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4 years ago

La ce distanta de la suprafata Pamintului intensitatea cimpului sau gravidational este egala cu 1 N/kg ?

1 answer:

6 0

Acceleration of gravity is proportional to 1/D² .
('D' is the distance from the Earth's center.)

We need (D / R)² = 9.8
('R' is the Earth's radius.)

D/R = √9.8 = 3.13

Distance from Earth's <u>center</u> = 3.13 R
Distance above Earth's <u>surface</u> = 2.13 R = about 13,570 km =====================================================

<span>Accelerarea de gravitate este proporțională cu 1 / D².
('D este distanța de centrul Pământului.)

Avem nevoie de (D / R) ² = 9,8
('R' este raza Pământului.)</span><span>

D / R = √9.8 = 3,13

Distanța de la <u>centrul</u> Pamantului = 3,13 R
Distanța de deasupra <u>suprafetei</u> Pamantului = 2.13 R = aproximativ <span><em>13,570 km</em></span></span>

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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

Nookie1986 [14]

<h2>Answers:</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)

$\frac{dF}{dr}dFdr=-2\frac{GMm}{{r}^{3}}$ (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.

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 $r=10000 km$

7 0

4 years ago

Read 2 more answers

Earth's atmosphere contains only small amounts of carbon dioxide because

Mamont248 [21]

Of biogeochemical cycles

Because certain biogeochemical cycles take place to lessen these gases from forming since they are not beneficial for life if too much.
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4 0

3 years ago

A satellite is put into an orbit at a distance from the center of the Earth equal to twice the distance from the center of the E

Sveta_85 [38]

Answer:

995 N

Explanation:

Weight of surface, w= 4000N

Gravitational constant, g, is taken as 9.81 hence mass, m of surface is W/g where W is weight of surface

m= 4000/9.81= 407.7472

Using radius of orbit of 6371km

The force of gravity of satellite in its orbit, $F=\frac {GMm}{(2r)^{2}}=\frac {GMm}{4(r)^{2}}$