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
scoray [572]
3 years ago
9

Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass m on a body of mass M is F = GmM r2

where G is the gravitational constant and r is the distance between the bodies.
(a) Find dF/dr. dF dr =

What is the meaning of dF/dr?

1) dF/dr represents the rate of change of the mass with respect to the distance between the bodies.
2) dF/dr represents the rate of change of the distance between the bodies with respect to the force.
3) dF/dr represents the amount of force per distance.
4) dF/dr represents the rate of change of the mass with respect to the force.
5) dF/dr represents the rate of change of the force with respect to the distance between the bodies.

What does the minus sign indicate?

1) The minus sign indicates that as the distance between the bodies increases, the magnitude of the force decreases.
2) The minus sign indicates that as the distance between the bodies increases, the magnitude of the force increases.
3) The minus sign indicates that the bodies are being forced in the negative direction.
4) The minus sign indicates that the force between the bodies is decreasing.
5) The minus sign indicates that as the distance between the bodies decreases, the magnitude of the force remains constant.

(b) Suppose it is known that the earth attracts an object with a force that decreases at the rate of 4 N/km when r = 20,000 km. How fast does this force change when r = 10,000 km? N/km
Physics
2 answers:
Nookie1986 [14]3 years ago
7 0
<h2>Answers:</h2>

<h2>(a) </h2>

According to Newton's Law of Gravitation, the Gravity Force is:

F=\frac{GMm}{{r}^{2}}     (1)

This expression can also be written as:

F=GMm{r}^{-2}    (2)

If we derive this force F respect to the distance r between the two masses:

\frac{dF}{dr}dFdr=\frac{d}{dr}(GMm{r}^{-2})dr     (3)

Taking into account GMm are constants:

\frac{dF}{dr}dFdr=-2GMm{r}^{-3}     (4)

Or

\frac{dF}{dr}dFdr=-2\frac{GMm}{{r}^{3}}     (5)

<h2> (b) dF/dr represents the rate of change of the force with respect to the distance between the bodies.  </h2><h2 />

In other words, this means how much does the Gravity Force changes with the distance between the two bodies.

More precisely this change is inversely proportional to the distance elevated to the cubic exponent.

As the distance increases, the Force decreases.

<h2>(c) The minus sign indicates that the bodies are being forced in the negative direction.  </h2>

This is because Gravity is an attractive force, as well as, a central conservative force.

This means it does not depend on time, and both bodies are mutually attracted to each other.

<h2>(d) </h2>

In the first answer we already found the decrease rate of the Gravity force respect to the distance, being its unit N/km:

\frac{dF}{dr}dFdr=-2\frac{GMm}{{r}^{3}}     (5)

We have a force that decreases with a rate 1 \frac{dF_{1}}{dr}dFdr=4N/km when r=20000km:

4N/km=-2\frac{GMm}{{(20000km)}^{3}}     (6)

Isolating -2GMm:

-2GMm=(4N/km)({(20000km)}^{3})     (7)

In addition, we have another force that decreases with a rate 2 \frac{dF_{2}}{dr}dFdr=X when r=10000km:

XN/km=-2\frac{GMm}{{(10000km)}^{3}}     (8)

Isolating -2GMm:

-2GMm=X({(10000km)}^{3})     (9)

Making (7)=(9):

(4N/km)({(20000km)}^{3})=X({(10000km)}^{3}       (10)

Then isolating X:

X=\frac{4N/km)({(20000km)}^{3}}{{(10000km)}^{3}}  

Solving and taking into account the units, we finally have:

X=-32N/km>>>>This is how fast this force changes when r=10000 km

AleksandrR [38]3 years ago
3 0

Answer:a) -2GmM / r^3

b) dF/dr represents the rate of change of the force with respect to the distance between the bodies

c) The minus sign indicates that as the distance between the bodies increases, the magnitude of the force decreases

d) 4 N/km, r=20,000, and r=10,000

-32 N/km

Explanation:

You might be interested in
How are scientific theories different than laws or hypotheses?
Gnoma [55]

Answer: Chilling with my homies

Chicken wings, Chicken wings

Hotdog and baloney

Chicken and macaroni

Chillin' wit mah homiiieees

Chicken wing chicken wing

Hot dogs and balogna

Chicken and macaroni

Chilling with mah Chilling with mah

Chicken chicken wing chicken chicken wing

Chicken chicken chicken chicken chicken wing

Chicken chicken chicken chicken wing

Chicken wings, Chicken wings

Hotdog and baloney

Chicken and macaroni

Chillin' wit mah homiiieees

Chicken wings, Chicken wings

Hotdog and baloney

Chicken and macaroni

Chillin' wit mah homiiieees homiiieeees

Chicken wings, Chicken wings

Hotdog and baloney

Chicken and macaroni

Chillin' wit mah homiiieees

Chillin' wit mah

Explanation:

im sorry i had to do it now pls give me brainliest thank u and have a blessed day:)

9 0
3 years ago
Read 2 more answers
Which type of macromolecules a cell brake down food?
kobusy [5.1K]

Answer:

Hope this helps you find the answer

Explanation:

The proteins, lipids, and polysaccharides that make up most of the food we eat must be broken down into smaller molecules before our cells can use them—either as a source of energy or as building blocks for other molecules.

8 0
3 years ago
In which direction does the sun appear to move across the sky
blsea [12.9K]

Answer:east

Explanation:Earth rotates or spins toward the east, and that's why the Sun, Moon, planets, and stars all rise in the east and make their way westward across the sky.

6 0
3 years ago
Read 2 more answers
If your average speed is 3 m/s, how far have you traveled in 1 second, 2 second, 3 seconds?
vichka [17]

Answer:

in 1 second 3m, in 2 seconds 6m, in 3 seconds 9m.

Explanation:

distance=speed × time

4 0
3 years ago
Read 2 more answers
A girl exerts a horizontal force of 109 N on a crate with a mass of 31.2 kg. HINT (a) If the crate doesn't move, what's the magn
vesna_86 [32]

Answer:

(a) Magnitude of static friction force is 109 N

(b) Minimum possible value of static friction is 0.356

Solution:

As per the question;

Horizontal force exerted  by the girl, F = 109 N

Mass of the crate, m = 31.2 kg

Now,

(a) To calculate the magnitude of static friction force:

Since, the crate is at rest, the forces on the crate are balanced and thus the horizontal force is equal to the frictional force, f:

F = f = 109 N

(b) The maximum possible force of friction between the floor and the crate is given by:

f_{m} = \mu_{s}N

where

N = Normal reaction = mg

Thus

f_{m} = \mu_{s}mg

For the crate to remain at rest, The force exerted on the crate must be less than or equal to the maximum force of friction.

f\leq f_{m}

f \leq \mu_{s}mg

109 \leq \mu_{s}\times 31.2\times 9.8

\mu_{s}\geq 0.356

7 0
2 years ago
Other questions:
  • Light is a ________ wave.<br> A. surface <br> B. transverse <br> C. longitudinal <br> D. mechanical
    9·1 answer
  • There have been different models of the atom over time. How has the competition between these models affected our understanding
    6·2 answers
  • F a light bulb produces 60.0 J of electrical energy and is 45% efficient, how much energy does it use?
    8·2 answers
  • three condensers are connected in series across a 150 volt supply. The voltages across them are 40,50 and 60 volts respectively,
    8·1 answer
  • NO LINKS PLEASE. brainly to the best answer.
    6·1 answer
  • An object is traveling at a velocity of 100 rn/s to the left for about 5 seconds. How far has the object traveled? (What is the
    8·1 answer
  • Which example best matches the term refraction? (17 Points)
    8·1 answer
  • Only the healthy foods we eat provide<br> energy to our body<br> true<br> false
    5·1 answer
  • Kepler's laws, satellites motion and weightlessness
    11·1 answer
  • How far apart are two conducting plates that have an electric field strength of 4. 4 kv/m between them, if their potential diffe
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!