1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
BigorU [14]
2 years ago
7

spaceship of mass m travels from the Earth to the Moon along a line that passes through the center of the Earth and the center o

f the Moon. (a) At what distance from the center of the Earth is the force due to the Earth twice the magnitude of the force due to the Moon
Physics
1 answer:
satela [25.4K]2 years ago
3 0

Answer:

the correct result is r = 3.71 10⁸ m

Explanation:

For this exercise we will use the law of universal gravitation

          F = - \frac{m_{1} m_{2} }{r^2}

We call the masses of the Earth M, the masses of the moon m and the masses of the rocket m ', let's set a reference system in the center of the Earth, the distance from the Earth to the moon is d = 3.84 108 m

rocket force -Earth

          F₁ = - \frac{m' M }{r^2}

rocket force - Moon

          F₂ = - \frac{m' m }{(d-r)^2}

in the problem ask for what point the force has the relation

          2 F₁ = F₂

let's substitute

          2 2 \frac{M}{r^2} = \frac{m}{(d-r)^2}

          (d-r) ² = \frac{m}{2M} r²

           d² - 2rd + r² = \frac{m}{2M} r²

           r² (1 -\frac{m}{2M}) - 2rd + d² = 0

Let's solve this quadratic equation to find the distance r, let's call

           a = 1 - \frac{m}{2M}

           a = 1 - \frac{7.36 10^{22} }{2 \  5398 10^{24}} = 1 - 6.15 10⁻³

           a = 0.99385

         

            a r² - 2d r + d² = 0

           r =  \frac  {2d \frac{+}{-}   \sqrt{4d^2 - 4 a d^2}} {2a}

           r = [2d ± 2d \sqrt{1-a}] / 2a

           r = \frac{d}{a}   (1 ± √ (1.65 10⁻³)) =  \frac{d}{a} (1 ± 0.04)

           r₁ = \frac{d}{a} 1.04

           r₂ = \frac{d}{a} 0.96

let's calculate

           r₁ = \frac{3.84 10^8}{0.99385} 1.04

           r₁ = 401.8 10⁸ m

          r₂ = \frac{3.84 10^8}{0.99385} 0.96

          r₂ = 3.71 10⁸ m

therefore the correct result is r = 3.71 10⁸ m

You might be interested in
Can you make the work output of a machine greater than the work input?
drek231 [11]
Nearly equal the output work is greater than the input work because of friction.All machines use some amount of input work to overcome friction.The only way to increase the work output is to increase the work you put into the machine.You cannot get more work out of a machine than you put into it.
4 0
3 years ago
How have batteries gotten better over time?
babymother [125]
The size has gotten smaller, they last longer, easier to carry around, safer, etc
5 0
3 years ago
Read 2 more answers
The four main elements in food that help energy to move from one trophic level to another are _____.
PolarNik [594]
I think these may help. protein, calcium
7 0
3 years ago
On a Saturday afternoon, you decide to pay a neighborhood kid to mow your lawn. The kid usesa manual push lawn mower with a mass
Mars2501 [29]

Answer with Explanation:

We are given that

A.Mass,m=12 kg

\theta=53^{\circ}

\mu_k=0.16

Speed,v=1.5m/s

Net force in x direction must be zero

F_{net}=0

Fsin\theta-f=0

Fsin\theta=f

Net force in y direction

N-mg-Fcos\theta=0

N=mg+Fcos\theta

f=\mu_kN=\mu_k(mg+Fcos\theta)

Fsin\theta=\mu_k(mg+Fcos\theta)

Fsin\theta=\mu_kmg+\mu_kFcos\theta

Fsin\theta-\mu_kFcos\theta=\mu_kmg

F(sin\theta-\mu_kcos\theta)=\mu_kmg

F=\frac{\mu_kmg}{sin\theta-\mu_kcos\theta}

Power,P=Fv

P=\frac{\mu_kmg}{sin\theta-\mu_kcos\theta}v

Where g=9.8m/s^2

B.Substitute the values

P=\frac{0.16\times 12\times 9.8}{sin53-0.16cos53}\times 1.5

P=40.17W

6 0
3 years ago
Why would physics be used to study the movement of ocean waves?
Lunna [17]
I think it’s c because the other ones are just options not facts
5 0
3 years ago
Other questions:
  •  Why does a child in a wagon seem to fall backward when you give the wagon a sharp pull forward? 15. What force is needed to acc
    10·1 answer
  • Ampres law is often written contourintegral B vector (r vector) middot dl vector = mu_0I_enclosed. The integral on the left is
    15·1 answer
  • A force of 34N stretches a very light ideal spring 0.73 m from equilibrium, What is the force constant (spring constant) of the
    5·1 answer
  • What would the velocity of a wave traveling in a medium change?
    8·1 answer
  • Suppose two children push horizontally, but in exactly opposite directions, on a third child in a sled. The first child exerts a
    12·1 answer
  • A person walks along a road 2 miles and rests. Then taking another road, he travels 3 miles; and switching to a dirt path, he wa
    12·2 answers
  • A child whose weight is 287 N slides down a 7.20 m playground slide that makes an angle of 31.0° with the horizontal. The coeff
    15·1 answer
  • What charge does an object have if it has an excess of electrons?
    6·1 answer
  • Draw Graph for the derivation of three equations of Motion​
    7·1 answer
  • PLSSSSSSSS SOMEONE HELP ME WITH THIS ONE!!
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!