac{W}{t}[/tex]

The SI unit of work done is Joules (J) and that of time is seconds (s).

J/s is equal to watts. Watt is the metric unit of power.

In football we see unbalanced forces. When 1 player exerts an unbalanced force on another player and causes a player to

Answers

Answer:

Fall

Explanation:

Catching a wave, a 77 kg surfer starts with a speed of 1.3 m/s, drops through a height of 1.65 m, and ends with a speed of 8.2 m/s. How much non-conservative work was done on the surfer?

Answers

Answer:

Explanation:

The total work done by the wave is expressed as;

Workdone = Potential energy + Kinetic energy

Workdone = mgh + 1/2mv²

m is the mass = 77kg

g is the acceleration due to gravity = 9.8m/s²

v is the velocity = 8.2m/s

h is the height = 1.65m

Substitute into the formula;

Workdone = 77(9.8)(1.65) + 1/2(77)8.2²

Workdone = 1245.09 + 2588.74

Workdone = 3833.83Joules

Hence the amount of non conservative work done on the sofa is 3833.83Joules

The non-conservation work done will be "3833.83 Joules".

Given:

Velocity, v = 8.2 m/sHeight, h = 1.65 mMass, m = 77 kg

We know,

→ [tex]Work \ done = Potential \ energy +Kinetic \ energy[/tex]

or,

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

By putting the values,

                     [tex]= 77\times 9.8\times 1.65+\frac{1}{2}\times 77\times (8.2)^2[/tex]

                     [tex]= 1245.09+2588.74[/tex]

                     [tex]= 3833.83 \ Joules[/tex]

Thus the above approach is right.

Learn more about work done here:

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C4. A 50.0 kg boy runs at 10.0 m/s, jumps on a cart and rolls off at 2.50 m/s. What is the mass of the cart

Answers

Answer:

The mass of the cart is 150 kg.

Explanation:

Given that,

Mass of a boy, m₁ = 50 kg

Initial speed of boy, u₁ = 10 m/s

Initial speed of car, u₂ = 0 (at rest)

The speed of the cart with the boy on it is 2.50 m/s, V = 2.5 m/s

Let m₂ is the mass of the cart. Using the conservation of momentum as follows :

[tex]m_1u_1+m_2u_2=(m_1+m_2)V\\\\50(10)+m_2(0)=(50+m_2)(2.5)\\\\500=125+2.5m_2\\\\375=2.5m_2\\\\m_2=150\ kg[/tex]

So, the mass of the cart is 150 kg.

Objects are lighter on the moon than they are on earth. if an object A weighs 25lbs on the Moon and another object B weighs 25 Newtons on earth, which has more mass?

a. Object a
b. Object b
c. Same mass
d. Other

Answers

Answer:

a. Object A

Explanation:

The mass of an object implies the quantity of matter in it, while the weight is the amount of gravitational force applied on an object.

The object A has a mass of 25 lbs, but object B on the earth has a weight, W, of 25 N.

So that,

For object A on the moon, mass = 25 lbs

For object B on the earth, W = 25 N,

W = m x g

25 = m x 10                (g = 10 m/[tex]s^{2}[/tex])

m = [tex]\frac{25}{10}[/tex]

   = 2.5 lbs

Mass of object B is 2.5 lbs.

Therefore, the mass of the object A is more than that of B.

A golf ball (m=26.7g) is struck a blow that makes an angle of 33.6 degrees with the horizontal. The drive lands 190m away on a flat fairway. The acceleration of gravity is 9.8 m/s^2 . If the golf club and ball are in contact for 7.13 ms, what is the average force of impact?

Answers

Answer:

Th average force impact is [tex]F = 168.298 \ N[/tex]

Explanation:

From the question we are told that  

   The mass of the golf ball is  [tex]m_g = 26.7 \ g = 0.0267 \ kg[/tex]

    The angle made is [tex]\theta = 33.6 ^o[/tex]

    The range of the golf ball  is [tex]R = 190 \ m[/tex]

     The duration of contact is [tex]\Delta t = 7.13 \ ms = 7.13 *10^{-3} \ s[/tex]

Generally the range of the golf ball is mathematically represented as

       [tex]R = \frac{v^2 sin2(\theta)}{g}[/tex]

Here v  is the velocity with which the golf club propelled it with, making  v the subject

       [tex]v = \sqrt{\frac{R * g}{sin 2 (\theta)} }[/tex]

=>     [tex]v = \sqrt{\frac{190 * 9.8}{sin 2 (33.6)} }[/tex]

=>     [tex]v = 44.94 \ m/s[/tex]

Generally the change in momentum of the golf ball is mathematically represented as

      [tex]\Delta p = m * (v - u )[/tex]

here u  is the initial  velocity of the ball before being stroked and the value is 0 m/s

       [tex]\Delta p = 0.0267 * ( 44.94 - 0 )[/tex]

=>    [tex]\Delta p = 1.19996 \ kg \cdot m/s[/tex]

Generally the  average force of impact is mathematically represented as      

         [tex]F = \frac{\Delta p }{\Delta t}[/tex]

=>        [tex]F = \frac{1.19996 }{7.13 *10^{-3}}[/tex]

=>        [tex]F = 168.298 \ N[/tex]

     

If you are riding your bike west to your friend’s house, and you ride the 1.25 miles in 5 minutes, what is your velocity, in miles per hour?

Answers

Answer:

velocity = 15 miles / hour

Explanation:

distance = 1.25 mile

time traveled = 5 min.

find velocity in miles / hour

solution:

use the formula: velocity = distance / time

velocity =     1.25 mile     x 60 min  

                     5 min            1 hour

velocity = 15 miles / hour

A spring gun fires a ball horizontally at 15 m/s. It is mounted on a flat car moving in a straight line at 25 m/s. relative to the ground, what is the horizontal speed of the ball when the gun is aimed forward?

Answers

Answer:

15 m/s

Explanation:

The Speed Of The Car Does Not Add To The Speed Of The Bullet

from a flying aeroplane abody should be dropped in advance to hit the target why​

Answers

the body should be dropped in advance as when the body is dropped it has the velocity of the plane. So, in air the body moves forward which we have to take into consideration in order to hit the target.

From a flying plane a body should dropped in advance to hit the target,Why? ... The body should be dropped in advance as when the body is dropped it has the velocity of the plane. So, in air the body moves forward which we have to take into consideration in order to hit the target.

Fast and safe heart rate for workouts is called muscular strength? True or false

Answers

Answer:

False

Explanation:

Answer:

False

Explanation:

Hope this helped, Have a Wonderful Day/Night!!

a heavty downpour and thundrstorm is probably caused by

Answers

Ah Hurricane, I Believe

* WILL GIVE BRAINLIEST TO CORRECT ANSWER *
Name a product that people commonly purchase by mass and not by weight.

Answers

I would say food but like they take weight too


In ultimate the disc may be passed in any direction.
True
False

Answers

I think is True: Because...

when you throw a disc you can throw it in any direction, many people call it "Flying Saucer" I'll give you an example ... When you throw something, for example a paper, you want to throw it at your classmate. You already know what address you want to send it to, then I say it is: True ...

Sorry if it's wrong :(

How much thermal energy (in kcal) is required to change a 43 g ice cube from a solid at - 16.5 oC to steam at 11.5 oC above boiling

Answers

Answer:

The total thermal energy required  is 8.93 Kcal

Explanation:

Given;

mass of the ice cube, m = 43 g

specific heat capacity of water, Cp = 4.18 J/gc

specific latent heat of fusion of ice, Cf = 334 J/g

First step, determine the heat needed to raise the temperature of the ice from -16.5 °C to 0° C

Q₁ = mCp[0 - (-16.5)]

Q₁ = 43 x 4.18(16.5)

Q₁ = 2965.71 J

Second step, determine the latent heat of fusion of ice at 0°C

Q₂ = mCf

Q₂ = 43 x 334

Q₂ = 14362 J

Third step, determine the quantity of heat required to raise the temperature of the water initially at 0°C to above 11.5 °C of boiling point of water.

The final temperature of the water = 11.5 °C + 100° C = 111.5 °C

Q₃ = mCp Δθ

Q₃ = 43 x 4.18 (111.5 - 0)

Q₃ = 20041 J

Total thermal energy required = Q₁ + Q₂ + Q₃

Total thermal energy required =  2965.71 J + 14362 J +  20041 J

Total thermal energy required = 37,368.71 J

Total thermal energy required = 8.93 Kcal

Which statement is part of Dalton's atomic theory?

Matter is composed of small particles called atoms.
Atoms can be divided into their subatomic particles.
Atoms are able to be seen with proper spectroscopy equipment.
Chemical reactions can change atoms from one type to another.

Answers

Answer:

Dalton’s atomic theory was a scientific theory on the nature of matter put forward by the English physicist and chemist John Dalton in the year 1808. It stated that all matter was made up of small, indivisible particles known as ‘atoms’.

Explanation:

Atoms can be divided into their subatomic particles.

The statement that is part of Dalton's atomic theory is as follows: Matter is composed of small particles called atoms.

What is Dalton's atomic theory?

John Dalton is a scientist that first stated the theory of chemical combination in 1803.

The components of these theory are as follows:

Elements consist of indivisible small particles called atoms.All atoms of the same element are identical i.e. different elements have different types of atom. Atoms can neither be created nor destroyed

Therefore, according to this question, the statement that is part of Dalton's atomic theory is as follows: Matter is composed of small particles called atoms.

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