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
Bess [88]
2 years ago
10

Suppose that F is an inverse square force field below, where c is a constant.

Mathematics
1 answer:
Andre45 [30]2 years ago
5 0

Answer:

Forces in our Universe

Step-by-step explanation:

a)

First of all we have,

F(r) = \frac{cr}{|r|^{3} }

and,

r = xi+yj+zk

We need to define a function that allows us to find said change based on r, so one of the functions that shows that change is,

f(r) = - c /|r|

That is,

\nabla f = F

For this case F is a conservative field and the line integral is independent of the path. Thus, defining  P_{1} = (x_{1}, y_{1}, z_{1}) and P_{2} = (x_{2}, y_{2}, z_{2}) . So the amount of work on the movement of the object from P1 to P2 is,

W=\int\limits_c  {F} \, dr

W= f(P_{1}-P_{2})

W= \frac{c}{(x_{2}^2+ y_{2}^2+ z_{2}^2)^{1/2} } -\frac{c}{(x_{1}^2+ y_{1}^2+ z_{1}^2)^{1/2}}

W= c(\frac{1}{d1}-\frac{1}{d2}  )

2) The gravitational force field is given by,

F(r) =-\frac{mMGr}{ |r|^3}

The maximum distance from the earth to the sun is 1.52*10 ^ 8 km and the minimum distance is 1.47*10 ^ 8km. The mass values of the bodies are given by m = 5.97*10 ^ {24}kg, M = 1.99 *19 ^ {30}kg and the constant G is 6.67 * 10 ^{ -11 } \frac{Nm ^ 2}{kg^2}

In this way we raise the problem like this,

c= -mMG

W= -mMG (\frac{1}{1.52*10 ^ 8} -\frac{1}{1.47*10 ^ 8} )

W= -(5.95*10^{24})(1.99*10^{30})(6.67*10^{-11})(-2.2377*10^{-10})

W \approx 1.77*10^{35}}J

You might be interested in
8|7+(-10)<br> Simplify:<br> 2-32
amid [387]

Answer:

8|7+(-10)=24  2-32= − 30

Step-by-step explanation:

6 0
3 years ago
What is 24.7832 rounded to
Margaret [11]

Answer:

2,500 cents

I hope this helps!

4 0
3 years ago
Read 2 more answers
A<br> If Lin sells 6 boxes of popcorn, will she make her goal? State yes or no.
Pavel [41]

Answer:

No.

First, multiply 6 x 4 ($4 is the amount of money he makes from each sale).

6 x 4 = $24

If Lin's goal is $32, and he sells 6 boxes of popcorn for only $24, then he will not reach his goal in that specified range.

8 0
2 years ago
Please help me i need a good grade
DedPeter [7]

Answer:

Step-by-step explanation:

midline: y = -2 (take the average of the min and max)

amplitude = 1.5 (distance from min or max to midline. Always a positive number)

period = 4pi

4 0
2 years ago
Read 2 more answers
What type of line is the graph of X equals -2
Ivahew [28]

Answer:

it is a vertical line going up at -2 on the x-axis

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • What term best describes a line and a point that lie in the same plane?
    9·1 answer
  • Which algebraic expression models the sum of 3 coins and c coins?
    12·1 answer
  • Simplify. x^2-3x-18/x+3
    7·1 answer
  • one square mile is equal to 640 acres what is the area in acres for the piece of land length 3 1/4 and width 5 2/4​
    10·1 answer
  • Plz simplify and answer 3x+7x−28+31−8x for x=2043
    15·2 answers
  • The diagram shows a door lock.
    8·1 answer
  • A cylinder has a height of 13 feet and a radius of 11 feet. What is its volume? Use a ~ 3.14
    15·1 answer
  • What is the constant of proportionality in this relationship ???? Help fast !!!
    15·1 answer
  • Hellllllllllpppppppppp please​
    12·1 answer
  • Can you pls help me ill will give 30 points
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!